class of facet defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from (1,k)-configuration inequalities.
class of facet defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from (1,k)-configuration inequalities.
作者：
Gottlieb, Elsie SterbinCUNY
Baruch Coll Dept Stat & Comp Informat Syst Zicklin Sch Business New York NY 10021 USA
The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. ...
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The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities.
This paper presents a transportation branch and bound algorithm for solving the generalized assignment problem. This is a branch and bound technique in which the sub-problems are solved by the available efficient tran...
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This paper presents a transportation branch and bound algorithm for solving the generalized assignment problem. This is a branch and bound technique in which the sub-problems are solved by the available efficient transportation techniques rather than the usual simplex based approaches. A technique for selecting branching variables that minimize the number of sub-problems is also presented.
Three classes of valid inequalities based upon multiple knapsack constraints are derived for the generalized assignment problem. General properties of the facet defining inequalities are discussed and, for a special c...
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Three classes of valid inequalities based upon multiple knapsack constraints are derived for the generalized assignment problem. General properties of the facet defining inequalities are discussed and, for a special case, the convex hull is completely characterized. In addition, we prove that a basic fractional solution to the linear programming relaxation can be eliminated by a facet defining inequality associated with an individual knapsack constraint.
The emergence of GPU-CPU heterogeneous architecture has led to a significant paradigm shift in parallel programming. How to effectively implement Parallel Genetic Algorithm (GA) in these environments has become one of...
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The emergence of GPU-CPU heterogeneous architecture has led to a significant paradigm shift in parallel programming. How to effectively implement Parallel Genetic Algorithm (GA) in these environments has become one of the current hot issues. GA's calculation and operators are closely related to specific problems, thereby significantly affecting the acceleration method of GA algorithms. The generalized assignment problem (GAP) is a classic NP-hard combinatorial optimization problem. The more widely used genetic algorithms to solve the GAP in the CPU are difficult to be parallelized in a GPU environment due to severe data dependencies. To address this problem, two algorithms suitable for the implementation on the GPU are proposed, namely RPE algorithm and NNE algorithm, which obtain significant performance speedup by alleviating data dependencies and mutually exclusive synchronization overheads. At the same time, considering the new GPU architecture features and programming models, three different granular implementations of parallel genetic algorithms to solve the GAP are proposed, namely GPGA(thread), GPGA(warpsp) and GPGA(cgroup), by utilizing the warp-specialization technology and the cooperative group mechanism. GPGA series algorithms obtain better solution quality and very significant performance improvements compared with Serial GA, GTS (the GPU-CPU hybrid implementation of Scatter Search with Tabu lists) and Lagrange Relaxation algorithm on a CPU by solving 16 typical large-scale GAP instances.
This paper discusses a heuristic for the generalized assignment problem (GAP). The objective of GAP is to minimize the costs of assigning J jobs to M capacity constrained machines, such that each job is assigned to ex...
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This paper discusses a heuristic for the generalized assignment problem (GAP). The objective of GAP is to minimize the costs of assigning J jobs to M capacity constrained machines, such that each job is assigned to exactly one machine. The problem is known to be NP-Hard, and it is hard from a computational point of view as well. The heuristic proposed here is based on column generation techniques, and yields both upper and lower bounds. On a set of relatively hard test problems the heuristic is able to find solutions that are on average within 0.13% from optimality.
The multilevel generalized assignment problem (MGAP) differs from the classical GAP in that agents can perform tasks at more than one efficiency level. Important manufacturing problems, such as lot sizing, can be form...
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The multilevel generalized assignment problem (MGAP) differs from the classical GAP in that agents can perform tasks at more than one efficiency level. Important manufacturing problems, such as lot sizing, can be formulated as MGAPs;however, the large number of variables in the related 0-1 integer program makes the use of commercial optimization packages impractical. In this paper, we present a heuristic approach to the solution of the MGAP, which consists of a novel application of tabu search (TS). Our TS method employs neighborhoods defined by ejection chains, that produce moves of greater power without significantly increasing the computational effort.
In this paper, we propose a variable depth search (VDS) algorithm for the generalized assignment problem (GAP), which is one of the representative combinatorial optimization problems, and is known to be NP-hard. The V...
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In this paper, we propose a variable depth search (VDS) algorithm for the generalized assignment problem (GAP), which is one of the representative combinatorial optimization problems, and is known to be NP-hard. The VDS is a generalization of the local search. The main idea of VDS is to change the size of the neighborhood adaptively so that the algorithm can effectively traverse larger search space within reasonable computational time. In our previous paper (M. Yagiura, T. Yamaguchi and T. Ibaraki, "A variable depth sl:arch algorithm for the generalized assignment problem," Proc. 2nd Metaheuristics international Conference (MIC97), (1997) 129-130 (full version is to appear in the post-conference book)), we proposed a simple VDS algorithm for the GAP, and obtained good results. To further improve the performance of the VDS, we examine the effectiveness of incorporating branching search processes to construct the neighborhoods. Various types of branching rules are examined, and it is observed that appropriate choices of branching strategies improve the performance of VDS. Comparisons with other existing heuristics are also conducted using benchmark instances. The proposed algorithm is found to be quite effective.
In this paper, we propose a variable depth search (VDS) algorithm for the generalized assignment problem (GAP), which is one of the representative combinatorial optimization problems, and is known to be NP-hard. The V...
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In this paper, we propose a variable depth search (VDS) algorithm for the generalized assignment problem (GAP), which is one of the representative combinatorial optimization problems, and is known to be NP-hard. The VDS is a generalization of the local search. The main idea of VDS is to change the size of the neighborhood adaptively so that the algorithm can effectively traverse larger search space within reasonable computational time. In our previous paper (M. Yagiura, T. Yamaguchi and T. Ibaraki, "A variable depth search algorithm for the generalized assignment problem," Proc. 2nd Metaheuristics International Conference (MIC97), (1997) 129-130 (full version is to appear in the post-conference book)), we proposed a simple VDS algorithm for the GAP, and obtained good results. To further improve the performance of the VDS, we examine the effectiveness of incorporating branching search processes to construct the neighborhoods. Various types of branching rules are examined, and it is observed that appropriate choices of branching strategies improve the performance of VDS. Comparisons with other existing heuristics are also conducted using benchmark instances. The proposed algorithm is found to be quite effective.
The multi-resource generalized assignment problem is encountered when a set of tasks have to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to the availability of...
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The multi-resource generalized assignment problem is encountered when a set of tasks have to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to the availability of a set of multiple resources consumed by that agent. This problem differs from the generalized assignment problem in that an agent consumes not just one but a variety of resources in performing the tasks assigned to him. This paper develops effective solution procedures for the multi-resource generalized assignment problem. Various relaxations of the problem are studied and theoretical relations among these relaxations are pointed out. Rules for reducing problem size are discussed and are shown to be effective through computational experiments. Heuristic solution procedures and an efficient branch and bound procedure are developed. Results of computational experiments testing these procedures are reported.
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