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98
A Hybrid MILP/CP Decomposition Approach for the Continuous Time Scheduling of . . .
, 2003
"... A hybrid Mixed-Integer Linear Programming (MILP)/Constraint Programming (CP) decomposition algorithm is proposed for the short-term scheduling of batch plants that rely on the State Task Network representation. The decisions about the type and number of tasks performed, as well as the assignment ..."
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Cited by 24 (12 self)
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A hybrid Mixed-Integer Linear Programming (MILP)/Constraint Programming (CP) decomposition algorithm is proposed for the short-term scheduling of batch plants that rely on the State Task Network representation. The decisions about the type and number of tasks performed, as well as the assignment of units to tasks are made by the MILP master problem. The CP
Constraint programming contribution to benders decomposition: a case study
- In CP-02
, 2002
"... Abstract. The aim of this paper is to demonstrate that CP could be a better candidate than MIP for solving the master problem within a Benders decomposition approach. Our demonstration is based on a case study of a workforce scheduling problem encountered in a large call center of Bouygues Telecom, ..."
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Cited by 20 (3 self)
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Abstract. The aim of this paper is to demonstrate that CP could be a better candidate than MIP for solving the master problem within a Benders decomposition approach. Our demonstration is based on a case study of a workforce scheduling problem encountered in a large call center of Bouygues Telecom, a French mobile phone operator. Our experiments show that CP can advantageously replace MIP for the implementation of the master problem due to its greater ability to efficiently manage a wide variety of constraints such as the ones occurring in time tabling applications. 1.
Identifying and Exploiting Problem Structures Using Explanation-based Constraint Programming
- Constraints
"... Abstract. Identifying structures in a given combinatorial problem is often a key step for designing efficient search heuristics or for understanding the inherent complexity of the problem. Several Operations Research approaches apply decomposition or relaxation strategies upon such a structure ident ..."
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Cited by 18 (2 self)
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Abstract. Identifying structures in a given combinatorial problem is often a key step for designing efficient search heuristics or for understanding the inherent complexity of the problem. Several Operations Research approaches apply decomposition or relaxation strategies upon such a structure identified within a given problem. The next step is to design algorithms that adaptively integrate that kind of information during search. We claim in this paper, inspired by previous work on impact-based search strategies for constraint programming, that using an explanation-based constraint solver may lead to collect invaluable information on the intimate dynamically revealed and static structures of a problem instance. Moreover, we discuss how dedicated OR solving strategies (such as Benders decomposition) could be adapted to constraint programming when specific relationships between variables are exhibited. 1.
Decomposition Techniques for Multistage Scheduling Problems Using Mixed-Integer and Constraint Programming Methods
- Comp. Chem. Engng
, 2002
"... In this paper two strategies are presented to reduce the combinatorial complexity when solving single stage and multistage optimization scheduling problems that involve cost minimization and due dates. These problems can naturally be decomposed into assignment and sequencing subproblems. The propose ..."
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Cited by 17 (10 self)
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In this paper two strategies are presented to reduce the combinatorial complexity when solving single stage and multistage optimization scheduling problems that involve cost minimization and due dates. These problems can naturally be decomposed into assignment and sequencing subproblems. The proposed strategies rely on either combining mixed-integer programming (MILP) to model the assignment part and constraint programming (CP) for modeling the sequencing part, or else combining MILP models for both parts. The subproblems are solved sequentially by adding integer cuts to the first MILP to generate new assignments. Results are presented for both single and multistage systems.
A Benders approach for the constrained minimum break problem
- EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 2007
"... This paper presents a hybrid IP/CP algorithm for designing a double round robin schedule with a minimal number of breaks. Both mirrored and non-mirrored schedules with and without place constraints are considered. The algorithm uses Benders cuts to obtain feasible home-away pattern sets in few itera ..."
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Cited by 15 (2 self)
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This paper presents a hybrid IP/CP algorithm for designing a double round robin schedule with a minimal number of breaks. Both mirrored and non-mirrored schedules with and without place constraints are considered. The algorithm uses Benders cuts to obtain feasible home-away pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances. Furthermore, the al-gorithm is capable of solving a number of previously unsolved benchmark problems for the Traveling Tournament Problem with constant distances.
Decomposition and learning for a hard real time task allocation algorithm
- Principles and Practice of Constraint Programming (CP 2004), Lecture Notes in Computer Science 3258
, 2004
"... Abstract. We present a cooperation technique using an accurate management of nogoods to solve a hard real-time problem which consists in assigning periodic tasks to processors in the context of fixed priorities preemptive scheduling. The problem is to be solved off-line and our solving strategy is r ..."
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Cited by 14 (0 self)
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Abstract. We present a cooperation technique using an accurate management of nogoods to solve a hard real-time problem which consists in assigning periodic tasks to processors in the context of fixed priorities preemptive scheduling. The problem is to be solved off-line and our solving strategy is related to the logic based Benders decomposition. A master problem is solved using constraint programming whereas subproblems are solved with schedulability analysis techniques coupled with an ad hoc nogood computation algorithm. Constraints and nogoods are learnt during the process and play a role close to Benders cuts. 1
Disruption management for resource-constrained project scheduling
- Journal of the Operational Research Society
, 2005
"... In this paper, we study the problem of how to react when an ongoing project is disrupted. The focus is on the resourceconstrained project scheduling problem with finish–start precedence constraints. We begin by proposing a classification scheme for the different types of disruptions and then define ..."
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Cited by 13 (0 self)
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In this paper, we study the problem of how to react when an ongoing project is disrupted. The focus is on the resourceconstrained project scheduling problem with finish–start precedence constraints. We begin by proposing a classification scheme for the different types of disruptions and then define the constraints and objectives that comprise what we call the recovery problem. The goal is to get back on track as soon as possible at minimum cost, where cost is now a function of the deviation from the original schedule. The problem is formulated as an integer linear program and solved with a hybrid mixed-inter programming/constraint programming procedure that exploits a number of special features in the constraints. The new model is significantly different from the original one due to the fact that a different set of feasibility conditions and performance requirements must be considered during the recovery process. The complexity of several special cases is analysed. To test the hybrid procedure, 554 20-activity instances were solved and the results compared with those obtained with CPLEX. Computational experiments were also conducted to determine the effects of different factors related to the recovery process.
Trajectory Optimization using Mixed-Integer Linear Programming
, 2002
"... This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions ..."
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Cited by 13 (1 self)
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This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions about terminal constraints in the optimization, such as assignment of waypoints to UAVs and the assignment of spacecraft to positions in a formation. These requirements lead to non-convex constraints and difficult optimizations. However, they can be formulated as mixed-integer linear programs (MILP) that can be solved for global optimality using powerful, commercial software. This thesis provides several extensions to previous work using MILP. The constraints for avoidance are extended to prevent plume impingement, which occurs when one spacecraft fire thrusters towards another. Methods are presented for efficient simplifications to complex problems, allowing solutions to be obtained in practical computation times. An approximation is developed to enable the inclusion of aircraft
SIMPL: A system for integrating optimization techniques
- Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2004), Lecture Notes in Computer Science 3011
, 2004
"... Abstract. In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability ..."
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Cited by 11 (4 self)
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Abstract. In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability to combine complementary strengths of the two solution technologies. This research has reached a stage at which further development would benefit from a general-purpose modeling and solution system. We introduce here a system for integrated modeling and solution called SIMPL. Our approach is to view CP and OR techniques as special cases of a single method rather than as separate methods to be combined. This overarching method consists of an infer-relax-restrict cycle in which CP and OR techniques may interact at any stage. We describe the main features of SIMPL and illustrate its usage with examples.
