一种求解复杂约束优化问题的粒子动力学演化算法

A New Particle Dynamical Evolutionary Algorithm for Solving Complex Constrained Optimization Problems

根据输运理论中的粒子输运方程、相空间能量最小原理和熵增法则,构造一种能够高效求解带约束条件优化问题的动力学演化算法(CPDEA)。并利用这种能量和熵的变化使整个粒子系统从非平衡达到平衡的理论来定义适应值函数,使得所有的个体都能够有机会参与杂交和变异,最终达到快速求出约束优化问题的所有全局最优解的目的。在数据实验中通过用该算法求解一些复杂的带约束条件的函数优化问题并得到较好的结果。同时实验还显示,该算法不仅能快速容易地求出复杂的带约束优化问题的所有全局最优解,而且还能避免求解问题的早熟现象。

In this paper a particle dynamic evolutionary algorithm（CPDEA） for solving constrained problems efficiently is presented according to the equation of particle transportation, the principle of energy minimizing and the law of entropy increasing in phase space of particles based on transportation theory. A fitness function of constrained optimization problems is defined based on the theory in which particle systems in phase space reach equilibrium from non-equilibrium. The energy of particle systems minimizes and the entropy of particle systems increases gradually in the evolving process of particles in order that all the individuals have chance to crossover and mutate. Finally all the optimal solutions are obtained quickly . In the numerical experiments , precise optimal solutions of the constrained problems are gotten by using this algorithm. Compared with traditional evolutionary algorithms, the experiments show that not only all the global solutions of complex constrained optimization problems can be solved in an easy and quick way , but also premature phenomenon can be avoided.