基于遗传算法的决策空间离散分布约束优化问题研究
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摘要
本文将工程优化调度问题中,被优化对象不能在某些特定区间内取值的要求,建模为待优化数学问题的决策变量定义区间不连续约束条件。针对该约束条件引入后,优化问题的决策空间离散分布,对数学特性要求严格的算法与约束条件处理方法无法使用的问题,进行算法选择与搜索策略设计。首先对比常见算法解决该类问题的适应性,选择遗传算法进行求解；其次,在遗传算法框架下,设计基于决策变量定义区间边界信息的不可行解修补方法,处理搜索过程中的不可行解,维持种群中可行解的比例；最后,考虑决策变量定义区间不连续约束条件对单目标、多目标与双层规划问题的影响,有针对性的改进算法搜索策略,并通过仿真实验说明改进的有效性。
主要研究内容如下：
1.对决策变量定义区间不连续约束条件进行特点分析,比较基于函数优化理论、运筹学理论的优化方法,以及智能优化方法对该类问题的适应性；选择遗传算法求解带有上述约束条件的优化问题。对遗传操作过程中,可能出现的三类不可行解进行特点与转化模式分析,设计解修补方法；通过与其他三类主要的不可行解处理方法仿真实验对比,说明该修补方法的有效性。
2.分析小生境技术与精英保留策略求解带有决策变量连续定义区间不连续约束条件单目标优化问题的适应性,说明精英保留策略适于解决该类问题。设计一类多精英保留策略,通过仿真实验说明该策略性能较好。并将之应用于解决考虑脱硫补偿电价与磨煤机接力区间的火电厂厂级负荷优化分配问题,取得良好效果。
3.对进化算法框架下的主流多目标优化算法进行适应性分析,选择决策变量定义区间不连续约束条件影响最小的快速非支配排序遗传算法(Non-Dominated Sorting Genetic Algorithm II, NSGAII)解决带有该类约束条件的多目标优化问题。针对NSGAII截断层拥挤距离计算只考虑同层解值域空间距离问题,改进拥挤距离计算方法,引入截断层与上一层的空间距离加速搜索过程逼近Pareto前沿。通过考虑快速性与经济性的火电厂厂级负荷优化分配仿真,说明不可行解修补方法与改进拥挤距离计算方法能有效处理决策空间不连续分布约束优化问题。
4.首先对带有决策变量定义区间不连续约束条件的双层规划问题进行算法适应性分析,说明基于极值理论与Karush-Kuhn-Tucker(KKT)条件的方法无法解决该类问题,而层次型遗传算法具有较好的适应性,另一方面说明既有的约束条件处理方法难以应用到该类问题中；其次,根据双层规划问题的交互式决策模式,改进-类层次型遗传算法,并通过数值算例仿真,说明其有效性。最后将改进型层次遗传算法应用于求解一类建模为双层规划的风电场—火电厂联合调度问题,并取得良好效果。
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.
主要研究内容如下：
1.对决策变量定义区间不连续约束条件进行特点分析,比较基于函数优化理论、运筹学理论的优化方法,以及智能优化方法对该类问题的适应性；选择遗传算法求解带有上述约束条件的优化问题。对遗传操作过程中,可能出现的三类不可行解进行特点与转化模式分析,设计解修补方法；通过与其他三类主要的不可行解处理方法仿真实验对比,说明该修补方法的有效性。
2.分析小生境技术与精英保留策略求解带有决策变量连续定义区间不连续约束条件单目标优化问题的适应性,说明精英保留策略适于解决该类问题。设计一类多精英保留策略,通过仿真实验说明该策略性能较好。并将之应用于解决考虑脱硫补偿电价与磨煤机接力区间的火电厂厂级负荷优化分配问题,取得良好效果。
3.对进化算法框架下的主流多目标优化算法进行适应性分析,选择决策变量定义区间不连续约束条件影响最小的快速非支配排序遗传算法(Non-Dominated Sorting Genetic Algorithm II, NSGAII)解决带有该类约束条件的多目标优化问题。针对NSGAII截断层拥挤距离计算只考虑同层解值域空间距离问题,改进拥挤距离计算方法,引入截断层与上一层的空间距离加速搜索过程逼近Pareto前沿。通过考虑快速性与经济性的火电厂厂级负荷优化分配仿真,说明不可行解修补方法与改进拥挤距离计算方法能有效处理决策空间不连续分布约束优化问题。
4.首先对带有决策变量定义区间不连续约束条件的双层规划问题进行算法适应性分析,说明基于极值理论与Karush-Kuhn-Tucker(KKT)条件的方法无法解决该类问题,而层次型遗传算法具有较好的适应性,另一方面说明既有的约束条件处理方法难以应用到该类问题中；其次,根据双层规划问题的交互式决策模式,改进-类层次型遗传算法,并通过数值算例仿真,说明其有效性。最后将改进型层次遗传算法应用于求解一类建模为双层规划的风电场—火电厂联合调度问题,并取得良好效果。
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.
引文
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