从行为运筹学角度,面向服务性目标,采用深度集成的方法对泊位和岸桥联合调度问题建立了混合整数非线性规划模型。为克服计算困难和最优性缺失等问题,将模型转化为混合整数二阶锥规划模型,并利用优化软件CPLEX对其求解。针对CPLEX中分支切割算法在某些实例上存在内存溢出、求解时间长等问题,采用外逼近算法对混合整数非线性规划模型进行求解:根据问题特点将模型分解为混合整数线性规划主问题和非线性规划子问题,其中,子问题可用解析方法求得最优解,同时利用一阶Taylor展开导出了非线性约束的外逼近。最后,基于数值实验比较了分支切割算法和外逼近算法的求解性能,验证了外逼近算法的收敛性,对模型中的关键参数进行了灵敏度分析。
In terms of the basic ideas of behavioral operation research,a service-oriented Mixed-Integer Nonlinear Programming(MINLP) model by using a deep integration method was formulated to deal with the berth allocation and quay crane assignment problem.To overcome the problems of computational intractability and optimality absence,the model was transformed into a Mixed-Integer Second Order Cone Programming(MISOCP) model,and the optimization software CPLEX was used to solve the model.Since the branch and cut algorithm was time-consuming and ran out of memory for some instances,MINLP model was solved by outer approximation algorithm.Based on the characteristics of the problem,the model was decomposed into a mixed-integer linear programming master problem and a nonlinear programming sub-problem.The optimal solution to the sub-problem was obtained by analytical method,and the outer approximation of nonlinear constraints was derived by using the first-order Taylor series expansion.Finally,solution performance of the branch and cut algorithm and the outer approximation algorithm was compared by numerical experiments.Moreover,convergence of the outer approximation algorithm was verified.The sensitivity analysis of key parameters in the model was also conducted.