求解MINLP的几类罚函数方法的分析和探讨

针对混合整数非线性约束优化问题(MINLP)的一般形式,通过罚函数的方法,给出了它的几种等价形式,并证明了最优解的等价性.将约束优化问题转化成更容易求解的无约束非线性优化问题,并把混合整数规划转化成非整数优化问题,从而将MINLP的求解简化为求解一个连续的无约束非线性优化问题,进而可用已有的一般无约束优化算法进行求解.

Analysis and Discussion on Several Penalty Methods For MINLP

Based on the general Mixed-integer Nonlinear Programming(MINLP) model,we propose several equivalent forms of such class of problems in virtue of penalty methods,the solutions of which are then proved to be equivalent from the theoretical point of view.In this paper,constrained optimization problems are converted into unconstrained ones,which are portable to resolve.In addition,mixed-integer problems are transformed into noninteger continuous ones,thus the MINLP model is simplified into solving an unconstrained continuous nonlinear optimization problems,the solution of which is solvable enough within the reach of existing nonlinear optimization algorithms.