基于冗余选择策略差分进化的供水管网多目标优化

Multi-objective Optimization of Water Distribution System Based on Differential Evolution of Redundant Selection Strategy

针对进化算法在大规模供水管网优化设计过程中计算效率低的问题,提出一种基于冗余选择策略差分进化算法。该方法在选择阶段往每一代种群中重复添加冗余数个当代最优解向量形成父代种群,适当降低种群多样性引导种群向更好的方向进化、快速获取近似最优解。以管网造价为经济性目标函数、节点富余水头方差为可靠性目标函数,建立供水管网优化设计的多目标数学模型,并采用BIN基准管网加以验证。利用冗余选择策略差分进化算法进行计算时,冗余度为6%可在保证解精度的情况下提高62.768%的计算效率,冗余度为1%~6%时得到的经济性指标和冗余度为1%~3%时得到的可靠性指标均优于标准差分进化算法,并得到F最佳取值范围为0.1~0.3,CR取0.4最佳。基于冗余选择策略差分进化算法可提高计算效率,能快速有效地获得供水管网优化问题的近似最优解,表现出良好性能。

In order to solve the problem of low computational efficiency of evolutionary algorithms in optimization design of large-scale water distribution systems(WDSs),a redundant differential evolution algorithm(RDEA)based on redundant selection strategy was proposed.Several redundant vectors of contemporary optimal solution were repeatedly added to each generation population to form the parent generation population in the selection stage of this method,and the population diversity was appropriately reduced to guide the population to evolve in a better direction and obtain the approximate optimal solution quickly.By taking the cost of the pipe network as the economic objective function and the variance of node surplus head as the reliable objective function,a multi-objective model for optimal design of WDSs was established and verified by BIN benchmark network.When using RDEA to calculate,redundancy of 6%could increase the calculation efficiency by 62.768%while the accuracy of solutions was guaranteed.The obtained economic indexes when redundancies were 1%-6%and the obtained reliability indexes when redundancies were 1%-3%,were better than those calculated by standard DEA(SDEA),and the best range of F was 0.1-0.3 and CR was 0.4.RDEA could improve the computational efficiency,and near-optimal solutions of WDSs were obtained quickly and effectively,which showed good performance.