Research On Multiobjective Particle Swarm Optimization Algorithms

Many applications can finally be transformed into multiobjectiveoptimization problems (MOPs), which are now widely solved by particleswarm optimization (PSO) for its simple concept, easy implementationand fast convergence.A great number of multiobjective test functions have been designedfor evolutionary algorithms, but few specifically for PSO. Through theanalysis of the convergence mechanism of multiobjective particle swarmoptimization (MOPSO), we look at the correspondence between variablerelation, optima projection, vector relation, convergence stability, andconvergence type. Based on this, we show which characteristics causedifficulties in reaching or maintaining the optima, and which causedifficulties such as failure in convergence or premature convergence.MOPSO meets two difficulties–guiding the search towards thePareto front and maintaining diversity of the obtained solutions, andtherefore many varieties of improvements have emerged. But little hasbeen done to systematically analyze these improvements, thus it is stilldifficult to design a proper MOPSO algorithm for a new problem.Through using crowd behaviour for reference, our crowd frameworksystematically summarizes these improvements, extracts them intoreusable strategies and categorizes them into modules by theiroptimization mechanisms. Strategies are analyzed and compared firsttheoretically and then practically, assisting us to select a proper strategyfor a module. The correlation between strategies from different modulesis also analyzed, assisting us to build a sequence of the modules thatshould each select a strategy. Therefore the design is greatly simplified.For a MOP, two particles may be incomparable, i.e., not dominatedby each other, which decreases the convergence and reduces the precisionthe algorithm can achieve. Therefore we propose dimensional update, i.e., evaluating the particle’s fitness after updating each variable of its position.Separate consideration of the impact of each variable decreases theoccurrence of incomparable relations, thus improves the performance.Besides, we propose best substitution and gene exchange to accelerate theconvergence, dispense with personal best for the algorithm can providesufficient diversity, and simplify the grid reduction to decreasecomputational cost.High dimension of the decision space greatly deteriorates theperformance of multiobjective particle swarm optimization (MOPSO),and the existing decomposition methods are not satisfying. Therefore wepropose a MOPSO based on separability and type. After learning suchcharacteristics of the decision variables, separable distance variables areoptimized separately, separable position or mixed variables are evaluatedseparately, whereas nonseparable variables are optimized and evaluatedas a whole. The assigned disturbance for position variables, mixedvariables, and distance variables gradually decreases. Furthermore, weadopt the ring topology to deal with multimodality, propose the mirrortransform to overcome deception, modify the grid reduction to decreasecomputational cost, and improve the global best selection to handlenonuniformity.To conclude, our work is helpful to the design of better MOPSOs.