So far the focus of almost all multior many-objective performance metrics has been the convergence and distribution of solutions in the objective space (Pareto-surface). Pareto-surface metrics such as IGD, HV, and Spread are simple and provide knowledge about the overall performance of the solution set. However, these measures do not provide any insight into the distribution or spread of a solu...

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

In [5] an evolutionary algorithm for detecting continuous Pareto optimal sets has been proposed. In this paper we propose a new evolutionary elitist approach combing a non-standard solution representation and an evolutionary optimization technique. The proposed method permits detection of continuous decision regions. In our approach an individual (a solution) is either a closed interval or a po...

This paper uses integrated Data Envelopment Analysis (DEA) models to rank all extreme and non-extreme efficient Decision Making Units (DMUs) and then applies integrated DEA ranking method as a criterion to modify Genetic Algorithm (GA) for finding Pareto optimal solutions of a Multi Objective Programming (MOP) problem. The researchers have used ranking method as a shortcut way to modify GA to d...

A newmultiobjective particle swarm optimization (MOPSO) technique for environmental/economic dispatch (EED) problem is proposed in this paper. The proposed MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of global best and local best individuals in multiobjective optimization domain. The proposedMOPSO technique has been implemented to solve the EED problemwith ...

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

Local search techniques have proved to be very efficient in evolutionary multi-objective optimization(MOO). However, the reasons behind the success of local search in MOO have not yet been well discussed. This paper attempts to investigate empirically the main factors that may have contributed significantly to the success of local search in MOO. It is found that for many widely used test proble...

 Evolutionary multi-objective optimization (EMOO) finds a set of Pareto solutions rather than any single aggregated optimal solution for a multi-objective problem. The purpose of this paper is to describe a newly developed evolutionary approach --Paretobased multi-objective differential evolution (MODE). In this paper, the concept of differential evolution, which is well-known in the continuou...

Abstract: In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal fr...

In this paper, a multi-objective reconfiguration problem has been solved simultaneously by a modified ant colony optimization algorithm. Two objective functions, real power loss and energy not supplied index (ENS), were utilized. Multi-objective modified ant colony optimization algorithm has been generated by adding non-dominated sorting technique and changing the pheromone updating rule of ori...