Multiple Criteria Decision-Making in Optimization Processes

Multiple Criteria Decision-Making (MCDM) is a collection of formal approaches designed to evaluate and compare alternative solutions in the presence of conflicting objectives. In optimisation contexts, decision-makers must often reconcile disparate goals—such as cost minimisation, performance maximisation, sustainability enhancement and risk reduction—each measured on different scales or units. Classical methods, including the Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Preference Ranking Organisation Method for Enrichment Evaluation (PROMETHEE) and VIKOR, provide systematic frameworks for weighting criteria and ranking alternatives. More recent advances have extended these techniques to address uncertainty—through fuzzy logic, intuitionistic and Pythagorean fuzzy sets—and to integrate multiple viewpoints via hybrid or composite procedures. Developments in normalisation strategies and the refinement of aggregation operators have enhanced the robustness and interpretability of results. Global applications span sustainable energy planning, urban logistics, healthcare resource allocation, credit scoring, and industrial process selection. By combining methodological rigour with practical adaptability, MCDM fosters transparent and evidence-based decision support in complex environments.

Research from Nature Portfolio

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Research from all publishers

A novel framework for multi-criteria assessment of classification models in credit scoring has been developed, employing a PROMETHEE-based sustainability analysis (PROSA). This approach incorporates consistency checks between training and validation sets and accounts for temporal data variation. Two alternative aggregation scenarios yielded near-identical rankings, with logistic regression models and parsimonious predictor sets emerging as top performers. Expert judgement corroborated the data-driven outcomes, demonstrating the method’s practical reliability.

A comprehensive evaluation of ten crisp-based MCDM methods—including COPRAS, CODAS, MOORA, TOPSIS, MABAC and VIKOR variants—was applied to economic performance data of G-20 countries across multiple time periods. By comparing outcomes against two real-world reference anchors, researchers identified CODAS as the most consistently correlated method. An analysis of normalisation techniques revealed that maximum-based normalisation outperformed alternatives, and a maximum-normalisation fuzzy CODAS procedure was proposed to enhance decision precision under mixed data types.

A systematic bibliometric review of MCDM research from 1977 to 2022 analysed over 23 000 documents and 33 000 authors. The study highlighted an annual growth rate exceeding 14 %, with AHP, TOPSIS, VIKOR, PROMETHEE and ANP dominating methodological usage. Geographic trends revealed leading contributions from China, India and Iran, while top journals included Expert Systems with Applications and Sustainability. The review underscored emerging needs for unified frameworks and advanced uncertainty modelling to support diverse application domains.

Multiple Criteria Decision-Making in Optimization Processes publication trend

The graph below shows the total number of articles in multiple criteria decision-making in optimization processes across all publications each year (not limited to Nature Index journals).

Technical terms

Multi-Objective Optimisation: A mathematical approach to find solutions that balance two or more conflicting objectives without reducing them to a single aggregate criterion.

Normalisation Techniques: Procedures to rescale heterogeneous data into dimensionless values, ensuring comparability across criteria in MCDM analyses.

Fuzzy Sets: Mathematical constructs that represent imprecise or uncertain information by allowing elements to belong to sets with varying degrees of membership.

CODAS: A MCDM method (Combinative Distance-based Assessment) that ranks alternatives based on distances from a reference point, combining relative and absolute measures.

PROSA: An extension of PROMETHEE tailored for sustainability assessment, characterised by reduced criteria compensation and interactive geometric analysis.

References

1. Framework for multi-criteria assessment of classification models for the purposes of credit scoring. Journal of Big Data (2023).
2. The Influence of Objective Weight Determination Methods on Electric Vehicle Selection in Urban Logistics. Journal of Intelligent Management Decision (2023).
3. A comprehensive MCDM assessment for economic data: success analysis of maximum normalization, CODAS, and fuzzy approaches. Financial Innovation (2024).
4. A Systematic Review of the Applications of Multi-Criteria Decision Aid Methods (1977–2022). Electronics (2022).
5. The Interval‐Valued Intuitionistic Fuzzy MULTIMOORA Method for Group Decision Making in Engineering. Mathematical Problems in Engineering (2015).
6. MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making. Complexity (2018).
7. Assessment and Comparison of Various MCDM Approaches in the Selection of Manufacturing Process. Advances in Materials Science and Engineering (2020).
8. Comparative Analysis of the Normalization Techniques in the Context of MCDM Problems. Decision Making Applications in Management and Engineering (2021).
9. Towards Strong Sustainability Management—A Generalized PROSA Method. Sustainability (2019).
10. Renewable Energy Technology Selection Problem Using Integrated H-SWARA-MULTIMOORA Approach. Sustainability (2018).