Evaluation of renewable energy technologies in Colombia: comparative evaluation using TOPSIS and TOPSIS fuzzy metaheuristic models

The growing global demand for energy, combined with the prevailing need to address environmental challenges, has driven the transition to more sustainable and renewable energy sources. Colombia, in its commitment to climate change mitigation, has Abstract The study investigates the weighting and hierarchization of renewable energy sources in specific geographical regions of Colombia using the TOPSIS and Diffuse TOPSIS metaheuristic models. 5 regions were analyzed, two of them with different scenarios: Caribbean 1 and 2, Pacific 1 and 2, Andean, Amazonian and Orinoquia. The results reveal significant differences in the evaluation of technologies between the two models. In the Caribbean 1, Diffuse TOPSIS gave a higher score to Solar Photovoltaics, while TOPSIS favored Hydropower. In the Caribbean 2, Solar Photovoltaic obtained similar scores in both models, but Wind was rated better by TOPSIS. In the Pacific Region 1, Biomass and large-scale Hydropower led according to both models. In the Pacific 2, Solar Photovoltaic was better evaluated by TOPSIS, while Wind was preferred by Diffuse TOPSIS. In the Andean Region, large-scale hydroelectric and Solar photovoltaic plants obtained high scores in both models. In the Amazon, Biomass led in both models, although with differences in scores. In Orinoquia, Solar Photovoltaic was rated higher by both models. The relevance of this research lies in its ability to address not only Colombia’s immediate energy demands, but also in its ability to establish a solid and replicable methodological framework. The application of metaheuristic methods such as TOPSIS and TOPSIS with fuzzy logic is presented as a promising strategy to overcome the limitations of conventional approaches, considering the complexity and uncertainty inherent in the evaluation of renewable energy sources. By achieving a more precise weighting and hierarchization, this study will significantly contribute to strategic decision-making in the implementation of sustainable energy solutions in Colombia, serving as a valuable model for other countries with similar challenges.


Introduction
The growing global demand for energy, combined with the prevailing need to address environmental challenges, has driven the transition to more sustainable and renewable energy sources.Colombia, in its commitment to climate change mitigation, has Page 2 of 28 Moreno Rocha and Arenas Buelvas Energy Informatics (2024) 7:62 identified the significant potential of distributed renewable energy in its various geographical regions (Liu et al. 2024).However, the efficient management and optimal selection of these energy sources are crucial challenges.In this context, the present research addresses the implementation of two innovative metaheuristic methods, TOPSIS and TOPSIS with fuzzy logic, for the weighting, prioritization and improved selection of renewable energy sources in Colombia (Dias et al. 2022).The transition to a more sustainable energy model is an imperative necessity in the global context.Colombia, a country characterized by its geographical diversity, is positioned as a favorable scenario for the exploration and use of renewable energy sources (Quynh 2024).Effective management of this natural wealth, however, becomes a complex and multidimensional task that requires advanced analytical approaches.In this scenario, the proposed research focuses on the implementation of two innovative metaheuristic methodologies: TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and TOPSIS with fuzzy logic (Rezaei et al. 2022).These methodologies, recognized for their ability to address complex decision-making problems, are key tools in the weighting, prioritization, and selection of renewable energy sources in Colombia (Rocha et al. 2022).In research such as (Falkonakis et al. 2024) Access to spare parts in the maritime industry is limited for most of a ship's life cycle.This limitation is due to both the geographical distance between ships and suppliers, as well as the limited turnaround time during which parts can be delivered.Although it is possible to manufacture some parts on board, this process is time-consuming and labor-intensive.Advanced manufacturing techniques could improve access to spare parts at sea by combining the desirable properties of materials and the flexibility of Direct Energy Deposition (DED) with the greater dimensional tolerances of Computer Numerical Control (CNC) manufacturing.The present study evaluates the comparative feasibility of implementing on-board advanced manufacturing techniques for offshore assets as a capital investment in different modes, compared to the option of not having advanced on-board manufacturing, using a multi-criteria decision analysis method.
To this end, an Order of Preference by Similarity to the Ideal Solution (TOPSIS) technique is used, considering the technical-economic and environmental aspects of the decision-making process, as well as the challenges inherent to this new area of research.Finally, the challenges, opportunities and pathways to on-board maintenance using additive manufacturing within the framework of a sustainable future for ships and offshore energy assets are discussed.Also in (Du et al. 2024) TOPSIS is applied to the government's high-quality development (HQD) initiative marks a shift in China's development paradigm from prioritizing speed to prioritizing quality with the aim of achieving comprehensive economic growth, social vitality, innovation capacity, industrial upgrading, regional cooperation, and green transformation.This initiative is increasingly discussed within the framework of mega-regions, and previous studies have shown that they are critical areas for advancing HQD visions.However, inequality within mega-regions has become a major constraint to this view.Specifically, there are significant disparities between the core cities of the megaregions and smaller neighboring cities in most HQD indicators.This article conceptualizes these smaller cities as secondary cities.Based on this, the article aims to understand and differentiate the specific challenges faced by secondary cities in the face of intra-regional inequality in the context of HQD.An assessment framework is constructed and the TOPSIS method is used to assess 34 core cities and 180 secondary cities.A typological approach is then introduced to develop a meaningful ranking of secondary cities based on the results of these assessments.K-means cluster analysis identifies five types of secondary cities with similar profiles.The analysis supports discussion on the characteristics and challenges of each type and can contribute to policy recommendations for balanced HQD in secondary cities of mega-regions.
On the one hand, TOPSIS, initially developed for decision-making in management and planning problems, stands out for its ability to evaluate alternatives in relation to multiple criteria (Jiang et al. 2024).In the context of the selection of renewable energy sources, TOPSIS allows the systematic comparison of options, considering technical, economic and environmental aspects (Zhu et al. 2023).By employing this approach, the research seeks to overcome the limitations of conventional methods by offering a comprehensive and weighted view of the different energy sources, taking into account their strengths and weaknesses in the specific context of each Colombian geographic region.While the inclusion of fuzzy logic in the TOPSIS method amplifies its ability to adapt to the complex and changing reality of renewable energy sources.The inherent variability of these sources, marked by climate fluctuation and other external factors, introduces a component of uncertainty that needs to be addressed (Liu and Zhao 2022).TOPSIS with fuzzy logic incorporates the flexibility to handle inaccurate or vague information, allowing for a more robust and realistic evaluation of energy alternatives (Jain et al. 2024).In this way, the research seeks not only to identify the most optimal options under ideal conditions, but also to consider less predictable scenarios, increasing the adaptability of the model to changing environmental conditions (Tsagkari et al. 2022).However, in (Alghassab 2024b) by using TOPSIS-FUZZY to consider that Saudi Arabia's strategy involves economic diversification and reducing dependence on oil, a shift towards sustainable and efficient energy management practices is required.Effective energy management is crucial to optimize energy consumption, reduce costs, and decrease the environmental footprint.Traditional energy management systems are often based on deterministic or rule-based techniques, which do not address the complexity and uncertainty inherent in household energy use patterns and user behaviors.In recent years, fuzzy logic-based solutions have emerged, which hold great promise for home energy management.Fuzzy logic excels at handling imprecise and uncertain inputs, making it ideal for modeling human-centric systems such as home energy management.This study presents an intelligent energy management system based on fuzzy logic, adapted to Saudi residential buildings.Using fuzzy logic approaches, the system seeks to optimize energy use, reduce peak demand, and improve energy efficiency.It automatically adjusts energy-consuming devices, such as air conditioning, lights, and appliances, based on user preferences, occupancy patterns, and energy prices in real-time, using fuzzy decision-making algorithms.The research not only demonstrates the success of this strategy through a comparative study, but also highlights its potential benefits for residential constructions in Saudi Arabia.In addition, it addresses obstacles and potential research opportunities for the adoption of smart energy management systems based on fuzzy logic, revealing a promising path towards a more sustainable and secure energy future.The findings of the study underscore the superiority of the comparative study alternative, revealing it as the most effective means of evaluating the performance and unique advantages of the fuzzy logic-based system relative to other established approaches to energy management.
In a global context where environmental sustainability has become imperative, the careful selection of renewable energy sources acquires crucial relevance, the choice of the right energy source for each region not only impacts the efficiency and sustainability of the energy supply, but also directly influences the reduction of greenhouse gas emissions and the preservation of local ecosystems (Carpitella et al. 2022).The efficient implementation of renewable energy not only represents an environmentally conscious strategy, but also an opportunity for economic and social development at the regional level (Baydaş et al. 2024).In this context, the proposed research not only seeks to offer technical solutions, but also to establish a comprehensive framework that addresses the strategic importance of the selection of renewable energy sources in the sustainable development of Colombia (Eguiarte et al. 2022).
At the international level, the selection of renewable energy sources has become a crucial issue on the global sustainability agenda, and several countries have adopted strategies to diversify their energy matrices, prioritizing the transition to cleaner and more sustainable resources (Wang et al. 2024a, b, c).The implementation of decision methods, such as TOPSIS and its variant with fuzzy logic, has gained prominence in this context (Pechsiri et al. 2023).The ability to assess multiple criteria and consider the uncertainty associated with renewable sources has proven to be essential in decision-making at the international level, where conditions and variables can vary significantly between regions (Shao et al. 2023).In (Alghassab 2024a) this study presents an intelligent energy management system based on fuzzy logic, adapted to Saudi residential buildings.Using fuzzy logic approaches, the system seeks to optimize energy use, reduce peak demand, and improve energy efficiency.It automatically adjusts energy-consuming devices, such as air conditioning, lights, and appliances, based on user preferences, occupancy patterns, and energy prices in real-time, using fuzzy decision-making algorithms.The research not only demonstrates the success of this strategy through a comparative study, but also highlights its potential benefits for residential constructions in Saudi Arabia.In addition, it addresses obstacles and potential research opportunities for the adoption of smart energy management systems based on fuzzy logic, revealing a promising path towards a more sustainable and secure energy future.The findings of the study underscore the superiority of the comparative study alternative, revealing it as the most effective means of evaluating the performance and unique advantages of the fuzzy logic-based system relative to other established energy management approaches.
In the Latin American region, geographic and climatic diversity presents unique challenges and opportunities in the selection of renewable energy sources.Countries such as Brazil, Chile and Mexico have led the implementation of renewable technologies, recognizing the importance of maximizing the potential of their natural resources (Turoń, 2022).The application of metaheuristic methods in energy decision-making aligns with the need to consider climate variability and geographic complexity (Diviya et al. 2024).Adapting approaches such as TOPSIS to the specific conditions of Latin America contributes to a more efficient and sustainable transition to renewable energy sources in the region.Colombia, immersed in a rich geographical diversity, faces particular challenges in the selection of renewable energy sources (Sun 2024).The implementation of decision-making methods becomes essential to weigh local factors, considering variables such as altitude, climate, and the specific topography of each region (Manuel et al. 2022a).The TOPSIS methodology, with its ability to evaluate alternatives based on multiple criteria, is presented as a particularly valuable tool in this context (Kumar et al. 2022).The application of fuzzy logic in the TOPSIS variant, on the other hand, makes it possible to adapt to the uncertainty inherent in the changing conditions of the Colombian environment, ensuring informed and strategic decisions in the implementation of renewable energies at the local level (Sithara et al. 2022).
International cooperation in the implementation of decision-making methods for the selection of renewable energy sources is presented as an essential catalyst to drive global sustainability, the exchange of best practices between countries, the standardization of analytical approaches and collaboration in advanced research contribute to a collective advance towards more sustainable energy matrices (Hegde et al. 2024).The application of metaheuristic methods not only strengthens decision-making capacity at the local, regional, and international levels, but also establishes a framework for continuous innovation and adaptability as environmental and technological conditions evolve (Zhou et al. 2024).In this context, the research and application of methodologies such as TOPSIS and TOPSIS with fuzzy logic become key elements to promote efficiency and sustainability in the selection of renewable energy sources at different geographical scales (Moreno Rocha et al. 2022), especially for regions such as LATAN and exclusively for countries such as Colombia, where the implementation of metaheuristic or decisionmaking methods in the energy sector is almost non-existent, in such a way that this research is a novelty, a pioneering research, a great contribution to this sector and leaves the doors and bases for future research to continue contributing to these topics.This research is considered to contribute to the achievement of the SDGs; SDG 7: Affordable and Clean Energy: This research focuses on the assessment of renewable energy technologies, which directly contributes to promoting access to affordable, reliable and sustainable energy for all.SDG 9: Industry, Innovation and Infrastructure: Considering the implementation of advanced technologies, such as additive manufacturing (3D printing) for the production of spare parts in the maritime sector and other technological advances in energy management, this research aims to promote innovation and technological development to achieve a more sustainable infrastructure.SDG 11: Sustainable Cities and Communities: Assessing the feasibility of implementing advanced manufacturing techniques on board marine assets and discussing the characteristics and challenges of secondary cities in the context of high-quality development have implications for sustainable urban planning and resource management in diverse communities.SDG 12: Responsible Consumption and Production: Research on the manufacture of spare parts on board marine assets using advanced manufacturing techniques and the effective management of energy in the home with fuzzy logic-based approaches contribute to promoting more sustainable production and consumption patterns and SDG 13: Climate Action: By discussing the transition to more sustainable energy practices and reducing dependence on oil in the case of Saudi Arabia, this research indirectly addresses the need to mitigate the effects of climate change and adapt to its impacts.
In this context, the essential question arises: How can Colombia optimize the weighting, prioritization and selection of renewable energy sources in its different geographical regions to maximize energy yield and minimize environmental impact?This central question triggers the need to research and develop novel and efficient approaches that enable informed and strategic decision-making in the transition to a more sustainable and diversified energy matrix.

Material and methodology
The methodology section of this article deploys a meticulous and rigorous approach to address the particular challenges associated with the evaluation of renewable energy sources in Colombia.The implementation of metaheuristic methods, specifically TOP-SIS and TOPSIS with fuzzy logic, constitutes the backbone of our methodological strategy.These approaches were carefully selected due to their demonstrated ability to deal with the complexity inherent in decision-making in a changing and diverse environment such as Colombia's (Kaya et al. 2022).The choice of TOPSIS and fuzzy logic TOPSIS as metaheuristic methods is the result of a careful assessment of their suitability to address the variables and uncertainty associated with the selection of renewable energy sources.TOPSIS, with its ability to handle multiple criteria and provide trade-offs, offers a robust basis for the weighting and prioritization of energy options (Mandal et al. 2024).On the other hand, the integration of fuzzy logic into TOPSIS is justified by its ability to model the imprecision inherent in the variability of renewable energy sources, ensuring a more realistic and adaptive approach (Zhang et al. 2022).
The methodology developed takes into account the geographical diversity of Colombia, characterized by variations in altitude, climates and topographies.The application of these methods is tailored to the particularities of each region, recognizing that there is no single approach that can encompass the complexity of the country's geographical conditions.The adaptability of TOPSIS and TOPSIS with fuzzy logic is presented as an essential element to ensure that renewable energy decisions are contextually relevant and strategically informed (Christian Moreno et al. 2022a, b).The methodology section details the key stages of implementation, from data collection to final evaluation (García-García 2022).Specific criteria, such as the availability of natural resources, environmental impact, and economic viability, are included to ensure a holistic assessment of each renewable energy source.In addition, sensitivity analyses are integrated to assess the robustness of the results against possible changes in environmental or technological conditions (Peters et al. 2022).
The validation of the results obtained by applying TOPSIS and TOPSIS with fuzzy logic is done through comparisons with conventional approaches and review by experts in the field (Yan Wang and Zhao 2024).This validation process ensures the reliability and practical applicability of the results, strengthening the contribution of this research to the emerging field of efficient renewable energy management in Colombia (Chistian Moreno et al. 2022a, b), for this research, 10 energy alternatives were used as evidenced in Table 1 and were implemented in 7 possible scenarios, according to the 5 geographical regions that comprise the study area, as evidenced in Table 2.
Colombia has a great diversity of natural and climatic resources that make it possible to generate renewable energy in all its geographical regions, by taking advantage of these resources in a sustainable, responsible way and with correct decision-making, the percentage of successful planning, execution and start-up of energy generation projects with non-conventional sources would increase (Jesús et al. 2021).

Caribbean Region (SC1)
The Caribbean Region of Colombia, known for its rich culture and Caribbean coastline, offers great potential for renewable energy generation.With a tropical climate, this region has abundant solar resources that make it ideal for the installation of solar photovoltaic energy systems.In addition, its extensive coastline provides opportunities for offshore wind energy, taking advantage of the winds that blow over the Caribbean Sea.Biomass is also a promising source in this region, given the availability of agricultural and forestry residues for energy production (Barbosa-granados et al. 2022).

Pacific Region (SC2)
The Pacific Region of Colombia, known for its biodiversity and coastline on the Pacific Ocean, has great potential for renewable energy generation.Its dense forests and humid climate offer optimal conditions for the production of energy using biomass and biogas, using organic waste and agricultural waste.In addition, its coastline exposed to Pacific winds makes it ideal for offshore wind energy, taking advantage of the strong winds that blow over the ocean (Emilia et al. 2022).

Andean Region (SC3)
The Andean Region of Colombia, characterized by its mountainous topography and fertile valleys, presents great potential for a variety of renewable energy sources.Its high mountains offer opportunities for large-scale hydropower, taking advantage of the mighty rivers that descend from the Andes Mountains.In addition, its temperate climate  and high altitude make it conducive to solar photovoltaic and wind energy in mountainous areas (Granados et al. 2022).

Amazon Region (SC4)
The Amazon Region of Colombia, known for its lush rainforest and unique biodiversity, offers great potential for renewable energy generation.Its dense vegetation and humid climate make it ideal for energy production using biomass and biogas, using organic waste and forest waste.In addition, its extensive network of rivers, such as the Amazon River and the Caquetá River, offers opportunities for large-scale hydropower, harnessing the flow and energy of these waterways (Guignard et al. 2022).

Orinoquia Region (SC5)
The Orinoquia Region of Colombia, characterized by its extensive plains and flowing rivers, offers great potential for renewable energy generation.Its wide lowland areas and tropical climate make it ideal for the installation of large-scale solar PV systems.In addition, its many rivers, such as the Meta River and the Orinoco River, offer opportunities for hydropower and biomass energy from agricultural and forestry residues (Granados et al. 2022).
As a synthesis of the methodology implemented in this research, it is expressed in Fig. 1, however, in the following subsections a general explanation of each of the steps is made.

Variables taken into account
The strategic selection of renewable energy alternatives in countries such as Colombia represents a multifaceted challenge, where the application of metaheuristic methods, particularly TOPSIS, is presented as a fundamental tool.In this context, the consideration of key criteria is of crucial importance.This text addresses the relevance of three essential criteria: the Initial Investment in USD/MWh, the Environmental Impact, and the Infrastructure Analysis.In addition, it explores the need to evaluate conflicts with other economic actors, highlighting the interconnection of these factors in strategic decision-making for sustainable development.It is important to note that the first criterion is obtained from its value of consultation in specialized literature, on the other hand, the values of the other criteria are obtained from the result of the implementation of an AHP process, research carried out previously.
• Initial investment in USD/MWh: economic rationale The criterion of Initial Investment in USD/MWh stands as a fundamental pillar in decision-making related to renewable energies.The economic efficiency of an energy alternative depends not only on its environmental performance, but also on the relationship between the initial investment and energy production over time (Zhang et al. 2024).Assessing this criterion provides a clear view of the long-term financial viability of renewable options, enabling planners and decision-makers to direct resources towards economically sustainable solutions that drive the energy transition (Manuel et al. 2022a).

• Environmental impact: long-term sustainability
Consideration of Environmental Impact stands as a moral and practical imperative in the choice of renewable energy sources.Measuring an alternative's environmental impact is not limited to its greenhouse gas emissions; It must cover the entire life cycle, from production to decommissioning (Wang et al. 2024a, b, c).Evaluating this criterion ensures the selection of options that not only reduce emissions, but also minimize other adverse impacts on local and global ecosystems, ensuring a sustainable future for generations to come (Manuel et al. 2022b).Environmental impact assessment in energy projects is essential for several reasons.First of all, it allows you to identify and mitigate the possible negative impacts that a project could have on its environment.From air, water or soil pollution to biodiversity loss, anticipating these adverse effects is key to implementing effective mitigation measures (Kausar et al. 2024).In addition, environmental assessment promotes sustainable development by ensuring that energy projects are developed in a balanced manner, considering current and future needs (Calvillo-Arriola and Sotelo-Navarro 2024).This involves not only power generation, but also the protection of the environment, natural resources and the health of local communities, complying with environmental legislation is another crucial aspect, as in many countries it is a legal requirement to obtain the necessary permits.The involvement of stakeholders, such as local communities and environmental organizations, is critical in this process (Wilkowska et al. 2024).Transparency and the inclusion of diverse opinions allow for a more informed and equitable decision-making process, environmental impact assessment helps in risk and cost management by identifying potential issues and estimating the resources needed to address them, environmental impact assessment is a critical tool to ensure that energy projects are developed responsibly, minimizing negative impacts and maximizing benefits to the environment and local communities (Raza et al. 2024).

• Infrastructure analysis: operational efficiency and successful deployment
The Infrastructure Analysis criterion is presented as a key determinant for the successful deployment of renewable energy projects.Planning and implementing efficient and adequate infrastructures are essential to ensure optimal operation over time (Işık et al. 2024).Factors such as geographic location, transmission capacity, and grid connectivity are crucial elements to evaluate.The consideration of this criterion in the selection phase makes it possible to anticipate possible operational challenges and optimize the efficiency of the infrastructure, ensuring the long-term success of the renewable initiative (Moreno Rocha et al. 2022).
• Conflicts with other economic actors: sustainable integration into the social and economic environment The assessment of Conflicts with Other Economic Actors highlights the need to consider the dynamics and relationships in the social and economic environment.In a country like Colombia, where the diversity of economic actors is remarkable, the identification and mitigation of potential conflicts becomes a critical factor.The sustainable integration of renewable energy alternatives requires careful analysis of potential tensions with local communities, existing industries, and other economic actors (Priyanto et al. 2024).Assessing this criterion ensures an energy transition that is not only technically feasible but also socially and economically inclusive (Manuel et al. 2024).Taken together, these criteria not only provide a holistic framework for the assessment of renewable energy options, but also underscore the need for a balanced approach that considers economic, environmental and social aspects (Yuanfu Wang et al. 2024a, b, c).The application of metaheuristic methods such as TOPSIS enhances this comprehensive assessment, enabling informed decisions that drive sustainability and sustainable development in Colombia's energy landscape (Manuel et al. 2022c).The study of the criterion "Conflicts with Other Economic Actors: Sustainable Integration into the Social and Economic Environment" is essential in an energy project for several reasons.First, energy projects often have a significant impact on local communities and economies (Flórez et al. 2022).These projects may lead to conflicts with other economic actors, such as farmers, fishermen or local businesses, which may be negatively affected by the development of the project in such a way that it is important to identify and address these potential conflicts proactively to ensure sustainable integration into the social and economic environment (Cantillo & Garza 2022).In addition, effective conflict resolution with other economic actors can contribute to the long-term viability and success of the project, protracted conflicts can delay or even stop the development of the project, which can result in significant economic losses for all parties involved, therefore, it is crucial for project developers to anticipate and manage these conflicts efficiently to avoid interruptions in the project process.Implementation (Eskjaer and Horsbøl 2023).Sustainable integration into the social and economic environment is also important to maintain the legitimacy and acceptance of the project by the local community and other stakeholders, energy projects that are perceived as intrusive or harmful to the local community may face resistance and opposition, which can negatively affect the reputation and image of the company responsible for the project.It is therefore essential to establish positive and collaborative relationships with local economic actors to ensure continued support and cooperation at all stages of the project (Gusheva et al. 2022).Moreno Rocha and Arenas Buelvas Energy Informatics (2024) 7:62 One of the variables to be taken into account in the implementation of the TOPSIS methodology was the price of the installation of 1 MW/h, according to the bibliography consulted, the prices according to the technology to be implemented range as follows: report, the levelized cost of geothermal power generation is in the range of $0.04 to $0.09 per kWh, or around $40 to $90 USDMW/h

Topsis methodology
The implementation of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method involves a series of systematic steps designed to evaluate and rank alternatives based on multiple criteria.The following are the key steps to apply the TOPSIS method effectively: 1. Problem identification and definition of criteria and alternatives: The first step is to clearly define the decision problem and determine the criteria that will be used to evaluate the alternatives.These criteria must be relevant and measurable.Likewise, the alternatives that will be evaluated must be identified.2. Decision matrix construction: A decision matrix is created where the rows represent the alternatives and the columns represent the criteria.The elements of the matrix are the values that indicate the performance of each alternative with respect to each criterion, see Eq. 1.
3. Normalization of the Decision Matrix and calculation of the radius of consistency: Because the criteria can have different units of measurement, it is necessary to normalize the values of the decision matrix to make them comparable.This is done using the normalization formula see Eqs. 2, 3 and 4: Consistency Index (CI) 4. Construction of the normalized weighted matrix: The normalized values are multiplied by the corresponding weights of the criteria to obtain the normalized weighted matrix.The weights reflect the relative importance of each criterion and must be determined in advance, see Eq. 5.
5. Determination of ideal and anti-ideal solutions: the ideal positive (best value for each criterion) and negative ideal (worst value for each criterion) solutions are identified, see Eqs. 6, 7, 8 and 9.
7. Calculation of the ideal solution similarity coefficient: the similarity coefficient for each alternative is determined, which indicates how close each alternative is to the positive ideal solution.8. Ranking of alternatives: Alternatives are ranked according to their Ci * Ci * similarity coefficients.The alternative with the highest coefficient is considered the best option.

Key definitions
A fuzzy set over the universal set is defined as: FG where represents the degree of belonging of the element µ F g : G[0, 1]g For F in such a way that for every FST it allows the partial belonging of an element in a set.The element belongs entirely to, if the value of the degree of membership is equal to one.On the other hand, the value of the degree of membership of is zero, if it does not belong to the set.The element is a partial membership of the fuzzy set, if the degree of membership is between 0 and 1: Different types of fuzzy numbers have been used to model linguistic variables such as triangular fuzzy numbers (TFN), trapezoidal fuzzy numbers, Gaussian fuzzy numbers, bell-shaped fuzzy numbers, etc. µ F g ǫ[0, 1]gǫGg F gg Fg F (Liang et al. 2022).Among these numbers, we have used TFN because of its simplicity in understanding and representing the linguistic information of decision-makers (Rezaei 2022).

Fuzzy TOPSIS
The Fuzzy TOPSIS method was proposed by Chen to solve MCDM problems under uncertainty.Linguistic variables are used by decision-makers to evaluate NFR weights and RF rankings.NFR weights are represented by and given by the decision-maker (Zhou et al. 2024).The rating of the, is represented by with respect to NFR b and specified by the decision-maker.This method includes the following steps a th FRFR a = (a = 1, • • • , q) S i ab i th (Nesticò et al. 2022): (i) Summing the weights of the NFRs and the ratings of the FRs specified by the decision-makers, expressed in Eqs. ( 19) and ( 20 (iii) Normalize the FDM of RFs using linear scale transformation.The standardized FDM is given by: M I (16) where w ab it is given by Eccl.( 27).where represents the distance between two fuzzy numbers.The vertex method is used to calculate the distance between two fuzzy numbers m(• • • ) (Khan et al.  2022): (vii) The order of classification of RFs is determined by the value of the proximity coefficient.The is calculated as follows: clos_coff a clos_coff a The best FR is close to the FPIS and farther away from the FNIS.
For the evaluation of the variables or criteria that were used in this research such as; the environmental impact, the analysis of the structure in installation and the operation, finally the possible conflicts with other economic actors, a Likert scale structure was used, where the experts consulted should give their appreciation or degree of importance according to their experience and knowledge, the nomenclatures used are seen in Table 3 (Rezaei 2022).Before carrying out the implementation of the TOPSIS and TOPSIS DIFFUSE methods, the selected criteria were weighted and ranked (Diviya et al. 2024).To carry out this process, the application of the hierarchical analytical method (AHP) was chosen, a methodology widely supported and used by the research community.The results of this phase are presented in detail in Table 2, providing a clear overview of the relative importance of each criterion in the context of the selection of renewable energy sources (Dias et al. 2022).
Table 4 not only reflects the aggregate results of the AHP process, but also provides a concrete example of the completion carried out by one of the 35 experts consulted in this research.The participation of experts in the field significantly enriches the weighting process, bringing specialized perspectives and practical experiences.It should be noted that, although a total of 35 people were consulted, only the responses of 14 experts in the AHP and TOPSIS methodologies were considered.This selection criterion was based on statistical rigor, excluding responses that did not meet the minimum values required for the radius and consistency index, thus guaranteeing the integrity and reliability of the data used in the development of subsequent methodologies.

Calculating the normalized matrix and calculating the weighted normalized matrix
The first fundamental step in the TOPSIS methodology is the calculation of the Normalized Matrix, see Tables 5 and 6, where each value in the original matrix is divided by the square root of the sum of the squares of the values in the same column (Savkovic et al.  2022).This normalizes the data, ensuring that all variables have the same relative scale (Chen and An 2024).Subsequently, in the Weighted Normalized Matrix step, the normalized values are multiplied by the weights assigned to each criterion.This weighting reflects the relative importance of each criterion in decision-making, allowing for a more accurate and contextualized evaluation of the alternatives (Alghassab 2024a).

Calculate the best ideal value and the worst ideal value
Determining the Best Ideal Value and the Worst Ideal Value is essential for establishing extreme benchmarks in decision-making, as shown in Table 7.In this step, you identify the alternatives that maximize and minimize each criterion, respectively (Adeel et al. 2022).The Best Ideal Value represents the ideal combination of criteria, while the Worst Ideal Value points to alternatives that meet the criteria poorly    (Zhang et al. 2024).These extreme values serve as benchmarks to assess how close or far the alternatives are from the ideals, facilitating the final ranking (Li et al. 2023).

Calculating Euclidean distance from the best ideal and calculating Euclidean distance from the worst ideal
Euclidean Distance is a key measure in TOPSIS, as it quantifies the relative proximity of each alternative to the ideal values, see Table 8.Calculating the Euclidean Distance from the Best Ideal involves determining the Euclidean distance between each alternative and the Best Ideal Value (Zhou et al. 2024).Similarly, the calculation from the Worst Ideal measures the Euclidean distance from the Worst Ideal Value.These distances provide a quantitative assessment of how close or far each alternative is from the extreme values, contributing to informed decision-making (Eguiarte et al. 2022).

Calculating the performance score
The last step in the TOPSIS methodology involves the calculation of the Performance Score for each alternative.This score is determined by dividing the Euclidean Distance from the Worst Ideal by the sum of the Euclidean Distance from the Best Ideal and the Euclidean Distance from the Worst Ideal (Fan et al. 2023).The Performance Score, which varies between 0 and 1, indicates the relative efficiency of each alternative relative to the ideals.A score closer to 1 reflects higher efficiency, while a score closer to 0 indicates lower efficiency (Yan Wang and Zhao 2024), see Table 9.This last step culminates in the final classification of the alternatives, facilitating the identification of the optimal option based on the established criteria (Cantillo et al. 2023).

Scenario 1 outcome
The results obtained from the TOPSIS and TOPSIS-Diffuse methodology in Table 10 reveal that small-scale Solar Photovoltaic and Hydroelectric are the most favored renewable energy generation technologies, with a score of 29 and 28% respectively.This relatively high score suggests that these technologies meet the evaluated criteria exceptionally positively.Solar photovoltaics, which convert sunlight into electricity efficiently and sustainably, is widely recognized for its potential in various environmental conditions.On the other hand, hydroelectric power, harnessing the energy of moving water, has proven to be a reliable source with low environmental impact in power generation.Conversely, Wave and Tidal get the lowest scores, at just 2% and 3%, respectively.These results suggest that these technologies may not be as suitable according to the criteria considered in the fuzzy assessment, possibly due to their lower level of development or applicability in the context evaluated.
In the conventional TOPSIS methodology as shown in Table 10, Solar Photovoltaic also stands out as the most promising renewable energy generation technology, with a score of 30.19%.This result reinforces the conclusion obtained in the TOPSIS Diffuse methodology, confirming Solar Photovoltaic as a highly favorable option in both methodologies.Biomass follows close behind, with a score of 24.46%, indicating its viability and potential as a diversified and sustainable renewable energy source.However, the distribution of scores is slightly different in this methodology compared to fuzzy, with greater variability across technologies.This may reflect differences in the evaluation criteria or in the perception of uncertainty between the two methodologies.Comparison between the datasets reveals a consistency in the preference for Solar PV as the best renewable energy generation technology in both methodologies.This result reinforces the confidence in Solar Photovoltaic as an outstanding option in the transition towards a more sustainable and cleaner energy matrix.However, while in the TOPSIS Diffuse methodology, small-scale hydroelectric power also obtains a high score, in the conventional TOPSIS methodology, wind power in any of its presentations is positioned as the second best option.This discrepancy could suggest that the uncertainty associated with the data and evaluation criteria could have affected the position of the Hydro in the fuzzy methodology.This finding highlights the importance of considering data uncertainty and sensitivity in decision-making in energy technology assessment.

Scenario 2 outcome
Table 11 shows that for scenario 2, Hydroelectric and Solar Photovoltaic are the most favored renewable energy generation technologies, both with a score of 25%, indicating that these two technologies are considered highly favorable according to the criteria used in the fuzzy assessment.Hydroelectric, which harnesses the energy of moving water, and Solar Photovoltaic, which converts sunlight into electricity, are well-established and reliable options in the energy landscape.On the other hand, Tidal Wave gets the lowest score, at 0%.This suggests that this technology may not be considered as a viable option based on the criteria evaluated in the fuzzy methodology.
In the conventional TOPSIS methodology as shown in Table 11, Solar Photovoltaic also stands out as one of the most promising renewable energy generation technologies, with a score of 27%.This result reinforces the conclusion obtained in the TOPSIS Diffuse methodology, confirming Solar Photovoltaic as a highly favorable option in both methodologies.Wind-Offshore follows close behind, with a score of 23%, indicating its viability and potential as a diversified and sustainable renewable energy source.However, the distribution of scores is slightly different in this methodology compared to fuzzy, with greater variability across technologies.Comparing the results between all the methodologies for these scenarios, reveals a consistency in the preference for Solar Photovoltaic as one of the best renewable energy generation technologies in both methodologies.However, there are some notable differences in the ranking of other technologies.For example, while Hydroelectric obtains a high score in the fuzzy methodology, its score is lower in the conventional methodology.This may suggest that the uncertainty associated with the data and the evaluation criteria might have affected their position in the fuzzy methodology.These discrepancies highlight the importance of considering data uncertainty and sensitivity in decision-making in energy technology assessment.

Scenario outcome 3
The evaluation using the TOPSIS Diffuse methodology shown in Table 12 reveals a distribution of scores that highlights small-scale hydropower as the most promising renewable energy generation technology, with a solid score of 30%, this technology, which harnesses the energy of moving water, has proven to be a reliable and low environmental impact option in power generation.In addition, Solar Photovoltaic and Wind also show significant scores of 23% and 22%, respectively, these results show the energy potentials of this geographical area.On the other hand, Wave and Tidal score low at 2% and 4%, respectively, suggesting that these technologies may not be as suitable based on the  criteria considered in the fuzzy assessment.In Table 12 by employing the conventional TOPSIS methodology, Biomass emerges as one of the most promising renewable energy generation technologies, with a solid score of 25.69%, this renewable energy source, derived from organic matter such as agricultural and forestry waste, has proven to be a versatile and sustainable option for electricity generation.Solar Photovoltaic, as in the previous methodology, also stands out as one of the most preferred with an importance percentage of 25.56.However, the Wave Wave obtains a relatively low score of 6.51%, suggesting that this technology may not be considered as a viable option based on the criteria evaluated in the conventional TOPSIS methodology.

Scenario 4 outcome
The TOPSIS Diffuse methodology, where the results are shown in Table 13, reveals a balanced evaluation of various renewable energy generation technologies.In this analysis, small-scale hydroelectric power stands out as an outstanding option, with a respectable score of 27%, followed by photovoltaic solar energy with 20%, which repeats again as one of the most preferred.However, tidal wave does not score at all, suggesting that it may not be a viable option in the context evaluated.Biomass, at 16%, also shows strong performance in the fuzzy assessment, highlighting their importance as reliable and sustainable renewable energy sources.
In contrast to the methodology, TOPSIS reveals a slightly different distribution of scores among the technologies evaluated.Offshore wind emerges as the most favorable option, with a solid score of 23.64%.This technology, which harnesses offshore wind to generate electricity, shows great potential in terms of efficiency and sustainability.Biomass also scores a significant 23.27%, indicating its importance as a versatile and widely available renewable energy source.However, for this methodology, the most preferred energy is solar photovoltaic with 24.30%, which makes it stand out above the others.However, as in the fuzzy methodology, the Tidal Wave does not score at all, suggesting that its feasibility may be questionable in the context evaluated.When comparing the results of both methodologies, there is a convergence in the preference for certain technologies, such as Solar Photovoltaic and Biomass, as viable options for renewable energy generation.However, there are differences in the classification of other technologies, such as offshore wind and small-scale hydropower.

Scenario outcome 5
In relation to the Andean region, the TOPSIS Diffuse methodology, see Table 14, reveals a diversified evaluation of renewable energy generation technologies.In this analysis, large-scale hydropower emerges as the most prominent option, with an impressive score of 30%.This technology, which harnesses the energy of water in large rivers and reservoirs, demonstrates its viability and effectiveness in generating clean and sustainable energy.Small-scale hydro and solar PV also show strong performance, with scores of 26% each, underscoring their importance as reliable and sustainable energy sources.However, both Geothermal and Wind do not score highs, suggesting that they may not be viable options based on the criteria considered in the fuzzy assessment.
In contrast for this same region, the TOPSIS methodology reveals a slightly different distribution of scores among the technologies evaluated.Large-scale hydro remains a prominent option, with a solid score of 29.55%.This result reinforces its position as one of the leading sources of renewable energy in terms of efficiency and generation capacity.Solar PV generation also shows solid performance, with a score of 24.46%, highlighting its importance as a versatile and sustainable energy source.On the other hand, Wind obtains a modest score of 3.15%, which suggests that its viability may be limited in the context evaluated.

Scenario outcome 6
Table 15 shows the analysis carried out using the TOPSIS Diffuse methodology and provides a complete overview of the renewable energy generation technologies evaluated.In this context, Biomass stands out as the most favorable option, with a solid score of 31%.This technology, which uses organic materials to produce energy, demonstrates its versatility and efficiency in generating clean and sustainable energy.Both Small-Scale Hydro and Large-Scale Hydro show similar performance, with scores of 21% each.This result underscores the continued importance of hydropower in the energy mix, both in large-scale projects and smaller-scale initiatives.On the other hand, Solar PV also demonstrates its viability with a score of 23%, although Wind gets a lower score of 4%, suggesting that its performance may be less consistent in the context evaluated.
In contrast, the TOPSIS methodology offers a slightly different perspective on the technologies evaluated.Here, Small-Scale Hydro and Large-Scale Hydro emerge as prominent options, with scores of 23.87% and 23.82%, respectively.These results reinforce the importance of hydropower in renewable energy generation, in both smallerand large-scale projects.Solar PV also shows a solid performance with a score of 23.87%, while Biomass scores slightly lower at 15.93%.On the other hand, Wind Wind registered  a significant increase in its score, reaching 12.50%, which suggests an improvement in its viability and effectiveness in the context evaluated.As a conclusion of the comparative study for the Amazon region, there is a convergence in the preference for certain technologies, such as Hydroelectric and Solar Photovoltaic, as outstanding options for the generation of renewable energy.However, there are differences in the classification of other technologies, such as Biomass and Wind.

Scenario outcome 7
The TOPSIS Diffuse methodology, the results of which are shown in Table 16, provides a detailed overview of the evaluation of renewable energy generation technologies.In this analysis, both Biomass and Solar PV emerge as the most prominent options, with impressive scores of 34% each.These results reinforce the importance of these technologies in the transition towards a more sustainable and cleaner energy matrix.On the other hand, the results of the TOPSIS methodology reveal a slightly different distribution of scores among the technologies evaluated.Here, both small-scale hydro and wind show solid performance, with scores of 22.61% and 21.97%, respectively, however, it is biomass energy that also repeats for this methodology as the most preferred.These results underscore the continued importance of these technologies in renewable energy generation, highlighting their versatility and effectiveness in different contexts and environmental conditions.
To conclude the study of the Orinoquia region, there is a convergence in the preference for certain technologies, such as Biomass and Solar Photovoltaic, as outstanding options for the generation of renewable energy.However, there are differences in the classification of other technologies, such as small-scale hydropower and wind.These discrepancies can be attributed to variations in the evaluation criteria or in the sensitivity of the data used in each methodology.

Conclusions and recommendations
The research on the weighting and hierarchization of renewable energy sources in different geographical regions of Colombia using the TOPSIS and Diffuse TOPSIS metaheuristic models has yielded significant and important results that will undoubtedly serve to lay a foundation for future research and in the planning of projects associated with renewable energy sources.In this research, a variability in the evaluation of renewable energy generation technologies is observed between the two models, which underlines the importance of considering multiple approaches in energy decision-making.The effectiveness of the Diffuse TOPSIS model to evaluate the viability of Solar Photovoltaics in several regions is highlighted, as well as the preference of the TOPSIS model for Hydropower in some areas of that country, these differences highlight the complexity of the evaluation of renewable energy sources and the need to use complementary approaches for informed and solid decision-making.
In Table 17, the results of the positions or hierarchizations of each of the alternatives implemented and evaluated in each of the scenarios are expressed, according to the indicated methodology, it is possible to demonstrate that the alternative with the greatest preference in each of the methodologies and scenarios is the alternative A6 that refers to the generation by photovoltaic solar source, likewise alternatives such as Biomass, Offshore Wind and Onshore are renewable sources that today could greatly boost the energy transition that is wanted to implement in Colombia.
Among the recommendations for future research, the following stand out; given the geographical and energy diversity of Colombia, it is recommended to take into account the unique characteristics of each region when selecting renewable energy technologies, this may include factors such as the availability of natural resources, the existing infrastructure and the specific energy needs of each area, in order to obtain a complete and accurate assessment of renewable energy options, it is recommended to combine the use of different models and methodologies, such as TOPSIS and Diffuse TOPSIS and compare them with other decision-making methodologies, this integration will allow a deeper understanding of the strengths and limitations of each technology in different contexts.Finally, given the constant evolution of technology and energy market conditions, it is suggested to continue with research in the field of renewable energy and evaluate new energy sources such as hydrogen.This may include additional studies on the effectiveness of metaheuristic models in the evaluation of energy technologies, as well as research on new innovations in the field of renewable energies.As a conclusion of this research, it is clear to highlight that this research provides valuable information for planning and decision-making in the Colombian energy sector, highlighting the importance of considering regional diversity and using multiple approaches in the evaluation of renewable energy sources.

Fig. 1
Fig. 1 Synthesis of the methodology pdc < p < d E = c 1, p 1 , d 1 F = c 2, p 2 , d 2(a) Addendum: (b) Multiplication: ) respectively r (Wang et al. 2024a, b, c): (ii) Construct the fuzzy decision matrix (FDM) of RFs M and NFRs, in accordance with Ecs.21) and 22): Y D 1 D 2 D b D p criteria) (23).d + b = max a d ab Y (cost criterion) (25).c − b = max a c ab (iv) Calculate the weighted normalised MDF, by multiplying the weights of the NFRs, by the elements of the standardised MDF W y b i ab (Rajagopal Reddy et al. 2023).
(v) Define the Diffuse Positive Ideal Solution (FPIS,) and the Diffuse Negative Ideal Solution (FNIS), as:F + F − (vi) Calculate the distances and distances of each FR using the following Ecs:m + b m − b

Table 1
List of alternatives

Table 2
Methodology implementation scenario

•
Photovoltaic solar energy: According to the International Renewable Energy Agency's (IRENA) "Renewable Power Generation Costs in 2022" report, the levelized cost of utility-scale solar PV generation is in the 30 to 50 range USDMW/h (Executive, n.d.; Transition, n.d.) • Offshore wind: According to the same IRENA report, the levelized cost of offshore wind power generation is in a range of $0.06 to $0.11 per kWh, or about $60 to $110 USDMW/h (Lechón et al. 2023).• Onshore wind: IRENA's "Renewable Power Generation Costs in 2022" report indicates that the levelized cost of onshore wind power generation stands at 40 to 80 USDMW/h (Ceballos-Santos et al. 2023).• Biomass: According to IRENA's "Renewable Power Generation Costs in 2022" report, the levelized cost of generating energy from biomass is in the range of 50 to 130 USDMW/h.• Tidal: 403 USDMW/h (IRENA 2019).• Wave: 600 USDMW/h (IRENA 2019) • Small-scale hydropower: IRENA's "Renewable Power Generation Costs in 2022" report shows that the levelized cost of small-scale hydropower generation is in the range of $0.03 to $0.05 per kWh, or about $30 to $50 per kWh.USDMW/h (Executive, n.d.) • Large-scale hydropower: According to the same IRENA report, the levelized cost of large-scale hydropower generation is in the range of $0.01 to $0.03 per kWh, which equates to about $10 to $30 USDMW/h (Transition, n.d.).• Geothermal: According to IRENA's "Renewable Power Generation Costs in 2022"

Table 3
Implemented Likert Scale

Table 4
Sample survey completed by expert

Table 5
Calculate normalized matrix

Table 6
Calculate the weighted normalized matrix

Table 7
Calculate the best ideal value and the worst ideal value

Table 8
Calculate the Euclidean distance

Table 9
Calculate the performance score

Table 10
Result of implementation of methodologies in Scenario 1

Table 11
Result of implementation of methodologies in Scenario 2

Table 12
Result of implementation of methodologies in Scenario 3

Table 13
Result of implementation of methodologies in Scenario 4

Table 14
Result of implementation of methodologies in Scenario 5

Table 15
Result of implementation of methodologies in Scenario 6

Table 16
Result of implementation of methodologies in Scenario 7

Table 17
Position of alternatives vs. scenarios according to each methodology