非线性0-1规划问题的连续化及其遗传算法解法  

A Continuous Approach to 0-I Nonlinear Problem and Its Solution With Genetic Algorithm

作　　者：隋允康[1] 贾志超[1] 杜家政[1] 

机构地区：[1]北京工业大学机械工程与应用电子技术学院,北京100022

出　　处：《北京工业大学学报》2008年第8期785-791,共7页Journal of Beijing University of Technology

基　　金：国家自然科学基金(10472003);高校博士点基金(2006005010).

摘　　要：为了求解非线性0-1离散规划问题,通过非线性等式的"离散性约束"将其转化为[0,1]区间上等价的连续变量非线性规划.对于目标函数非线性、约束线性的0-1规划问题,可以使用乘子法来解决含"离散性约束"的非线性优化问题.对于目标函数和约束函数均为非线性的问题,可以采用约束松驰法将离散性约束松弛为不等式约束.两种方法处理后均使用遗传算法程序GENOCOP求解.乘子法求解得到的结果比较准确,约束松弛法属于近似方法,可以求解带非线性不等式约束的问题.用本文的方法对多个非线性0-1规划同题的算例进行了计算,并将计算结果同枚举法的计算结果比较,结果表明该方法准确、有效.To solve the nonlinear 0-1 programming problem, it is transformed into an equivalent continuous nonlinear programming on the domain of [0, 1 ] by a nonlinear equality discrete constraint. For the 0-1 programming problem with nonlinear object and lineav constraint, the problem with disorete constraint canbe solved with nultiplier method. For the problem with conhinean object and nonlinear constraint, the discrete constraint can be relaxed to a non-equality constraint with the constraint relexing method. Both are solved by the Genetic Algorithm GENOCOP. The result of multiplier method is more accurate. Constraint relaxing method is an approximate method, can be used to solve the 0-1 programming problem with nonlinear constraint. Examples are presented and compared with enumerating method, and the results show that the approach is accurate and effective.

关 键 词：非线性0-1规划 连续化方法 遗传算法 GENOCOP 

分 类 号：O343[理学—固体力学]