This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several j...
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This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several jobs simultaneously and the objective is to minimize the maximal lateness. The constraint programming formulation proposed relies on the decomposition of the problem into finding an assignment of the jobs to the batches, and then minimizing the lateness of the batches on a single machine. This formulation is enhanced by a new optimization constraint which is based on a relaxed problem and applies cost-based domain filtering techniques. Experimental results demonstrate the efficiency of cost-based domain filtering techniques. Comparisons to other exact approaches clearly show the benefits of the proposed approach: it can optimally solve problems that are one order of magnitude greater than those solved by a mathematical formulation or by a branch-and-price. (c) 2012 Elsevier B.V. All rights reserved.
Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for larg...
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Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a constraint programming and Integer programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1 second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application. (C) 2012 Elsevier B.V. All rights reserved.
This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed...
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This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed to solve the problem to optimality for small instances. Tight lower bounds and a 4-approximation algorithm are developed. A constraint programming-based method is also proposed. Numerical results demonstrate that the proposed algorithms can obtain high quality solutions and have a competitive performance. Sensitivity analysis indicates that the performance of the proposed algorithms is also robust on different problem structures.
Software Defined Networking (or SDN) allows to apply a centralized control over a network of commuters in order to provide better global performances. One of the problem to solve is the multicommodity flow routing whe...
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Software Defined Networking (or SDN) allows to apply a centralized control over a network of commuters in order to provide better global performances. One of the problem to solve is the multicommodity flow routing where a set of demands have to be routed at minimum cost. In contrast with other versions of this problem, we consider here problems with congestion that change the cost of a link according to the capacity used. We propose here to study centralized routing with constraint programming and Column Generation approaches. Furthermore, selfish routing is studied through with constraint Games. Selfish routing is important for the perceived quality of the solution since no user is able to improve his cost by changing only his own path. We present real and synthetic benchmarks that show a good scalability.
Modeling discrete optimization problems is not straightforward. It is often the case that precompiling a subproblem that involves only a few tightly constrained variables as a table constraint can improve solving time...
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Modeling discrete optimization problems is not straightforward. It is often the case that precompiling a subproblem that involves only a few tightly constrained variables as a table constraint can improve solving time. Nevertheless, enumerating all the solutions of a subproblem into a table can be costly in time and space. In this work we propose using Multivalued Decision Diagrams (MDDs) and formulas in Deterministic Decomposable Negation Normal Form (d-DNNFs) rather than tables to compute and store all solutions of a subproblem. This, in turn, can be used to enhance the solver thanks to stronger propagation via specific propagators for these structures. We show how to precompile part of a problem into both these structures, which can then be injected back in the model by substituting the constraints it encodes, or simply adding it as a redundant constraint. Furthermore, in the case of MDDs, they can also be used to create edge-valued MDDs for optimization problems with an appropriate form. From our experiments we conclude that all three techniques are valuable in their own right, and show when each one should be chosen over the others.
constraint programming (CP) is an efficient technique for solving combinatorial (optimization) problems. In modern constraint solver, a CP Model is defined over reversible variables that take values in domains and pro...
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constraint programming (CP) is an efficient technique for solving combinatorial (optimization) problems. In modern constraint solver, a CP Model is defined over reversible variables that take values in domains and propagators which filter the domains of the variables. constraint propagation scheme schedules the propagators. A reasonable constraint propagation algorithm can improve the efficiency of solving CP problems. In this paper, we propose two efficient parallel propagation schemes based on multi-thread technique for table constraint. First, we give the formal definition of the parallel consistency and prove that the parallel propagation scheme is equivalent to the classic serial propagation scheme. Then, we propose two parallel propagation schemes: static submission and dynamic submission, which exploit work stealing thread pool and atomic operations to parallelize the classic propagation of table constraint. Finally, extensive experiments on various types of problems show that the two parallel schemes outperform their original serial version on a large number of instances. The results demonstrate the competitiveness of parallel propagation algorithms on solving extensional constraints.
constraint programming is a powerful tool for modeling various problems in operations research. Its strength lies in the use of predicates, or global high-level constraints, on a few variables to efficiently model com...
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constraint programming is a powerful tool for modeling various problems in operations research. Its strength lies in the use of predicates, or global high-level constraints, on a few variables to efficiently model complex and varied problem structures. In this paper, we consider the predicate at-least. It bounds the number of variables in a set that may receive a specific value. This is a generalization of the standard logic condition expressed when the sum of binary variables is expressing a lower bound on the cardinality of a set. We have completely determined the convex hull representation of this predicate and provide a polynomial separation algorithm for inclusion in branch-and-bound integer programming software.
Incorporating outsourcing in scheduling is addressed by several researchers recently. However, this scope is not investigated thoroughly, particularly in the job shop environment. In this paper, a new job shop schedul...
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Incorporating outsourcing in scheduling is addressed by several researchers recently. However, this scope is not investigated thoroughly, particularly in the job shop environment. In this paper, a new job shop scheduling problem is studied with the option of jobs outsourcing. The problem objective is to minimise a weighted sum of makespan and total outsourcing cost. With the aim of solving this problem optimally, two solution approaches of combinatorial optimisation problems, i.e. mathematical programming and constraint programming are examined. Furthermore, two problem relaxation approaches are developed to obtain strong lower bounds for some large scale problems for which the optimality is not proven by the applied solution techniques. Using extensive numerical experiments, the performance of the solution approaches is evaluated. Moreover, the effect the objectives's weights in the objective function on the performance of the solution approaches is also investigated. It is concluded that constraint programming outperforms mathematical programming significantly in proving solution optimality, as it can solve small and medium size problems optimally. Moreover, by solving the relaxed problems, one can obtain good lower bounds for optimal solutions even in some large scale problems.
Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions and problem-specific...
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Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions and problem-specific desires that may only be discovered or articulated by the user after further analysis of solver output. We propose a general framework for problems of a combinatorial nature that can generate a set of of multiple (near-)optimal, diverse solutions that are further infused with desirable features. We call our approach solution engineering. A key novelty is that desirable solution properties need not be explicitly modeled in advance. We customize the framework to both the mathematical programming and constraint programming technologies, and we subsequently demonstrate its practicality by implementing and then conducting computational experiments on existing test instances from the literature. Our computational results confirm the very real possibility of generating sets of solutions infused with features that might otherwise remain undiscovered.
DLV2 is an AI tool for Knowledge Representation and Reasoning which supports Answer Set programming (ASP) – a logic-based declarative formalism, successfully used in both academic and industrial applications. Given a...
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