A sequential LCP method for bilevel linear programming

In this paper, we discuss an SLCP algorithm for the solution of Bilevel Linear Programs (BLP) which consists of solving a sequence of Linear Complementarity Problems (LCP) by using a hybrid enumerative method. This latter algorithm incorporates a number of procedures that reduce substantially the search for a solution of the LCP or for showing that the LCP has no solution. Computational experience with the SLCP algorithm shows that it performs quite well for the solution of small- and medium-scale BLPs with sparse structure. Furthermore, the algorithm is shown to be more efficient than a branch-and-bound method for solving the same problems.     

A modified method for constructing efficient solutions structure of MOLP

This paper deals with a recently proposed algorithm for obtaining all weak efficient and efficient solutions in a multi objective linear programming (MOLP) problem. The algorithm is based on solving some weighted sum problems, and presents an easy and clear solution structure. We first present an example to show that the algorithm may fail when at least one of these weighted sum problems has not a finite optimal solution. Then, the algorithm is modified to overcome this problem. The modified algorithm determines whether an efficient solution exists for a given MOLP and generates the solution set correctly (if exists) without any change in the complexity.     

Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities

This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made.     

A Meta-heuristic with Orthogonal Experiment for the Set Covering Problem

This paper reports an evolutionary meta-heuristic incorporating fuzzy evaluation for some large-scale set covering problems originating from the public transport industry. First, five factors characterized by fuzzy membership functions are aggregated to evaluate the structure and generally the goodness of a column. This evaluation function is incorporated into a refined greedy algorithm to make column selection in the process of constructing a solution. Secondly, a self-evolving algorithm is designed to guide the constructing heuristic to build an initial solution and then improve it. In each generation an unfit portion of the working solution is removed. Broken solutions are repaired by the constructing heuristic until stopping conditions are reached. Orthogonal experimental design is used to set the system parameters efficiently, by making a small number of trials. Computational results are presented and compared with a mathematical programming method and a GA-based heuristic.     

论理想流体与线弹性结构的耦联振动

本文对理想流体与线弹性结构的耦联振动问题作理论分析和数值分析.文中证明了耦联振动的固有频率存在并且均为正实数.将流-固耦合系统分析转化为单一结构物在真空中的自由振动分析后,频率方程中不再含有流体变元.使问题得以大大简化.给出了数值解的收敛性证明,以保证解的可靠性.文中还综合里兹法、边界元和有限元方法,提出一种分析转化后结构的混合算法.利用该算法,只需对现有结构分析程序稍作改进,就可分析那些理想流场与结构的耦合问题.一些数例说明了算法的有效性.     

Constructing efficient solutions structure of multiobjective linear programming

It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure.     

Application of the alternating direction method of multipliers to separable convex programming problems

This paper presents a decomposition algorithm for solving convex programming problems with separable structure. The algorithm is obtained through application of the alternating direction method of multipliers to the dual of the convex programming problem to be solved. In particular, the algorithm reduces to the ordinary method of multipliers when the problem is regarded as nonseparable. Under the assumption that both primal and dual problems have at least one solution and the solution set of the primal problem is bounded, global convergence of the algorithm is established.     

Analysis of mathematical programming problems prior to applying the simplex algorithm

Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them efficiently. The steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and discussed. An algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.     

冲裁件有约束最优剪切方式的设计

本文讨论冲裁件有约束最优剪切方式的设计问题 .阐明最优剪切排样方式的规范结构 ;采用分支定界法求解冲裁件无约束排样问题 ;将有约束排样问题转换为求解一系列的无约束排样问题 ,并通过对解的性质分析提高算法效率 .实验计算结果说明本文算法十分有效 .最后给出一例题的最优排样方式 .     

Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search

In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010) and Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)     

Global search algorithms for minimum concave-cost network flow problems

We present algorithms for the single-source uncapacitated version of the minimum concave cost network flow problem. Each algorithm exploits the fact that an extreme feasible solution corresponds to a sub-tree of the original network. A global search heuristic based on random extreme feasible initial solutions and local search is developed. The algorithm is used to evaluate the complexity of the randomly generated test problems. An exact global search algorithm is developed, based on enumerative search of rooted subtrees. This exact technique is extended to bound the search based on cost properties and linear underestimation. The technique is accelerated by exploiting the network structure.     

Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty

This paper presents a three-stage optimization algorithm for solving two-stage deviation robust decision making problems under uncertainty. The structure of the first-stage problem is a mixed integer linear program and the structure of the second-stage problem is a linear program. Each uncertain model parameter can independently take its value from a real compact interval with unknown probability distribution. The algorithm coordinates three mathematical programming formulations to iteratively solve the overall problem. This paper provides the application of the algorithm on the robust facility location problem and a counterexample illustrating the insufficiency of the solution obtained by considering only a finite number of scenarios generated by the endpoints of all intervals. This work was supported by the National Science Foundation through Grant DMI-0200162.     

Super-fast validated solution of linear systems

Validated solution of a problem means to compute error bounds for a solution in finite precision. This includes the proof of existence of a solution. The computed error bounds are to be correct including all possible effects of rounding errors. The fastest known validation algorithm for the solution of a system of linear equations requires twice the computing time of a standard (purely) numerical algorithm. In this paper we present a super-fast validation algorithm for linear systems with symmetric positive definite matrix. This means that the entire computing time for the validation algorithm including computation of an approximated solution is the same as for a standard numerical algorithm. Numerical results are presented.     

On an open problem in spherical facility location

In this paper we partially resolve an open problem in spherical facility location. The spherical facility location problem is a generalization of the planar Euclidean facility location problem. This problem was first studied by Katz and Cooper and by Drezner and Wesolowsky where a Weszfeld-like algorithm was proposed. This algorithm is very simple and does not require a line search. However, its convergence has been an open problem for more than ten years. In this paper, we prove that the sequence generated by the algorithm converges to the unique optimal solution under the condition that the oscillation of the sequence converges to zero. We conjecture that the algorithm is a descent algorithm and prove that the sequence generated by the algorithm converges to the optimal solution under this conjecture.     

Integrated scheduling of crane handling and truck transportation in a maritime container terminal

This paper studies the interactions between crane handling and truck transportation in a maritime container terminal by addressing them simultaneously. Yard trucks are shared among different ships, which helps to reduce empty truck trips in the terminal area. The problem is formulated as a constraint programming model and a three-stage algorithm is developed. At the first stage, crane schedules are generated by a heuristic method. At the second stage, the multiple-truck routing problem is solved based on the precedence relations of the transportation tasks derived from the first stage. At the last stage a complete solution is constructed by using a disjunctive graph. The three procedures are linked by an iterative structure, which facilitates the search for a good solution. The computational results indicate that the three-stage algorithm is effective for finding high-quality solutions and can efficiently solve large problems.     

An exact feature selection algorithm based on rough set theory

Feature reduction based on rough set theory is an effective feature selection method in pattern recognition applications. Finding a minimal subset of the original features is inherent in rough set approach to feature selection. As feature reduction is a Nondeterministic Polynomial‐time‐hard problem, it is necessary to develop fast optimal or near‐optimal feature selection algorithms. This article aims to propose an exact feature selection algorithm in rough set that is efficient in terms of computation time. The proposed algorithm begins the examination of a solution tree by a breadth‐first strategy. The pruned nodes are held in a version of the trie data structure. Based on the monotonic property of dependency degree, all subsets of the pruned nodes cannot be optimal solutions. Thus, by detecting these subsets in trie, it is not necessary to calculate their dependency degree. The search on the tree continues until the optimal solution is found. This algorithm is improved by selecting an initial search level determined by the hill‐climbing method instead of searching the tree from the level below the root. The length of the minimal reduct and the size of data set can influence which starting search level is more efficient. The experimental results using some of the standard UCI data sets, demonstrate that the proposed algorithm is effective and efficient for data sets with more than 30 features. © 2014 Wiley Periodicals, Inc. Complexity 20: 50–62, 2015     

Solving the 2D Maxwell equations by a Laguerre spectral method

A spectral method for solving the 2D Maxwell equations with relaxation of electromagnetic parameters is presented. The method is based on an expansion of the solution in terms of Laguerre functions in time. The operation of convolution of functions, which is part of the formulas describing the relaxation processes, is reduced to a sum of products of the harmonics. The Maxwell equations transform to a system of linear algebraic equations for the solution harmonics. In the algorithm, an inner parameter of the Laguerre transformis used. With large values of this parameter, the solution is shifted to high harmonics. This is done to simplify the numerical algorithm and to increase the efficiency of the problem solution. Results of a comparison of the Laguerre method and a finite-difference method in accuracy both for a 2D medium structure and a layered medium are given. Results of a comparison of the spectral and finite-difference methods in efficiency for axial and plane geometries of the problem are presented.     

Generalized dynamic programming methods in integer programming

When regarded as a shortest route problem, an integer program can be seen to have a particularly simple structure. This allows the development of an algorithm for finding thek ^th best solution to an integer programming problem with max{O(kmn), O(k logk)} operations. Apart from its value in the parametric study of an optimal solution, the approach leads to a general integer programming algorithm consisting of (1) problem relaxation, (2) solution of the relaxed problem parametrically by dynamic programming, and (3) generation ofk ^th best solutions until a feasible solution is found. Elementary methods based on duality for reducingk for a given problem relaxation are then outlined, and some examples and computational aspects are discussed.     

Local search and suffix tree for car-sequencing problem with colors

This paper describes an approximation solution method for the car sequencing problem with colors. Firstly, we study the optimality of problems with a single ratio constraint. This study also introduces a data structure for efficient calculation of the penalties related to ratio constraints. We describe the constructive greedy algorithm and variable neighborhood search adjusted for the problem with colors. Tabu metaheuristic is used to improve the results obtained by VNS. We then represent the cars with their constraints as letters over an alphabet and apply the algorithm to spell the motifs in order to improve the number of batch colors without decreasing the costs associated to the set of ratio constraints. The algorithm achieves 19 out of the 64 best results for instance sets A and B. These instances are the reference instances for Challenge ROADEF.     

移动传感器网络中的最大价值路径扫描覆盖算法

扫描覆盖是当前移动传感器网络的一个重要覆盖技术,其主要通过规划移动传感器的巡逻路径对事件兴趣点（Points of Interest,POI）进行定期监测,从而以相对于普通覆盖方案更低廉的成本实现对POI监控．研究最大价值路径扫描覆盖,即使用移动传感器扫描覆盖分布在一条路径上的POI集合,使得被覆盖POI的价值总和达到最大．首先设计了一个基于线性规划随机取整的近似算法,通过将问题松弛并刻画为一个线性规划,然后对线性规划最优解取整得到一个扫描覆盖方案．该算法可在O（mn^3.5L）时间内求解,并具有可证明的近似比1-1/e．其次,通过扩展基于贪心策略的集合覆盖算法,设计了一个时间复杂度为O（m²n²）的贪心算法,其主要思想为循环选取一个单位巡逻范围覆盖POI价值最大的传感器．为优化运行时间,基于MVSCP问题的特殊结构将算法时间进一步改进至O（m log m+mn²）．最后,通过仿真实验分析所设计算法的实际性能.实验结果表明,线性规划随机取整算法运行时间低至整数规划算法的百分之一,但其所求解的质量只略低于整数规划算法;改进的贪心算法虽然不具有可证明的近似比,但其实际所求解的质量并不弱于线性规划随机取整算法,并且具有三者中最佳的运行时间．