A COMPARATIVE ANALYSIS OF EVOLUTIONARY COMPUTATION TECHNIQUES AND THE PERFORMANCE OF MULTI-OBJECTIVE GENETIC ALGORITHMS IN SOLVING LINEAR OPTIMIZATION PROBLEMS

Abstract

In today's world of decision-making and operations research, multi-objective optimization is becoming more and more important since real-world goals are often at odds with each other. Linear programming and scalarization approaches are examples of conventional optimizations techniques that have been used a lot on single-objective issues. However, they typically don't do a good job of capturing the complexity of multi-objective situations. In this case, Multi-Objective Evolutionary Algorithms (MOEAs), especially Genetic Algorithms (GAs), are a good choice since they may provide a wide range of Pareto-optimal solutions. Even while GAs is used a lot to solve non-linear optimization issues, we still don't know much about how well they work for multi-objective linear optimization problems (MOLOPs). This study carefully compares well-known GA-based MOEAs like NSGA-I, NSGA-II, NSGA-III, and NPGA to see which one is best in solving MOLOPs. The research looks at important performance measures such solution variety, convergence accuracy, and computing economy in the limited and predictable setting of linear models. We use real-world linear optimization issues from fields like logistics, transportation, and resource allocation as case studies to see how well each solution works.

One of the most important things this study does is provide a structured GA-based framework only for linear issue situations that includes effective selection, crossover, and mutation procedures. We use conventional multi-objective assessment measures including Hypervolume Indicator, Generational Distance, and Spacing to evaluate performance.

The results are likely to fill in a major vacuum in research by showing if stochastic evolutionary methods provide big benefits for solving linear multi-objective problems, which have always been seen to be the job of precise solvers. This study not only adds to our theoretical knowledge of MOEAs in linear settings, but it also gives decision-makers useful information on how to find strong, scalable, and computationally efficient solutions for difficult optimization problems.