Expedients for solving some specially structured mixed-integer programs

In this paper we consider dual angular and angular structured mixed integer programs which arise in some practical applications. For these problems we describe efficient methods for generating a desirable set of Benders' cuts with which one may initialize the partitioning scheme of Benders. Our research is motivated by the computational experience of McDaniel and Devine who have shown that the set of Benders' cuts which are binding at the optimum to the linear relaxation of the mixed integer program, play an important role in determining an optimal mixed integer solution. As incidental results in our development, we provide some useful remarks regarding Benders' and Dantzig-Wolfe's decomposition procedures. The computational experience reported seems to support the expedients recommended in this paper.     

A genetic algorithm with neighborhood search for the resource‐constrained project scheduling problem

The resource‐constrained project scheduling problem (RCPSP) consists of a set of non‐preemptive activities that follow precedence relationship and consume resources. Under the limited amount of the resources, the objective of RCPSP is to find a schedule of the activities to minimize the project makespan. This article presents a new genetic algorithm (GA) by incorporating a local search strategy in GA operators. The local search strategy improves the efficiency of searching the solution space while keeping the randomness of the GA approach. Extensive numerical experiments show that the proposed GA with neighborhood search works well regarding solution quality and computational time compared with existing algorithms in the RCPSP literature, especially for the instances with a large number of activities. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Solution algorithms for the parallel replacement problem under economy of scale

We consider the parallel replacement problem in which machine investment costs exhibit economy of scale which is modeled through associating both fixed and variable costs with machine investment costs. Both finite- and infinite-horizon cases are investigated. Under the three assumptions made in the literature on the problem parameters, we show that the finite-horizon problem with time-varying parameters is equivalent to a shortest path problem and hence can be solved very efficiently, and give a very simple and fast algorithm for the infinite-horizon problem with time-invariant parameters. For the general finite-horizon problem without any assumption on the problem parameters, we formulate it as a zero-one integer program and propose an algorithm for solving it exactly based on Benders' decomposition. Computational results show that this solution algorithm is efficient, i.e., it is capable of solving large scale problems within a reasonable cpu time, and robust, i.e., the number of iterations needed to solve a problem does not increase quickly with the problem size. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 279–295, 1998     

A risk function for the stochastic modeling of electric capacity expansion

We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other applications. The goals of the model are deciding which energy types must be installed, and when. Another goal is providing an initial generation plan for short periods of the planning horizon that might be adequately modified in real time assuming penalties in the operation cost. Uncertainty is modeled under the assumption that the demand is a random vector. The cost of the risk associated with decisions that may need some tuning in the future is included in the objective function. The proposed scheme to solve the nonlinear stochastic optimization model is Generalized Benders' decomposition. We also exploit the Benders' subproblem structure to solve it efficiently. Computational results for moderate‐size problems are presented along with comparison to a general‐purpose nonlinear optimization package. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:662–683, 2001     

Exponential size neighborhoods for makespan minimization scheduling

We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst‐case approximation guarantees for the local optima of such neighborhoods. The so‐called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographic‐jump neighborhood decreases the approximation guarantee from 2 to 3/2. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Robust tower location for code division multiple access networks

Designing Code Division Multiple Access networks includes determining optimal locations of radio towers and assigning customer markets to the towers. In this paper, we describe a deterministic model for tower location and a stochastic model to optimize revenue given a set of constructed towers. We integrate these models in a stochastic integer programming problem with simple recourse that optimizes the location of towers under demand uncertainty. We develop algorithms using Benders' reformulation, and we provide computational results. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A nested benders decomposition approach for telecommunication network planning

Despite its ability to result in more effective network plans, the telecommunication network planning problem with signal‐to‐interference ratio constraints gained less attention than the power‐based one because of its complexity. In this article, we provide an exact solution method for this class of problems that combines combinatorial Benders decomposition, classical Benders decomposition, and valid cuts in a nested way. Combinatorial Benders decomposition is first applied, leading to a binary master problem and a mixed integer subproblem. The subproblem is then decomposed using classical Benders decomposition. The algorithm is enhanced using valid cuts that are generated at the classical Benders subproblem and are added to the combinatorial Benders master problem. The valid cuts proved efficient in reducing the number of times the combinatorial Benders master problem is solved and in reducing the overall computational time. More than 120 instances of the W‐CDMA network planning problem ranging from 20 demand points and 10 base stations to 140 demand points and 30 base stations are solved to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

The quay crane scheduling problem with time windows

The quay crane scheduling problem consists of scheduling tasks for loading and unloading containers on cranes that are assigned to a vessel for its service. This article introduces a new approach for quay crane scheduling, where the availability of cranes at a vessel is restricted to certain time windows. The problem is of practical relevance, because container terminal operators frequently redeploy cranes among vessels to speed up the service of high‐priority vessels while serving low‐priority vessels casually. This article provides a mathematical formulation of the problem and a tree‐search‐based heuristic solution method. A computational investigation on a large set of test instances is used to evaluate the performance of the heuristic and to identify the impact of differently structured crane time windows on the achievable vessel handling time. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

任务分配问题的对称群方法

探讨了无人飞行器(UAV)编队的任务分配问题。任务分配是UAV协同控制的基础,其解是任务区域内各任务的一个排列。求解UAV任务分配问题的有效方法是能在合理的计算时间内找到近似最优解的启发式算法。用对称群描述UAV任务分配的搜索空间,基于右乘运算构造搜索邻域。仿真结果验证了群论禁忌搜索算法的有效性。     

Concave minimization over a convex polyhedron

A general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed-charge problem, the separable concave programming problem, the quadratic problem, and the 0-1 mixed integer problem are discussed. Computer results for the fixed-charge problem are also presented.     

A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production

This article considers the order batching problem in steelmaking and continuous‐casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment constraints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large‐scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression

The importance of subset selection in multiple regression has been recognized for more than 40 years and, not surprisingly, a variety of exact and heuristic procedures have been proposed for choosing subsets of variables. In the case of polynomial regression, the subset selection problem is complicated by two issues: (1) the substantial growth in the number of candidate predictors, and (2) the desire to obtain hierarchically well‐formulated subsets that facilitate proper interpretation of the regression parameter estimates. The first of these issues creates the need for heuristic methods that can provide solutions in reasonable computation time; whereas the second requires innovative neighborhood search approaches that accommodate the hierarchical constraints. We developed tabu search and variable neighborhood search heuristics for subset selection in polynomial regression. These heuristics are applied to a classic data set from the literature and, subsequently, evaluated in a simulation study using synthetic data sets. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Search techniques for a nonlinear multiprocessor scheduling problem

The problem of assigning computer program modules to functionally similar processors in a distributed computer network is investigated. The modules of a program must be assigned among processors in such a way as to minimize interprocessor communication while taking advantage of affinities of certain modules to particular processors. This problem is formulated as a zero-one quadratic programming problem, but is more conveniently modeled as a directed acyclic search graph. The model is developed and a backward shortest path labeling algorithm is given that produces an assignment of program modules to processors. A non-backtracking branch-and-bound algorithm is described that uses a local neighborhood search at each stage of the search graph.     

考虑随机回放的卫星数传调度问题的一种求解方法

针对考虑随机回放的卫星数传调度问题,从置换空间到调度解空间的映射方法和置换空间的搜索算法两方面进行了研究.提出了一种时间窗优先的置换序列映射算法,并证明该映射算法可以将置换序列映射到调度解空间上的最优解.提出了一种遗传随机搜索算法,基于有记忆功能的随机邻域搜索,在置换空间上搜索产生优化调度的置换序列.仿真计算表明,遗传随机搜索算法可以增强遗传算法的局部搜索能力,在搜索结果上平均获得了2.72%的改进.     

On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles

Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn‐rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large‐scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insight—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Technical note: A computationally efficient algorithm for undiscounted Markov decision processes with restricted observations

We present a computationally efficient procedure to determine control policies for an infinite horizon Markov Decision process with restricted observations. The optimal policy for the system with restricted observations is a function of the observation process and not the unobservable states of the system. Thus, the policy is stationary with respect to the partitioned state space. The algorithm we propose addresses the undiscounted average cost case. The algorithm combines a local search with a modified version of Howard's (Dynamic programming and Markov processes, MIT Press, Cambridge, MA, 1960) policy iteration method. We demonstrate empirically that the algorithm finds the optimal deterministic policy for over 96% of the problem instances generated. For large scale problem instances, we demonstrate that the average cost associated with the local optimal policy is lower than the average cost associated with an integer rounded policy produced by the algorithm of Serin and Kulkarni Math Methods Oper Res 61 (2005) 311–328. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

运动场馆火灾烟气蔓延规律数值模拟研究

运动场馆规模大、人员密集、功能复杂、用电负荷大、配电线路多、火灾荷载大,一旦发生火灾可能导致群死群伤恶性事故的发生。研究运动场馆火灾情况下烟气变化规律,能够更好的指导消防安全设计。以某运动场馆为例,应用火灾模拟软件对其火灾情况下烟气蔓延过程进行数值模拟研究,分析了常见自然排烟方式对烟气层的高度、温度、氧气浓度、一氧化碳浓度变化的影响,从而为运动场馆防排烟设计提供依据。     

The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Variations on a cutting plane method for solving concave minimization problems with linear constraints

A cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts. This paper relates the question of finiteness of Tui's method to the so-called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method. The paper then presents several branch-and-bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed-charge transportation problem.     

Detection of a Markovian target with optimization of the search efforts under generalized linear constraints

This paper deals with search for a target following a Markovian movement or a conditionally deterministic motion. The problem is to allocate the search efforts, when search resources renew with generalized linear constraints. The model obtained is extended to resource mixing management. New optimality equations of de Guenin's style are obtained. Practically, the problem is solved by using an algorithm derived from the FAB method. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 117–142, 2002; DOI 10.1002/nav.10009