Geometric Particle Swarm Optimization for Multi-objective Optimization Using Decomposition

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optimizers for continuous problems, and recently it has been successfully extended to the multi-objective domain. However, no investigation on the application of PSO within a multi-objective decomposition framework exists in the context of combinatorial optimization. This is precisely the focus of the paper. More specifically, we study the incorporation of Geometric Particle Swarm Optimization (GPSO), a discrete generalization of PSO that has proven successful on a number of single-objective combinatorial problems, into a decomposition approach. We conduct experiments on manyobjective 1/0 knapsack problems i.e. problems with more than three objectives functions, substantially harder than multi-objective problems with fewer objectives. The results indicate that the proposed multi-objective GPSO based on decomposition is able to outperform two version of the wellknow MOEA based on decomposition (MOEA/D) and the most recent version of the non-dominated sorting genetic algorithm (NSGA-III), which are state-of-the-art multi-objective evolutionary approaches based on decomposition

Constraint handling within MOEA/D through an additional scalarizing function

The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) has shown high-performance levels when solving complicated multi-objective optimization problems. However, its adaptation for dealing with constrained multi-objective optimization problems (cMOPs) keeps being under the scope of recent investigations. This paper introduces a novel selection mechanism inspired by the e-constraint method, which builds a bi-objective problem considering the scalarizing function (used into the decomposition approach of MOEA/D) and the constraint violation degree as an objective function. During the selection step of MOEA/D, the scalarizing function is considered to choose the best solutions to the cMOP. Preliminary results obtained over a set of complicated test problems drawn from the CF test suite indicate that the proposed algorithm is highly competitive regarding state-of-the-art MOEAs adopted in our comparative study.Peer ReviewedPostprint (author's final draft

Generating Uniformly Distributed Points on a Unit Simplex for Evolutionary Many-Objective Optimization

Most of the recently proposed evolutionary many-objective optimization (EMO) algorithms start with a number of predefined reference points on a unit simplex. These algorithms use reference points to create reference directions in the original objective space and attempt to find a single representative near Pareto-optimal point around each direction. So far, most studies have used Das and Dennis’s structured approach for generating a uniformly distributed set of reference points on the unit simplex. Due to the highly structured nature of the procedure, this method does not scale well with an increasing number of objectives. In higher dimensions, most created points lie on the boundary of the unit simplex except for a few interior exceptions. Although a level-wise implementation of Das and Dennis’s approach has been suggested, EMO researchers always felt the need for a more generic approach in which any arbitrary number of uniformly distributed reference points can be created easily at the start of an EMO run. In this paper, we discuss a number of methods for generating such points and demonstrate their ability to distribute points uniformly in 3 to 15-dimensional objective spaces.Also part of the Theoretical Computer Science and General Issues book sub series (LNTCS, volume 11411)Knowledge-Driven Decision Support (KDDS