Given an undirected graph whose edges are labeled or colored, edge weights indicating the cost of an edge, and a positive budget B, the goal of the cost constrained minimum label spanning tree (CCMLST) problem is to f...
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Given an undirected graph whose edges are labeled or colored, edge weights indicating the cost of an edge, and a positive budget B, the goal of the cost constrained minimum label spanning tree (CCMLST) problem is to find a spanning tree that uses the minimum number of labels while ensuring its cost does not exceed B. The label constrained minimum spanning tree (LCMST) problem is closely related to the CCMLST problem. Here, we are given a threshold K on the number of labels. The goal is to find a minimum weight spanning tree that uses at most K distinct labels. Both of these problems are motivated from the design of telecommunication networks and are known to be NP-complete [15]. In this paper, we present a variable neighborhood search (VNS) algorithm for the CCMLST problem. The VNS algorithm uses neighborhoods defined on the labels. We also adapt the VNS algorithm to the LCMST problem. We then test the VNS algorithm on existing data sets as well as a large-scale dataset based on TSPLIB [12] instances ranging in size from 500 to 1000 nodes. For the LCMST problem, we compare the VNS procedure to a genetic algorithm (GA) and two local search procedures suggested in [15]. For the CCMLST problem, the procedures suggested in [15] can be applied by means of a binary search procedure. Consequently, we compared our VNS algorithm to the GA and two local search procedures suggested in [15]. The overall results demonstrate that the proposed VNS algorithm is of high quality and computes solutions rapidly. On our test datasets, it obtains the optimal solution in all instances for which the optimal solution is known. Further, it significantly outperforms the GA and two local search procedures described in [15]. (C) 2009 Elsevier Ltd. All rights reserved.
Security constrained unit commitment (SCUC) is one of the most important daily tasks that independent system operators (ISOs) or regional transmission organizations (RTOs) must accomplish in daily electric power marke...
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Security constrained unit commitment (SCUC) is one of the most important daily tasks that independent system operators (ISOs) or regional transmission organizations (RTOs) must accomplish in daily electric power market. Security constraints have long been regarded as difficult constraints for unit commitment problems. If the inactive security constraints can be identified and eliminated, the SCUC problem can be greatly simplified. In this paper, a necessary and sufficient condition for a security constraint to be inactive is established. It is proved that all inactive constraints can be identified by solving a series of small-scale mixedinteger linear programming (MILP) problems. More importantly, an analytical sufficient condition is established and most of the inactive constraints can be quickly identified without solving MILP or linear programming (LP) problems. A very important feature of the conditions obtained is that they are only related to the load demands and parameters of the transmission network. Numerical testing is performed for three power grids and the results are impressive. Over 85% of the security constraints are identified as inactive and the crucial transmission lines affecting the total operating cost are among those associated with the remaining security constraints, providing useful information for transmission planning.
Recent advances on the understanding of valid inequalities from the infinite group relaxation has opened the possibility of finding a computationally effective extension to GMI cuts. In this paper, we investigate the ...
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Recent advances on the understanding of valid inequalities from the infinite group relaxation has opened the possibility of finding a computationally effective extension to GMI cuts. In this paper, we investigate the Computational impact Of using a subclass of minimally valid inequalities from this relaxation oil a wide set of instances. (C) 2009 Elsevier B.V. All rights reserved.
In today's competitive environment, agility and leanness have become two crucial strategic concerns for many manufacturing firms in their efforts to broaden market share. Recently, the build-to-order (BTO) manufac...
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In today's competitive environment, agility and leanness have become two crucial strategic concerns for many manufacturing firms in their efforts to broaden market share. Recently, the build-to-order (BTO) manufacturing strategy is becoming a popular operation strategy to achieve both in a mass-scale customization process. BTO system combines the characteristics of make-to-order strategy with a forecast driven make-to-stock strategy. As a means to improve customer responsiveness, customized products are assembled according to specific orders while standard components are pre-manufactured based on short-term forecasts. Planning of the two subsystems using a two-phase sequential approach offers both operational and modeling incentives. In this paper, we formulate a two-phase mixedinteger linear programming (MILP) model for material procurement, components fabrication, product assembly and distribution scheduling of a BTO supply chain system. In the proposed approach, the entire problem is first decomposed into two subsystems and evaluated sequentially. The first phase deals with assembling and distribution scheduling of customizable products, while the second phase addresses fabrication and procurement planning of components and raw-materials. The objective of both models is to minimize the aggregate costs associated with each subsystem, while meeting customer service requirements. The search space for the first phase problem involves a complex landscape with too many candidate solutions. A genetic algorithm based solution procedure is proposed to solve the sub-problem efficiently. (C) 2010 Published by Elsevier Ltd.
In this paper, we analyze flexible models for capacitated discrete location problems with setup costs. We introduce a major extension with regards to standard models which consists of distinguishing three different po...
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In this paper, we analyze flexible models for capacitated discrete location problems with setup costs. We introduce a major extension with regards to standard models which consists of distinguishing three different points of view of a location problem in a logistics system. We develop mathematical programming formulations for these models using discrete ordered objective functions with some new features. We report on the computational behavior of these formulations tested on a randomly generated battery of instances.
The facility location problem has been studied in many industries including banking network, chain stores, and wireless network. Maximal covering location problem (MCLP) is a general model for this type of problems. M...
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The facility location problem has been studied in many industries including banking network, chain stores, and wireless network. Maximal covering location problem (MCLP) is a general model for this type of problems. Motivated by a real-world banking facility optimization project, we propose an enhanced MCLP model which captures the important features of this practical problem, namely, varied costs and revenues, multitype facilities, and flexible coverage functions. To solve this practical problem, we apply an existing hybrid nested partitions algorithm to the large-scale situation. We further use heuristic-based extensions to generate feasible solutions more efficiently. In addition, the upper bound of this problem is introduced to study the quality of solutions. Numerical results demonstrate the effectiveness and efficiency of our approach. Note to Practitioners-This paper is motivated by a practical banking facility location problem. The problem is how to choose the facilities (bank branches) location in order to maximize the facility network's profits. It is a large-scale optimization problem in the real world. We formulate this problem with an extended MCLP model and apply a hybrid nested partitions algorithm. Our approach is efficient since it combines the mathematical programming and problem specific heuristic information. Practitioners who want to use this approach should pay attention to the utility of problem structure and model formulation. This approach is also applicable to other location problems, such as the retail chain stores, gas stations, city public facilities, and so on.
For the uncapacitated two-level production-in-series T period lot-sizing model, a dynamic program with running time O(T-2 log T) and a compact and tight extended formulation with O(T-3) variables and O(T-2) equality c...
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For the uncapacitated two-level production-in-series T period lot-sizing model, a dynamic program with running time O(T-2 log T) and a compact and tight extended formulation with O(T-3) variables and O(T-2) equality constraints are presented. Limited computational comparisons of various formulations of two-level production/transportation problems with multiple clients are reported. (C) 2010 Elsevier B.V. All rights reserved.
Given a general mixedinteger program, we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We identify t...
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Given a general mixedinteger program, we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixedinteger rounding framework but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of mixedinteger programs coming from network design problems by a factor two on average. We show that almost 10% of the instances in general testsets contain consistent embedded networks. For these instances the computation time is decreased by 18% on average.
This paper presents a solution method for the general (mixedinteger) parametric linear complementarity problem pLCP(q(theta),M), where the matrix M has a general structure and integrality restriction can be enforced ...
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This paper presents a solution method for the general (mixedinteger) parametric linear complementarity problem pLCP(q(theta),M), where the matrix M has a general structure and integrality restriction can be enforced on the solution. Based on the equivalence between the linear complementarity problem and mixedinteger feasibility problem, we propose a mixed integer programming formulation with an objective of finding the minimum 1-norm solution for the original linear complementarity problem. The parametric linear complementarity problem is then formulated as multiparametric mixed integer programming problem, which is solved using a multiparametric programming algorithm. The proposed method is illustrated through a number of examples.
Over the years, various techniques have been proposed to speed up the classical Benders decomposition algorithm. The work presented in the literature has focused mainly on either reducing the number of iterations of t...
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Over the years, various techniques have been proposed to speed up the classical Benders decomposition algorithm. The work presented in the literature has focused mainly on either reducing the number of iterations of the algorithm or on restricting the solution space of the decomposed problems. In this article, a new strategy for Benders algorithm is proposed and applied to two case studies in order to evaluate its efficiency. This strategy, referred to as covering cut bundle (CCB) generation, is shown to implement in a novel way the multiple constraints generation idea. The CCB generation is applied to mixedinteger problems arising from two types of applications: the scheduling of crude oil and the scheduling problem for multi-product, multi-purpose batch plants. In both cases, CCB significantly decreases the number of iterations of the Benders method, leading to improved resolution times.
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