Efficient incrementing heuristics for generalized p-location problems

Central European Journal of Operations Research - This paper studies effective solving techniques for large p-location problems, in which generalized disutility is applied to incorporate stochastic...     

Efficient and effective heuristics for the coordinated capacitated lot-size problem

Coordinating procurement decisions for a family of products that share a constrained resource, such as an ocean shipping container, is an important managerial problem. However due to the problem’s difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. This paper proposes two heuristics, for the capacitated, coordinated dynamic demand lot-size problem with deterministic but time-varying demand. In addition to inventory holding costs, the problem assumes a joint setup cost each time any member of the product family is replenished and an individual item setup cost for each item type replenished. The objective is to meet all customer demand without backorders at minimum total cost. We propose a six-phase heuristic (SPH) and a simulated annealing meta-heuristic (SAM). The SPH begins by assuming that each customer demand is met by a unique replenishment and then it seeks to iteratively maximize the net savings associated with order consolidation. Using SPH to find a starting solution, the SAM orchestrates escaping local solutions and exploring other areas of the solution state space that are randomly generated in an annealing search process. The results of extensive computational experiments document the effectiveness and efficiency of the heuristics. Over a wide range of problem parameter values, the SPH and SAM find solutions with an average optimality gap of 1.53% and 0.47% in an average time of 0.023 CPU seconds and 0.32 CPU seconds, respectively. The heuristics are strong candidates for application as stand alone solvers or as an upper bounding procedure within an optimization based algorithm. The procedures are currently being tested as a solver in the procurement software suite of a nationally recognized procurement software provider.     

Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem

In this paper, we consider the capacitated multi-facility Weber problem with rectilinear distance. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the rectilinear distance separating them. We first give a new mixed integer linear programming formulation of the problem by making use of a well-known necessary condition for the optimal facility locations. We then propose new heuristic solution methods based on this formulation. Computational results on benchmark instances indicate that the new methods can provide very good solutions within a reasonable amount of computation time.     

Efficient implementation of heuristics for the continuous network design problem

In this paper, we present an efficient implementation of heuristic procedures for solving the continuous network design problem where network users behave according to Wardrop's first principle of traffic equilibrium. Numerical results involving a standard benchmark problem are given. Also, it is shown that the cost mapping arising in the Iterative-Optimization-Assignment algorithm is integrable if and only if the volume-delay function is of either the BPR or some logarithmic form.Research supported by the National Sciences and Engineering Research Council of Canada (Grant A5789) and the Academic Research Program of the Department of National Defense (Grant FUHBP).     

Bi-Objective Median Subtree Location Problems

A number of network design problems can be built on the following premise: given an undirected tree network, T, with node set, V, identify a single subtree, t, containing nodes, v, so that the subtree is located optimally with respect to the remaining, subset of unconnected nodes {V–v}. Distances between unconnected nodes and nodes in the subtree t can be defined on paths that are restricted to lie in the larger tree T (the restricted case), or can be defined on paths in an auxiliary complete graph G (the unrestricted case). The unrestricted case represents a class of problems that is not explicitly recognized in the literature, which is of intermediate complexity relative to the widely studied restricted case, and the general problem in which the underlying graph is general. This paper presents the Median Subtree Location Problem (MSLP), formulated as a bicriterion problem that trades off the cost of a subtree, t, against the population-weighted travel distance from the unconnected nodes to nodes on the subtree where both objectives are to be minimized. Integer programs were formulated for the travel restricted and travel unrestricted cases and were tested using linear programming and branch and bound to resolve fractions. Tradeoff curves between cost and travel burden were developed for sample networks.     

Multicriteria Planar Ordered Median Problems

In this paper, we deal with the determination of the entire set of Pareto solutions of location problems involving Q general criteria. These criteria include median, center, or centdian objective functions as particular instances. We characterize the set of Pareto solutions of all these multicriteria problems for any polyhedral gauge. An efficient algorithm is developed for the planar case and its complexity is established. Extensions to the nonconvex case are also considered. The proposed approach is more general than previously published approaches to multicriteria location problems.The research of the third and fourth authors was partially supported by Grants BFM2001-2378, BFM2001-4028, BFM2004-0909, and HA2003-0121.     

Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation

In this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation. For flowtime minimisation, we propose the strategy employed by the NEH heuristic to construct partial solutions. Results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which, on reward, prove to be much more CPU time-consuming. Additionally, the suggested approach is well balanced with respect to makespan and flowtime minimisation. Based on the previous results, two algorithms are proposed for the sequencing problem with multiple objectives – makespan and flowtime minimisation. These algorithms provide the decision maker with a set of heuristically efficient solutions such that he/she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime. Computational experience shows both algorithms to perform better than the current heuristics designed for the two-criteria problem.     

A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan

We treat a problem of scheduling n jobs on a three stages hybrid flowshop of particular structure (one machine in the first and third stages and two dedicated machines in stage two). The objective is to minimize the makespan. This problem is NP-complete. We propose two heuristic procedures to cope with realistic problems. Extensive experimentation with various problem sizes are conducted and the computational results show excellent performance of the proposed heuristics.     

Efficient heuristics for the workover rig routing problem with a heterogeneous fleet and a finite horizon

Onshore oil fields may contain hundreds of wells that use sophisticated and complex equipments. These equipments need regular maintenance to keep the wells at maximum productivity. When the productivity of a well decreases, a specially-equipped vehicle called a workover rig must visit this well to restore its full productivity. Given a heterogeneous fleet of workover rigs and a set of wells requiring maintenance, the workover rig routing problem (WRRP) consists of finding rig routes that minimize the total production loss of the wells over a finite horizon. The wells have different loss rates, need different services, and may not be serviced within the horizon. On the other hand, the number of available workover rigs is limited, they have different initial positions, and they do not have the same equipments. This paper presents and compares four heuristics for the WRRP: an existing variable neighborhood search heuristic, a branch-price-and-cut heuristic, an adaptive large neighborhood search heuristic, and a hybrid genetic algorithm. These heuristics are tested on practical-sized instances involving up to 300 wells, 10 rigs on a 350-period horizon. Our computational results indicate that the hybrid genetic algorithm outperforms the other heuristics on average and in most cases.     

Classical and Inverse Median Location Problems under Uncertain Environment

In this paper, we first consider the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain variables. The uncertainty distribution of the optimal objective value of the p-median problem is given and the concepts of the α-p-median, the most p-median and the expected p-median are introduced. Then, it is shown that the uncertain p-median problem is NP-hard on general networks. However, if the underlying network is a tree, an ef...     

双圈覆盖问题

Seyntour[1]与Szekeres[5]猜想，每一个无割边的图G具有一个圈集合 使G中的每个边存在于 的两个圈中。本证明此猜想成立当且仅当它对没有非平凡的三个边割的图成立。     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

BDD-based heuristics for binary optimization

In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.     

Rounding-based heuristics for nonconvex MINLPs

We propose two primal heuristics for nonconvex mixed-integer nonlinear programs. Both are based on the idea of rounding the solution of a continuous nonlinear program subject to linear constraints. Each rounding step is accomplished through the solution of a mixed-integer linear program. Our heuristics use the same algorithmic scheme, but they differ in the choice of the point to be rounded (which is feasible for nonlinear constraints but possibly fractional) and in the linear constraints. We propose a feasibility heuristic, that aims at finding an initial feasible solution, and an improvement heuristic, whose purpose is to search for an improved solution within the neighborhood of a given point. The neighborhood is defined through local branching cuts or box constraints. Computational results show the effectiveness in practice of these simple ideas, implemented within an open-source solver for nonconvex mixed-integer nonlinear programs.     

Clustering heuristics for set covering

We introduce a new class of set covering heuristics, based on clustering techniques. In its simplest form, a heuristic in this class may be described as follows: firstly, partition the column set into clusters formed by columns that are close to each other (e.g. in the Hamming distance sense). Then select a best (e.g. a cheapest) column in each cluster; if the selected columns form a coverC, then extract fromC a prime cover and stop; else, modify the partition (e.g. by increasing the number of clusters) and repeat. We describe two implementations of this general algorithmic strategy, relying on the Single Linkage and the Leader clustering algorithm, respectively. Numerical experiments performed on 72 randomly generated test problems with 200 or 400 rows and 1000 columns indicate that the above two heuristics often yield cheaper covers than other well-known (greedy-type) heuristics when the cost-range is not too narrow.The present work is based on R.K. Kwatera's dissertation, written under the supervision of B. Simeone. A preliminary version was presented at EURO VIII, Paris, July 1988.     

向量均衡问题强有效解的稳定性

在可行集扰动而向量值映射不扰动、可行集与向量值映射均扰动、可行集扰动而集值映射不扰动以及可行集与集值映射均扰动四种情况下,分别讨论了向量均衡问题强有效解的稳定性.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

An Efficient Algorithm for Min-Max Convex Semi-Infinite Programming Problems

In this article, we consider the convex min-max problem with infinite constraints. We propose an exchange method to solve the problem by using efficient inactive constraint dropping rules. There is no need to solve the maximization problem over the metric space, as the algorithm has merely to find some points in the metric space such that a certain criterion is satisfied at each iteration. Under some mild assumptions, the proposed algorithm is shown to terminate in a finite number of iterations and to provide an approximate solution to the original problem. Preliminary numerical results with the algorithm are promising. To our knowledge, this article is the first one conceived to apply explicit exchange methods for solving nonlinear semi-infinite convex min-max problems.     

An Efficient Algorithm for Non-Point Source Pollution Management Problems

A dynamic programming (DP) algorithm is proposed for a class of non-point source pollution control problems. The formulation deals with the selection of a spatial distribution of management practices in such a way as to meet a control agency's sediment pollution target. The inherently combinatorial nature of these problems — stemming from the discrete nature of the decision variables, which are production, conservation and mechanical control practices — gives them a special integer programming structure. This paper focuses on the DP formulation and the computer implementation of this algorithm. The approach is shown to be informative, robust and relatively efficient. Furthermore, the paper demonstrates that dynamic programming can be used to generate sensitivity analysis information for multiple-choice knapsack problems.     

Stability Results for Efficient Solutions of Vector Optimization Problems

Using the additive weight method of vector optimization problems and the method of essential solutions, we study some continuity properties of the mapping which associates the set of efficient solutions S(f) to the objective function f. To understand such properties, the key point is to consider the stability of additive weight solutions and the relationship between efficient solutions and additive weight solutions.