TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem

Abstract

A common technique used to solve multi-objective optimization problems consists of first generating the set of all Pareto-optimal solutions and then ranking and/or choosing the most interesting solution for a human decision maker (DM). Sometimes this technique is referred to as generate first–choose later. In this context, this paper proposes a two-stage methodology: a first stage using a multi-objective evolutionary algorithm (MOEA) to generate an approximate Pareto-optimal front of non-dominated solutions and a second stage, which uses the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) devoted to rank the potential solutions to be proposed to the DM. The novelty of this paper lies in the fact that it is not necessary to know the ideal and nadir solutions of the problem in the TOPSIS method in order to determine the ranking of solutions. To show the utility of the proposed methodology, several original experiments and comparisons between different recognized MOEAs were carried out on a welded beam engineering design benchmark problem. The problem was solved with two and three objectives and it is characterized by a lack of knowledge about ideal and nadir values.

Dynamic computational resource allocation for CFD simulations based on pareto front optimization

“…Numerous approaches exist on how to select a solution from the Pareto-front. If the ideal point is known, one can rank the obtained solution and select the best one such as in [16]. If the ideal solution is not known, a strategy of finding a "knee" in the obtained solutions can be used as described in [3].…”

Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness

“…This additional scaling is commonly suggested in literature (e.g., in [4,11,12]). The transfer function (40) is obtained by substituting (39) in (32).…”

“…Depending on the number of design objectives, the visualization and graphical interpretation of the Pareto Front approximation is crucial. Some novel ideas to rank the potential solutions obtained by evolutionary algorithms in application to engineering problems are exposed in [32]. Likewise, an approach to the knee solution of the Pareto Front approximation for optimization problems with many objectives is addressed in [33].…”

Machine Learning Approach to Develop a Novel Multi-Objective Optimization Method for Pavement Material Proportion

“…The technique for order of preference by similarity to ideal solution (TOPSIS) is a multi-criteria decision analysis method, which was originally developed by Ching-Lai Hwang and Yoon [39,40]. The TOPSIS method compares and selects a set of alternatives by normalising scores for each criterion and calculating the geometric distance between each alternative and the ideal alternative, which is the best score in each criterion.…”