A multi-objective tabu search algorithm based on decomposition for multi-objective unconstrained binary quadratic programming problem

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

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.

A Multi-Objective Particle Swarm Optimization Based on Grid Distance

In modern intelligent algorithms and real-industrial applications, there are many fields involving multi-objective particle swarm optimization algorithms, but the conflict between each objective in the optimization process will easily lead to the algorithm falling into local optimal. In order to prevent the algorithm from quickly falling into local optimization and improve the robustness of the algorithm, a multi-objective particle swarm optimization algorithm based on grid distance (GDMOPSO) was proposed, which has to improve the diversity of the algorithm and the search ability. Based on the MOPSO algorithm, a new external archive control strategy was established by using the grid technology and Pareto-dominant ordering principle, and the learning samples were improved. The proposed GDMOPSO is compared with a group of benchmark function tests and four classical algorithms. The results of experiment show that our proposed algorithm can effectively avoid premature convergence in terms of generational distance and hyper-volume (HV) indicator compared with other four classical MOPSO algorithms.