Dynamic Multi-Objective Optimization Using PSO

Abstract

Abstract. Dynamic multi-objective optimization problems occur in many situations in the real world. These optimization problems do not have a single goal to solve, but many goals that are in conflict with one another -improvement in one goal leads to deterioration of another. Therefore, when solving dynamic multi-objective optimization problem, an algorithm attempts to find the set of optimal solutions, referred to as the Pareto-optimal front. Each dynamic multi-objective optimization problem also has a number of boundary constraints that limits the search space. When the particles of a particle swarm optimization (PSO) algorithm move outside the search space, an approach should be followed to manage violation of the boundary constraints. This chapter investigates the effect of various approaches to manage boundary constraint violations on the performance of the dynamic Vector Evaluated Particle Swarm optimization (DVEPSO) algorithm when solving DMOOP. Furthermore, the performance of DVEPSO is compared against the performance of three other state-of-the-art dynamic multi-objective optimization algorithms. IntroductionMany problems in the real-world change over time and require more than one goal to be optimized. However, these goals, or objectives, are normally in conflict with one another, where an improvement in one objective results in deterioration of another objective. Therefore, a single solution does not exist and the goal becomes

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

“…An environmental change may involve the objective function (or functions if a dynamic multi-objective problem is considered [24,25]), input variables, problem instances and constraints (e.g., dynamic constrained optimization [26]). Formally, a DOP can be defined as follows: DOP = optimize f (x, t) subject to X(t) ⊆ S , t ∈ T, (1) where S is the search space, t is the time, f : S × T → R is the objective function that assigns a value (i.e., R) to each possible solution x ∈ S and X(t) is the set of feasible solutions x ∈ X(t) ⊆ S at time t [13,15].…”

“…A multi-swarm PSO was proposed where each swarm solves a single objective function independently and communicates with other swarms to transfer the knowledge [206,207]. In order to maintain diversity, a percentage of the swarm are reinitialized whenever a dynamic change is detected by sentry particles.…”

Benchmarks for dynamic multi-objective optimisation algorithms

“…Five DMOAs were used for the experiments, namely the Dynamic Nondominated Sorting Genetic Algorithm II (DNSGA-II)-A [Deb et al 2007], DNSGA-II-B [Deb et al 2007], the dynamic cooperative competitive Evolutionary Algorithm (dCOEA) [Goh and Tan 2009b], the Dynamic Multi-objective Particle Swarm Optimisation (DMOPSO) algorithm [Lechuga 2009], and the Dynamic Vector Evaluated Particle Swarm Optimisation (DVEPSO) algorithm [Helbig and Engelbrecht 2013b]. All DMOAs were evaluated on a modified version of DIMP2 with a concave POF, ZJZ (Equation (16)), FDA2 (Equation (6)), FDA2 Camara , FDA3 (Equation (7)), FDA3 Camara , FDA5 (Equation (9)), FDA5 iso (Equation (31)), FDA5 dec (refer to Section 5.2), dMOP2 (Equation (14)), dMOP3 (Equation (15)), dMOP2 iso (Equation (32)), dMOP2 dec (refer to Section 5.2), HE1 (Equation (19)), HE2 (Equation (20)), HE6 (Equation (37)), HE7 (Equation (38)), and HE9 (Equation (40)).…”

A novel differential evolution for dynamic multiobjective optimization with adaptive immigration scheme

“…Dynamic optimization problems including single-objective optimization problems [4][5][6] and multi-objective optimization problems [7][8][9]. In the last few years, the researches on the dynamic single objtedive optimization problems have got some achievements [10,11].…”

“…To achieve this goal the dynamic algorithm is firstly able to detect the changes in the environment and then make the appropriate response to these changes. Some researches have focused on the research of DMOPs and have made some accomplishments [9,12,13].…”