Research On The Differential Evolution Algorithm For Nolinear Mixed Integer Programming Problems

Evolutionary algorithm, as a heuristic optimization method, is derived form thetheory of biological evolution in nature, such as genetic algorithm, harmony searchalgorithm and differential evolution algorithm. At present, these algorithms have beenwidely used in the practical problems, especially in nolinear mixed integerprogramming problem. However, any method has limitations. The improvement ofthe algorithm is necessary.In view of the nonlinear mixed integer programming problem, this paper studiedthe differential evolution algorithm. Firstly, the origin, main steps, improvementstrategies and application are given respectively; then the parameters of the improveddifferential evolution algorithm, put forward to the improved differential evolutionalgorithm; finally different genetic co-evolutionary algorithm is proposed. The mainresearch contents can be summarized as follows.(1) The basic situation of the differential evolution algorithm is given in details.Lay the foundation for subsequent research.(2) An improved differential evolution(IDE) algorithm is proposed for the themixed integer programming problems. The new population initialization technologyand dynamic non-linear scaling factor are applied to enhance optimization capabilityof algorithm. We strengthen influence of constraint matrix to deal with constraint ofproblems. Introduction of special truncation procedure to handle integer restrictionsand selection operator based on Deb constraint rules update the population. The testresults show that the IDE algorithm possess higher success rate and precision thanMI-LXPM algorithm.(3) The difference genetic co-evolutionary algorithm (D-GCE) is proposed stillfor the the mixed integer programming problems. First, the constrained mixed integerprogramming problem be converted to unconstrained bi-objective optimizationproblems. Secondly, selection mechanism coalesce Pareto dominance and superiorityof feasible solution methods to choose excellent individual as the next generation ofpopulation. For continuous part of the population, D-GCE algorithm using differentialevolution algorithm, and for discrete part of the population, D-GCE algorithm usinggenetic algorithm. It’s effectively solve the problem exist discrete variables andcontinuous problems. Numerical experiments on24test functions have shown that thenew approach is efficient. The comparison results between the D-GCE and the otherevolutionary algorithms indicate that the proposed D-GCE algorithm is competitivewith and in some cases superior to, other existing algorithms in terms of the quality,efficiency, convergence rate, and robustness of the final solution.In general, the differential evolution algorithm is analyzed comprehensively.Finally, whole research contents are summarized, and further research directions areindicated.