一种具有非线性约束线性规划全局优化算法

本文提出了一种新的适用于处理非线性约束下线性规划问题的全局优化算法。该算法通过构造子问题来寻找优于当前局部最优解的可行解。该子问题可通过模拟退火算法来解决。通过求解一系列的子问题,当前最优解被不断地更新,最终求得全局最优解。最后,本算法应用于几个典型例题,并与罚函数法相比较,数值结果表明该算法是可行的,有效的。     

带性能约束的矩形图元布局优化模型及不干涉性算法

本文讨论了以航天卫星仪器舱布局优化设计为背景的、带性能约束的矩形图元布局优化模型及不干涉性判别算法,主要讨论了模型的性质,并将这一模型转化为带反凸约束的凸规划问题。应用文献(4)给出的最优性条件及定界锥分拆算法,可求得带性能约束的矩形图元布局优化问题的全局最优解。     

不可分离凸背包问题的拉格朗日分解和区域分割方法

本文对线性约束不可分离凸背包问题给出了一种精确算法．该算法是拉格朗日分解和区域分割结合起来的一种分枝定界算法．利用拉格朗日分解方法可以得到每个子问题的一个可行解，一个不可行解，一个下界和一个上界．区域分割可以把一个整数箱子分割成几个互不相交的整数子箱子的并集，每个整数子箱子对应一个子问题．通过区域分割可以逐步减小对偶间隙并最终经过有限步迭代找到原问题的最优解．数值结果表明该算法对不可分离凸背包问题是有效的．     

求解无线传感器网络路由问题的蚁群最优化算法及其收敛性

首先将无线传感器网络的路由问题转化成求解最小Steiner树问题,然后给出了求解无线传感器网络路由的蚁群优化算法,并对算法的收敛性进行了证明．最后对找到最优解后信息素值的变化进行了分析．即在限制信息素取值的条件下,当迭代次数充分大时,该算法能以任意接近于1的概率找到最优解,并且当最优解找到后,最优树边上的信息素单调增加,而最优解以外边上的信息素在有限步达到最小值．     

具有性能约束的三维布局优化模型的主要性质

本文研究了简化的旋转卫星舱内的三维布局优化问题,建立了一个具有性能约束的三维布局优化模型,给出了其主要性质,并证明了性能目标函数为局部Lipschitz连续函数,且其局部最优解即为全局最优解.     

基于粒子群算法的非线性二层规划问题的求解算法

粒子群算法（Particle Swarm Optimization，PSO）是一种新兴的优化技术，其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现，可调参数少，已得到了广泛研究和应用。本文根据该算法能够有效的求出非凸数学规划全局最优解的特点，对非线性二层规划的上下层问题求解，并根据二层规划的特点，给出了求解非线性二层规划问题全局最优解的有效算法。数值计算结果表明该算法有效。     

基于量子粒子群算法的电力系统负荷多目标优化分配

针对电力系统经济负荷优化分配问题,提出了一种基于量子粒子群的多目标优化算法.该算法通过将改进后的量子进化算法融合到粒子群中,采用量子位对粒子的当前位置进行编码,用量子旋转门实现对粒子最优位置的搜索,用量子非门实现粒子位置的变异以避免早熟收敛.这种搜索机制能够遍历解空间,增强种群的多样性,并能用量子位的概率幅将最优解表述为解空间中的多种表述形式,从而增强全局最优的可能性.最后,通过算例进行仿真分析,结果表明算法的搜索能力和优化效率均优于普通粒子群算法.     

制造单元布局问题的双目标模型与算法研究

单元制造系统的布局对于提高系统的效率起着十分重要的作用。以最小化物料周转量和设施面积为目标,建立了一个单元制造系统布局的双目标优化模型,在该模型中不同制造单元的布局、单元内部不同设施的位置与方向这几个问题可以同时进行优化。基于模拟退火邻域解的变尺度生成机制和双目标抽样准则设计了模型的求解算法。算例表明本文算法所得Pareto解集优于经典的NSGA-Ⅱ算法。     

多周期公用工程系统运行的模型,优化方法与应用

针对多周期公用工程系统的运行优化问题，考虑了设备的启停费用的情况下。建立了混合整数非线性规划模型并证明了最优解的存在性。针对该运行优化问题本将其分解成若干子问题，然后利用改进的Hooke-Jeeves优化算法求解每个子问题。应用于具体实例，其数值结果与其它方法得到的相比。运行时间短，且更适合多周期公用工程问题的求解。     

并列选择单亲遗传算法在自动化立体仓库货位优化中的应用

针对传统遗传算法在求解自动化立体仓库货位优化多目标模型中容易陷于局部最优解以及交叉变异过程中产生大量不可行解等问题,提出了并列选择单亲遗传算法.算法采用了0,1矩阵编码、并列选择算子、单亲变异算子等,有效避免了交叉变异操作产生不可行解的问题.通过对控制参数进行较合理地选取,算法能够综合考虑各子目标的相对优秀个体,从中选取出全局近似最优解,有效降低了算法陷于局部最优解的概率.利用该算法对36种货物的自动化立体仓库货位进行优化,通过比较优化前后的货位对应的拣选时间及货架重心可以看出,优化后的货位对应的拣选效率及货架稳定性均有明显提高.     

The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function

This paper studies the two-dimensional layout optimization problem.An optimization model withperformance constraints is presented.The layout problem is partitioned into finite subproblems in terms ofgraph theory,in such a way of that each subproblem overcomes its on-off nature optimal variable.A minimaxproblem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we presentthe optimality function for every subproblem and prove that the first order necessary optimality condition issatisfied at a point if and only if this point is a zero of optimality function.     

卫星舱布局的半无限优化模型及最优性条件

本文以人造卫星仪器舱布局问题为背景，建立了一个半无限优化模型。应用图论、群对集合的作用、轨道等，把该问题分解为有限多个子问题，在每个子问题中克服了关于优化变量的时断时续性质。针对每个子问题分析了模型中各函数的性质，并构造了一个局部等价于子问题的极大极小问题。利用这个极大极小问题及子问题中各函数的方向可微性给出了子问题的一阶最优性条件。     

The layout problem of two kinds of graph elements with performance constraints and its optimality conditions

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn’t change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.     

Scaled Optimal Path Trust-Region Algorithm

Trust-region algorithms solve a trust-region subproblem at each iteration. Among the methods solving the subproblem, the optimal path algorithm obtains the solution to the subproblem in full-dimensional space by using the eigenvalues and eigenvectors of the system. Although the idea is attractive, the existing optimal path method seems impractical because, in addition to factorization, it requires either the calculation of the full eigensystem of a matrix or repeated factorizations of matrices at each iteration. In this paper, we propose a scaled optimal path trust-region algorithm. The algorithm finds a solution of the subproblem in full-dimensional space by just one Bunch–Parlett factorization for symmetric matrices at each iteration and by using the resulting unit lower triangular factor to scale the variables in the problem. A scaled optimal path can then be formed easily. The algorithm has good convergence properties under commonly used conditions. Computational results for small-scale and large-scale optimization problems are presented which show that the algorithm is robust and effective.     

圆形区域分散布局问题研究

针对圆形区域分散布局问题, 文中给出了一个带约束的非线性规划模型. 当布局点数量较少时, 通过将模型转化为无约束优化问题, 利用梯度方法进行求解; 对于布局点数量较多的情况, 提出了一个界为1/2的多项式时间的近似算法, 并进行了相应的算例分析, 进一步来验证算法解的合理性. 研究的结论及方法一定程度上丰富和完善了圆形区域的分散布局理论.     

A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints

We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (Journal of the Operational Research Society 61(9):1404–1419, 2010) and uses Benders decomposition to form a master problem and a subproblem. The new dynamic partition scheme that we present ensures that the algorithm converges to the global optimum. Partitioning is done to overcome the non-convexity of the Benders subproblem. In addition Lagrangean relaxation provides bounds that enable fathoming in the branching tree and warm-starting the Benders algorithm. Numerical tests show significantly reduced solution times compared to the original algorithm. When the lower level problem is stochastic our algorithm can easily be further decomposed using scenario decomposition. This is demonstrated on a realistic case.     

On the Optimal Correction of Infeasible Systems of Linear Inequalities

We study the optimum correction of infeasible systems of linear inequalities through making minimal changes in the coefficient matrix and the right-hand side vector by using the Frobenius norm. It leads to a special structured unconstrained nonlinear and nonconvex problem, which can be reformulated as a one-dimensional parametric minimization problem such that each objective function corresponds to a trust region subproblem. We show that, under some assumptions, the parametric function is differentiable and strictly unimodal. We present optimally conditions, propose lower and upper bounds on the optimal value and discuss attainability of the optimal value. To solve the original problem, we propose a binary search method accompanied by a type of Newton–Lagrange method for solving the subproblem. The numerical results illustrate the effectiveness of the suggested method.

     

David G. Luenberger,Linear and nonlinear programming, 2nd edition,Addison-Wesley,Reading (1984), xv + 492 pages, $35.50

This paper considers a stochastic version of the linear continuous type knapsack problem in which the cost coefficients are random variables. The problem is to find an optimal solution and an optimal probability level of the chance constraint. This problem P₀ is first transformed into a deterministic equivalent problem P. Then a subproblem with a positive parameter is introduced and a close relation between P and its subproblem is shown. Further, an auxiliary problem of the subproblem is introduced and a direct relation between P and the auxiliary problem is derived through a relation connecting the subproblem and its auxiliary problem. Fully utilizing these relations, an efficient algorithm is proposed that finds an optimal solution of P in at most O(n⁴) computational time where n is the number of decision variables. Finally, further research problems are discussed.     

Contour line construction for a new rectangular facility in an existing layout with rectangular departments

In a recent paper, Savas et al. [S. Savas, R. Batta, R. Nagi, Finite-size facility placement in the presence of barriers to rectilinear travel, Operations Research 50 (6) (2002) 1018–1031] consider the optimal placement of a finite-sized facility in the presence of arbitrarily shaped barriers under rectilinear travel. Their model applies to a layout context, since barriers can be thought to be existing departments and the finite-sized facility can be viewed as the new department to be placed. In a layout situation, the existing and new departments are typically rectangular in shape. This is a special case of the Savas et al. paper. However the resultant optimal placement may be infeasible due to practical constraints like aisle locations, electrical connections, etc. Hence there is a need for the development of contour lines, i.e. lines of equal objective function value. With these contour lines constructed, one can place the new facility in the best manner. This paper deals with the problem of constructing contour lines in this context. This contribution can also be viewed as the finite-size extension of the contour line result of Francis [R.L. Francis, Note on the optimum location of new machines in existing plant layouts, Journal of Industrial Engineering 14 (2) (1963) 57–59].