Analytical and Comparative Study for Optimization Problems

Abstract

Finding an optimal solution to some problem, like minimizing and maximizing the objective function, is the goal of Single-Objective Optimization (SOP). Real-world problems, on the other hand, are more complicated and involve a wider range of objectives, several objectives should be maximized in such problems. No single solution could be enhanced in all objectives without deteriorating at least one other goal, which is the definition of Pareto-optimality. Understanding the idea of Multi-Objective Optimization (MOP) is thus necessary to find the optimum solution. Multi-objective evolutionary algorithm (MOEA) are made to simultaneously assess many objectives and find Pareto-optimal solutions, MOEA can resolve multi-objective and single-objective optimization problems. This paper aims to introduce a survey study for optimization problem solutions by comparing techniques, advantages, and disadvantages of SOP and MOP with metaheuristics and evolutionary algorithms. From this study, we conduct that the efficiency of MOP lies in the present more than one SOP, but it takes a longer time to process and train and is not suitable for all applications, While SOP is faster and more useful in stock and profit maximization applications. And the posterior techniques are considered the dominant approach to solving multi-objective problems by the use of the field of metaheuristics. Index Terms— Multi-Objective Evolutionary Algorithm, Multi-Objective Optimization, Optimization problem, Objective Function, Single-Objective Optimization.