A particle gradient evolutionary algorithm for solving multi-objective problems

• Published in: Applied mathematics and computation Vol. 187; no. 2; pp. 1173 - 1186
• Main Authors: Li, Kangshun, Yue, Xuezhi, Kang, Lishan, Chen, Zhangxin
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.04.2007; Elsevier
• Subjects: Calculus of variations and optimal control; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Entropy; Evolutionary computation; Exact sciences and technology; Free energy; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Particle gradient; Sciences and techniques of general use; Particle gradient; Entropy; Free energy; Evolutionary computation; Energy function; Evolutionary algorithm; Optimization method; Design; Particle; Particle system; Minimum energy; Phase space; Gradient; Orbit; Non equilibrium system; Rank; Systems theory; Algorithm; Equilibrium; Value function; Numerical analysis; Applied mathematics; Experimental design; Optimal solution; Minimum principle; Problem solving
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.09.010

In this paper a particle gradient evolutionary algorithm (PGEA) for solving complex multi-objective optimization problems is presented according to the gradient of particles, the transportation orbit of particles, the minimum principle of free energy decreasing, and the law of entropy increasing of particle systems in the phase space based on a transportation theory. This algorithm includes two sub-algorithms: the first is to define the PGEA energy and entropy, a rank function, and a niche function and then calculate the rank function values of every particle in the phase space; the second is to solve for the optimal Pareto front of a multi-objective optimization problem. The theory of a particle system changing from non-equilibrium to equilibrium is used to design the algorithm in order to drive all the individuals in the population to have a chance to participate in the evolving operation to obtain the Pareto optimal solutions of the multi-objective problems quickly and evenly. Our experiments show that this algorithm cannot only converge to the global Pareto optimal front quickly, uniformly, and precisely, but also can avoid the premature phenomenon of multi-objective problems.