Multi-objective distance minimization problems – applications in technical systems

Abstract

Abstract This article describes the Distance Minimisation Problem (DMP) from a metaheuristic optimisation point of view. The problem is motivated by real applications and can be used to test the performance of optimisation methods like Evolutionary Algorithms. After formally describing the problem and its extensions using different metrics or dynamics, we perform experiments with well-known metaheuristic methods to demonstrate the performance on various DMP instances. The results show that modern algorithms like NSGA-II and SMPSO can struggle with this kind of problem under certain conditions, especially when Manhattan distances are used. On the other hand, specialised methods like GRA lack diversity of solutions in some cases. This indicates that even modern and powerful metaheuristic algorithms need to be chosen with care and with the respective optimisation task in mind.