Stochastic Optimization Algorithms for Determining Optimal Weights in Multi-criteria Decision Analysis
摘要
The increasing application of intelligent systems for making smart decisions necessitates their continuous improvement in line with technological advancements and the needs of end users. This makes Artificial Intelligence (AI) methods an ideal solution for such applications. This study enhances the Energy Scope (ES) model by transforming it from a single-criteria to a multi-criteria decision analysis (MCDA) approach. This transformation allows end users the flexibility to introduce their own criteria, which will influence the system’s final optimal decision with a certain impact percentage. The objective of this research is to determine the optimal weight values assigned to the criteria using AI methods. Typically, the process is reversed, requiring prior knowledge of each criterion’s weight during optimization, what is provided by experts. However, by applying stochastic optimization algorithms to explore a multidimensional space, the study derives the optimal weight distribution for the given criteria. Specifically, Genetic Algorithm, Simulated Annealing, and Ant Colony Optimization algorithms were implemented. The obtained optimal weights for the selected criteria—total cost, total global warming potential, acidification, land use, and water use—are as follows. For the GA algorithm: \(0.01092, 0.49327, 0.03746, 0.37870, 0.07964\) , respectively. For the SA algorithm: \(0.00896, 0.21115, 0.60254, 0.16070, 0.01664\) , respectively. For the ACO algorithm: \(0.02628, 0.49935, 0.07884, 0.39422, 0.00128\) , respectively. The computational times required were \(27\) hours for GA and SA, while ACO required \(29\) hours. The estimated weight values for all three algorithms are approximately the same, allowing for the potential implementation of any of them within the ES model. Although time-consuming, a single weight estimation for a representative country like Belgium enables the reuse of these values when applying the model in other EU countries, assuming similar climatic and geographical conditions.