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167
Adaptive Penalty Methods For Genetic Optimization Of Constrained Combinatorial Problems
 INFORMS Journal on Computing
, 1996
"... The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have ..."
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Cited by 26 (12 self)
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The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have suggested the use of both static and dynamic penalty functions for genetic search, this paper presents a general adaptive penalty technique which makes use of feedback obtained during the search along with a dynamic distance metric. The effectiveness of this method is illustrated on two diverse combinatorial applications; (1) the unequalarea, shapeconstrained facility layout problem and (2) the seriesparallel redundancy allocation problem to maximize system reliability given cost and weight constraints. The adaptive penalty function is shown to be robust with regard to random number seed, parameter settings, number and degree of constraints, and problem instance. 1. Introduction ...
A Lagrangian Relaxation Network for Graph Matching
 IEEE Trans. Neural Networks
, 1996
"... A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing ..."
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Cited by 26 (7 self)
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A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions." Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetrybreaking selfamplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and selfamplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variable...
Reliability Models for Facility Location: The Expected Failure Cost Case
 Transportation Science
, 2004
"... Classical facility location models like the Pmedian problem (PMP) and the uncapacitated fixedcharge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, l ..."
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Cited by 26 (9 self)
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Classical facility location models like the Pmedian problem (PMP) and the uncapacitated fixedcharge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a tradeo# curve between the daytoday operating cost and the expected cost taking failures into account, and use these tradeo# curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.
Adaptive problemsolving for largescale scheduling problems: A case study
, 1996
"... Although most scheduling problems are NPhard, domain specific techniques perform well in practice but are quite expensive to construct. In adaptive problemsolving, domain specific knowledge is acquired automatically for a general problem solver with a flexible control architecture. In this approac ..."
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Cited by 25 (3 self)
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Although most scheduling problems are NPhard, domain specific techniques perform well in practice but are quite expensive to construct. In adaptive problemsolving, domain specific knowledge is acquired automatically for a general problem solver with a flexible control architecture. In this approach, a learning system explores a space of possible heuristic methods for one wellsuited to the eccentricities of the given domain and problem distribution. In this article, we discuss an application of the approach to scheduling satellite communications. Using problem distributions based on actual mission requirements, our approach identifies strategies that not only decrease the amount of CPU time required to produce schedules, but also increase the percentage of problems that are solvable within computational resource limitations. 1.
Scheduling Of Manufacturing Systems Using The Lagrangian Relaxation Technique
 IEEE Transactions on Automatic Control
, 1993
"... Scheduling is one of the most basic but the most difficult problems encountered in the manufacturing industry. Generally, some degree of timeconsuming and impractical enumeration is required to obtain optimal solutions. Industry has thus relied on a combination of heuristics and simulation to solve ..."
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Cited by 25 (9 self)
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Scheduling is one of the most basic but the most difficult problems encountered in the manufacturing industry. Generally, some degree of timeconsuming and impractical enumeration is required to obtain optimal solutions. Industry has thus relied on a combination of heuristics and simulation to solve the problem, resulting in unreliable and often infeasible schedules. Yet, there is a great need for an improvement in scheduling operations in complex and turbulent manufacturing environments. The logical strategy is to find scheduling methods which consistently generate good schedules efficiently. However, it is often difficult to measure the quality of a schedule without knowing the optimum. In this paper, the practical scheduling of three manufacturing environments are examined in the increasing order of complexity. The first problem considers scheduling singleoperation jobs on parallel, identical machines; the second one is concerned with scheduling multipleoperation jobs with simple ...
An Ejection Chain Approach for the Generalized Assignment Problem
 INFORMS Journal on Computing
, 1999
"... this paper, we propose an ejection chain approach under the framework of tabu search (TS) for the generalized assignment problem (GAP), which is known to be NPhard (Sahni and Gonzalez 1976). GAP seeks a minimum cost assignment of n jobs to m agents subject to a resource constraint for each agent. A ..."
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Cited by 22 (7 self)
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this paper, we propose an ejection chain approach under the framework of tabu search (TS) for the generalized assignment problem (GAP), which is known to be NPhard (Sahni and Gonzalez 1976). GAP seeks a minimum cost assignment of n jobs to m agents subject to a resource constraint for each agent. Among various heuristic algorithms developed for GAP are: a combination of the greedy method and local search by Martello and Toth (1981, 1990); a tabu search and simulated annealing approach by Osman (1995); a genetic algorithm by Chu and Beasley (1997); VDS methods by Amini and Racer (1995) and Racer and Amini (1994); a tabu search approach by Laguna et al. (1995) (which is proposed for a generalization of GAP); a set partitioning heuristic by Cattrysse et al. (1994); a relaxation heuristic by Lorena and Narciso (1996); a GRASP and MAXMIN ant system combined with local search and tabu search by Lourenco and Serra (1998); a linear relaxation heuristic by Trick (1992); and so on. Many exact algorithms have also been proposed (e.g., Nauss 2003, Savelsbergh 1997). A simpler version of an ejection chain approach has also been proposed for the GAP in Laguna et al. (1995). Our ejection chain is based on the idea described in Glover (1997)
Fast and efficient mode and quantizer selection in the rate distortion sense for H.263
, 1996
"... In this paper, a fast and efficient method for selecting the encoding modes and the quantizers for the ITU H.263 standard is presented. H.263 is a very low bit rate video coder which produces satisfactory results at bit rates around 24 kbits/second for low motion quarter common intermediate format ( ..."
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Cited by 20 (13 self)
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In this paper, a fast and efficient method for selecting the encoding modes and the quantizers for the ITU H.263 standard is presented. H.263 is a very low bit rate video coder which produces satisfactory results at bit rates around 24 kbits/second for low motion quarter common intermediate format (QCIF) color sequences such as "Mother and Daughter". Two major target applications for H.263 are video telephony using public switched telephone network lines and video telephonyover wireless channels. In both cases, the channel bandwidth is very small, hence the efficiency of the video coder needs to be as high as possible. The presented algorithm addresses this problem by finding the smallest frame distortion for a given frame bit budget. The presented scheme is based on Lagrangian Relaxation and Dynamic Programming (DP). It employs a fast evaluation of the operational rate distortion curve in the DCT domain and a fast iterative search which is based on a Bezier function.
A Class of Stochastic Programs with Decision Dependent Uncertainty
 MATHEMATICAL PROGRAMMING
, 2005
"... The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decisions. We address a class of problems where the optimization decisions influence the time of information discovery for a subset of the uncertain para ..."
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Cited by 20 (9 self)
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The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decisions. We address a class of problems where the optimization decisions influence the time of information discovery for a subset of the uncertain parameters. We extend the standard modeling approach by presenting a disjunctive programming formulation that accommodates stochastic programs for this class of problems. A set of theoretical properties that lead to reduction in the size of the model is identified. A Lagrangean duality based branch and bound algorithm is also presented.
Exact Solution of the Quadratic Knapsack Problem
 Informs Journal on Computing
, 1998
"... The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coefficients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checkin ..."
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Cited by 20 (2 self)
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The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coefficients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We propose an exact branchandbound algorithm for QKP, where upper bounds are computed by considering a Lagrangian relaxation which is solvable through a number of (continuous) knapsack problems. Suboptimal Lagrangian multipliers are derived by using subgradient optimization and provide a convenient reformulation of the problem. We also discuss the relationship between our relaxation and other relaxations presented in the literature. Heuristics, reductions and branching schemes are finally described. In particular, the processing of each node of the branching tree is quite fast: We do not update the Lagrangian multipliers, and use suitabl...