Genetic Algorithm Based Research On Constrained Optimization Problems With Discretely Distributed Decision Spaces

When solving engineering optimizing and scheduling problems, some objects are restrained from certain working ranges, in which they cannot work properly. Those working ranges are modeled as constraints of undefined regions on decision variables in this paper. By treating these constraints, the request, optimized values should not fall into prohibited regions, is satisfied.Because decision variables have undefined regions, the original convex decision space of the corresponding problem becomes non-convex, since it is separated into several convex sub decision spaces. This makes algorithms, which based on optimal theory of function and operational research theory unavailable, and some constraints handling methods out of commission. Based on adaptability analysis of existing optimization algorithms, genetic algorithm (GA) is chosen to solve constrained optimization problem (COP) with such constraints. However, existing constraints handling methods, e.g. penalty function are not able to deal with infeasible solutions in genetic operations, and a boundary information based decision variables repairing methods is formulated, which keeps feasible solutions above a certain level, assures stability of genetic algorithm. The proposed solutions repairing method is used in three types of problems, including single objective COP, multiple objective COP and bi-level single objective COP. Besides, targeted improvements are also done on corresponding algorithms chosen for those problems, which aim at solving constraints inducing issues. Simulations are used to illustrate rightness and effectiveness of the proposed solutions repairing method and improvements.Essentials of research:1. Based on problem adaptability of existing optimization algorithms, including function optimization and operation research theory based algorithms, intelligent optimization algorithms, genetic is chosen to solve COPs, which has decision variables with un-defined regions between upper and lower bound. Analyzing transformation between of three types infeasible solutions existed, a repairing method is proposed, which uses only boundary information of decision variable. Simulations and comparisons with other similar constraints handling measures are adopted to show its performance.2. Analyzing the performance differences of niche and elite preservation strategy in solving COPs with discretely distributed decision spaces (DDDS), and elite preservation is adopted. New multiple elite preservation strategy is designed for recording those solutions with a better fit-value. And simulation comparisons are done to illustrate fitness of the strategy in solving this problem. The proposed strategy is implemented in solving a real thermal power plant load distributed (PPLD) problem, which considers both desulfurization-compensating price and relying ranges of coal mills. Besides, better performance achieved.3. Performance assessment of major GA based multiple objectives optimization algorithms show that, non-dominated sorting genetic algorithm Ⅱ (NSGAⅡ) is the best one in solving COPs with DDDS. However, crowding distance calculation of NSGAⅡ does not consider distance between different layers, which reduce the ability of reaching Pareto front. New crowding distance criterion takes both elements into account is proposed, which show effectiveness in simulations on PPLD with DDDS considering economic and speed performance.4. Firstly, adaptability analysis of optimization algorithms on bi-level programming (BLP) with DDDS in lower lever is accomplished, and results show traditional optimization theory with Kaursh-Kuhn-Tucker (KKT) condition cannot handle these constraints, but GA is suitable. Secondly, improvements are made on a kind of hierarchical GA, which used to solve BLP, which generalized its application scope to any BLP problems. Finally, numerical simulations are adopted to illustrate effectiveness of those improvements combined with infeasible solution repairing methods. Besides, measures taken above can provide sub-optimal feasible solutions when global optimal solution does not exist. This method is adopted to solve a wind farm—thermal power plant joint generation scheduling problem, and simulation results show effectiveness.