线性约束非线性函数全局优化算法的研究

Global optimal algorithm for nonlinear programming problems subjected to linear constraints

提出了一种适于处理线性约束条件下非线性规划问题的λ编码稳态遗传算法(λSSGA).首先对线性可行域进行凸分析后将原优化问题I转化为一个仅包含可行域极点信息的等价问题II.问题II具有小边界的约束条件,通过采用特定的凸交叉算子、交换变异算子和倒位算子可以保证算法在遗传操作的过程中不会产生无效的编码,而且能在概率意义上保证λ编码模式在整个可行解空间上充分可达.其次从理论上推导出了得到线性可行区域全部极点的方法,证明了问题I和问题II的等价性.仿真结果表明λSSGA算法在具有较快的收敛速度和精度的同时,还可以有效地维持群体的多样性,得到问题全局的最优解.

A global optimal algorithm (the λ steady state genetic algorithm,λSSGA) is presented to solve nonlinear programming problems,which are subjected to linear constraints.By convex analyzing,the primal optimal problem I can be converted to an equivalent problem II,in which only the convex extremes of feasible space are included.The problem II has simpler constraints than problem I.In the evolving of the λSSGA algorithm,the invalid genetic operating can be avoided by using convex crossover operator,swap mutate operator and inverse operation.It can also explore the entire feasible space in the sense of probability.A method is derived to get all extremes (BFS) of linear constraints,and the equivalence of problem I and problem II is also proven.Finally,the simulation analysis shows that the algorithm not only has fast convergence speed and high precision of solution,but also can maintain the diversity of the population and reach a global optimum of non-concave objective function.