具有线性约束的分片线性函数的最优化方法

分片线性模型有着广泛应用范围 ,对分片线性模型及其最优化问题的研究具有普遍的意义。该文以规范型分片线性函数为例 ,提出了基于分片的邻区域搜索算法 ,通过定义相邻区域 ,应用线性规划寻找最优解。通过该算法和遗传算法相结合 ,可利用进化算法的探索能力和模型信息以实现全局优化。在仿真实验中 ,采用随机生成的分片线性函数对这种算法和传统遗传算法进行了对比 ,结果表明 ,它具有很好的搜索性能 ,当搜索空间很大或具有边界约束时 ,它较传统遗传算法更优越

Global optimization of piecewise linear (PWL) function with a linear constraint

This paper analyzes the global optimization of a Piecewise Linear (PWL) function, subject to a linear constraint. The optimization on any linear sub area can be formulated as a linear programming problem, so a piecewise based search method is designed for local optimization which defines neighboring areas and employs linear programming to find minimums in the sub areas, and then determines the next area. The optimization is combined with Genetic Algorithm to form a hybrid algorithm. Simulation results using the hybrid algorithm for solving random problems show that the hybrid algorithm has quite excellent performance, especially for high dimension problems and those with linear boundaries.