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163
Branchandprice: Column generation for solving huge integer programs
 Oper. Res
, 1998
"... We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which th ..."
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Cited by 348 (14 self)
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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. Wethen discuss computational issues and implementation of column generation, branchandbound algorithms, including special branching rules and e cient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. 1
ATabu search heuristic for the vehicle routing problem with soft time windows
 Transportation science
, 1997
"... Centre de recherche sur les transports — Publication CRT9584 Département d’informatique et de recherche opérationnelle — Publication #1012 ..."
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Cited by 155 (13 self)
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Centre de recherche sur les transports — Publication CRT9584 Département d’informatique et de recherche opérationnelle — Publication #1012
The Vehicle Routing Problem with Time Windows  Part II: Genetic Search
, 1996
"... This paper is the second part of a work on the application of new search techniques for the vehicle routing problem with time windows. It describes GENEROUS, the GENEtic ROUting System, which is based on the natural evolution paradigm. Under this paradigm, a population of solutions evolves from one ..."
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Cited by 85 (1 self)
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This paper is the second part of a work on the application of new search techniques for the vehicle routing problem with time windows. It describes GENEROUS, the GENEtic ROUting System, which is based on the natural evolution paradigm. Under this paradigm, a population of solutions evolves from one generation to the next by "mating" parent solutions to form new offspring solutions that exhibit characteristics inherited from their parents. For this vehicle routing application, a specialized methodology is devised for merging two vehicle routing solutions into a single solution that is likely to be feasible with respect to the time window constraints. Computational results on a standard set of test problems are reported, and comparisons are provided with other heuristics.
DRIVE: Dynamic Routing of Independent VEhicles
, 1996
"... We present DRIVE (Dynamic Routing of Independent VEhicles), a planning module to be incorporated in a decision support system for the direct transportation at Van Gend & Loos BV. Van Gend & Loos BV is the largest company providing road transportation in the Benelux with about 1400 vehicles t ..."
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Cited by 73 (2 self)
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We present DRIVE (Dynamic Routing of Independent VEhicles), a planning module to be incorporated in a decision support system for the direct transportation at Van Gend & Loos BV. Van Gend & Loos BV is the largest company providing road transportation in the Benelux with about 1400 vehicles transporting 160,000 packages from thousands of senders to tens of thousands of addressees per day. The heart of DRIVE is a branchandprice algorithm. Approximation and incomplete optimization techniques as well as a sophisticated column management scheme have been employed to create the right balance between solution speed and solution quality. DRIVE has been tested by simulating a dynamic planning environment with reallife data and has produced very encouraging results.
Constraint Programming Based Column Generation with Knapsack Subproblems
 Journal of Heuristics
, 1999
"... . We present how to apply Constraint Based Column Generation to a large class of subproblems, namely Constrained Knapsack Problems (CKP). They evolve e.g. from Cutting Stock Problems (see [7]) with additional constraints on the cutting patterns. Focussing on Constrained Knapsack Problems, we deve ..."
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Cited by 55 (17 self)
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. We present how to apply Constraint Based Column Generation to a large class of subproblems, namely Constrained Knapsack Problems (CKP). They evolve e.g. from Cutting Stock Problems (see [7]) with additional constraints on the cutting patterns. Focussing on Constrained Knapsack Problems, we developed a new reduction algorithm for KP. It is being used as propagation routine for the CKP with O(n log n) preprocessing time and O(n) time per call. This sums up to an amortized time of O(n) for (log n) calls. Keywords: Constrained Based Column Generation, Constrained Knapsack Problems, Cutting Stock Problems, Reduction Algorithms. 1 Introduction Recently, a new framework for the integration of CP and OR within column generation approaches was developed, the so called Constraint Based Column Generation [11]. It describes a generic way of how to treat arbitrary constraints for the constrained subproblem in the column generation phase. The approach has been successfully used for the C...
An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows
 Transportation Science
, 1996
"... This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branchand bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily o ..."
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Cited by 48 (5 self)
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This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branchand bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such spacecomplexity issues. The datadriven mechanism at its core more fully exploits pruning rules developed in operations research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomon's wellknown test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2. Introduction In the last few years, constraint programming (cp) has b...
A CostRegular based Hybrid Column Generation Approach
, 2006
"... Constraint Programming (CP) offers a rich modeling language of constraints embedding efficient algorithms to handle complex and heterogeneous combinatorial problems. To solve hard combinatorial optimization problems using CP alone or hybrid CPILP decomposition methods, costs also have to be taken ..."
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Cited by 42 (5 self)
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Constraint Programming (CP) offers a rich modeling language of constraints embedding efficient algorithms to handle complex and heterogeneous combinatorial problems. To solve hard combinatorial optimization problems using CP alone or hybrid CPILP decomposition methods, costs also have to be taken into account within the propagation process. Optimization constraints, with their costbased filtering algorithms, aim to apply inference based on optimality rather than feasibility. This paper introduces a new optimization constraint, costregular. Its filtering algorithm is based on the computation of shortest and longest paths in a layered directed graph. The support information is also used to guide the search for solutions. We believe this constraint to be particularly useful in modelling and solving Column Generation subproblems and evaluate its behaviour on complex Employee Timetabling Problems through a flexible CPbased column generation approach. Computational results on generated benchmark sets and on a complex realworld instance are given.
Solving The Convex Cost Integer Dual Network Flow Problem
 MANAGEMENT SCIENCE
, 1999
"... In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form (i,j)Q ij ij F(w)+ iP ii B( ) ), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the f ..."
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Cited by 41 (5 self)
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In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form (i,j)Q ij ij F(w)+ iP ii B( ) ), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the form i  j w ij , (i, j) Q), with lower and upper bounds on variables. Let n = P, m = Q, and U be the largest magnitude in the lower and upper bounds of variables. We call this problem the convex cost integer dual network flow problem. In this paper, we describe several applications of the convex cost integer dual network flow problem arising in dialaride transit problems, inverse spanning tree problem, project management, and regression analysis. We develop network flow based algorithms to solve the convex cost integer dual network flow problem. We show that using the Lagrangian relaxation technique, the convex cost integer dual network flow problem can be transformed to a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes. Its special structure allows the convex cost primal network flow problem to be solved in O(nm log n log(nU)) time using a costscaling algorithm, which is the best available time bound to solve the convex cost integer dual network flow problem.
Polyhedral approaches to machine scheduling
, 1996
"... We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition ..."
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Cited by 40 (8 self)
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We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition to those just required for the validity of the initial formulation, in order to obtain useful lower bounds and structural insights. We review formulations based on time–indexed variables; on linear ordering, start time and completion time variables; on assignment and positional date variables; and on traveling salesman variables. We point out relationship between various models, and provide a number of new results, as well as simplified new proofs of known results. In particular, we emphasize the important role that supermodular polyhedra and greedy algorithms play in many formulations and we analyze the strength of the lower and upper bounds obtained from different formulations and relaxations. We discuss separation algorithms for several classes of inequalities, and their potential applicability in generating cutting planes for the practical solution of such scheduling problems. We also review some recent results on approximation algorithms based on some of these formulations.
Discrete Optimization in Public Rail Transport
 Math. Programming
, 1997
"... this paper occur at the tactical level. Strategic planning focuses on resource acquisition for the period from five to fifteen years ahead. Network planning problems may be viewed as the main strategic issues, but, in order to evaluate possible strategic alternatives, the subsequent stages including ..."
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Cited by 40 (5 self)
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this paper occur at the tactical level. Strategic planning focuses on resource acquisition for the period from five to fifteen years ahead. Network planning problems may be viewed as the main strategic issues, but, in order to evaluate possible strategic alternatives, the subsequent stages including at least line planning and train schedule generation have to be considered. The disadvantages of the hierarchical planning are obvious, since the optimal output of a subtask which serves as the input of a subsequent task, will not result, in general, in an overall optimal solution.