An Improved Multi-Objective Particle Swarm Optimization Based on Utopia Point Guided Search

An Improved Multi-Objective Particle Swarm Optimization Based on Utopia Point Guided Search

Swapnil Prakash Kapse (Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India) and Shankar Krishnapillai (Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India)
Copyright: © 2018 |Pages: 26
DOI: 10.4018/IJAMC.2018100104


This article demonstrates the implementation of a novel local search approach based on Utopia point guided search, thus improving the exploration ability of multi- objective Particle Swarm Optimization. This strategy searches for best particles based on the criteria of seeking solutions closer to the Utopia point, thus improving the convergence to the Pareto-optimal front. The elite non-dominated selected particles are stored in an archive and updated at every iteration based on least crowding distance criteria. The leader is chosen among the candidates in the archive using the same guided search. From the simulation results based on many benchmark tests, the new algorithm gives better convergence and diversity when compared to existing several algorithms such as NSGA-II, CMOPSO, SMPSO, PSNS, DE+MOPSO and AMALGAM. Finally, the proposed algorithm is used to solve mechanical design based multi-objective optimization problems from the literature, where it shows the same advantages.
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Multi-objective optimization algorithms aim at improving the convergence to the True Pareto-optimal front, and also maintain good diversity of population (Sierra & Coello, 2006). Closeness of the obtained Pareto-optimal front to the Pareto optimal Front is referred to as convergence and the uniform distribution of solutions is referred to as diversity (Baviskar & Krishnapillai, 2016). Various evolutionary algorithms are proposed in the field of multi-objective optimization such as NSGA, SPEA, NSGA-II, AMALGAM, SMPSO and CMOPSO which will be discussed in the succeeding sections. Zitzler and Thiele (1991) presented Strength Pareto Evolutionary Algorithm (SPEA), which used an archive population set to store previously generated non- dominated solutions and update it as and when new non- dominated solutions and found. PSO belongs to swarm intelligence category of techniques. PSO is a population based heuristic optimization method which is motivated by the behaviour of birds in a flock foraging for food and introduced by Kennedy (1995). Introduction of inertia weight in PSO improved the convergence of PSO (Shi & Eberhart 1998). The original PSO was introduced for single objective optimization and hence it was modified to Multi-Objective Particle Swarm Optimization (MOPSO) using a ring topology by Moore and Chapman (1999). Coello et al. (2002) proposed a multi- objective approach to PSO wherein the concept of Pareo dominance was used to determine the flight direction. Later, PSO was further modified and improved due to its good ability of swarm to explore the design variable space (Nguyen & Kachitvichyanukul, 2010) Furthermore, having the advantage of fast convergence, introduction of mutation operator proved helpful for exploration. (Stacey & Jancic, 2003). Constriction mechanism for controlling the maximum velocity was introduced in Speed- constrained multi-objective PSO (SMPSO) which also improved the search ability of algorithm (Nebro et al. 2009). Implementation of crowding distance approach for elite solution improved the diversity (Zhongkai et al, 2010). The strategy of population recombination with a novel mutation operator prevents MOPSO from getting trapped in local optimal solutions (Li Ming et al, 2016). A Co-evolutionary Memetic Particle Swarm Optimizer (CMPSO)was introduced by Zhou et al. (2012) where the author used five different local searches for particle improvement. Using the novel gene- therapy method, the diversity was improved by Lin (2013) with a large number of iterations. Chen (2014) introduced a new local search based algorithm where the strategy of non- dominated sorting was utilized for population selection. Many unconstrained multi- objective problems were solved whereas few functions got trapped in the local optimal solution. Reference point based many objective optimization evolutionary algorithm with the structure of NSGA-II was introduced by Deb et al. (2013) called NSGA-III. Implementing the concept of centroid and inertia weight, an algorithm to overcome trapping unto local optima was overcome (Chen et al. 2014). Mashwani et al. (2014) proposed a Multi- objective memetic algorithm based on decomposition (DE+PSO) where PSO acts as a local search operator and differential evolution (DE) was the main search tool. The above algorithm was further improved (Mashwani et al., 2016) by introducing a Pareto archive strategy (PAES) and simplex crossover to obtain better chromosomes. An improved niche strategy was developed for Multi-modal scalarization of multiple objective evolutionary algorithm which evaluated multiple Pareto- optimal solutions in one iteration (Tutum et al., 2015). Multi- objective optimization was solved by the mechanism of reference point approach and non- dominated sorting strategy by Saeda et al, (2015 & 2016). A new version of NSGA, referred to as Elite-NSGA-III, was proposed by implementing improved strategies to preserve elitism (Ibrahim et al. 2016). Recently, Abouhawwash et al. (2017) introduced evolutionary multi- objective optimization algorithms integrated with Karush Kuhn Tucker proximity measures for improving convergence.

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