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An efficient backtracking heuristic for the resource allocation problem with compatibility and exclusivity constraints

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  • Ahmed Khassiba

    (Capgemini Engineering, Sud-Ouest)

Abstract

We study a resource allocation problem featuring specific constraints, called exclusivity constraints, in addition to regular compatibility constraints. Resources are to be allocated to independent modules, each having a list of compatible resources. A resource can be allocated to several modules. However, some modules exhibit exclusivity constraints, requiring each of them to be allocated to one dedicated compatible resource, not shared with any other module. Such a resource allocation problem arises in the deployment of simulation modules on computational resources in a distributed simulation platform, where the simulation requester may require some modules to be allocated to dedicated resources for a better soft real-time execution, or for instrumentation purposes. In this paper, we introduce the problem of resource allocation with compatibility and exclusivity constraints and show it reduces to the list-coloring problem in a threshold graph. We deduce that our problem is NP-complete in the general case, while it can be solved in polynomial time, in two special cases. We propose a heuristic backtracking algorithm enhanced by pruning rules and exploiting the subproblems’ special structure. Compared to four list coloring heuristics adapted to our problem, our heuristic algorithm can be considered as the method of choice to find high-quality solutions in short computing times.

Suggested Citation

  • Ahmed Khassiba, 2025. "An efficient backtracking heuristic for the resource allocation problem with compatibility and exclusivity constraints," Journal of Heuristics, Springer, vol. 31(1), pages 1-29, March.
    • Handle: RePEc:spr:joheur:v:31:y:2025:i:1:d:10.1007_s10732-024-09538-x
    DOI: 10.1007/s10732-024-09538-x
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    References listed on IDEAS

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    1. Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.
    2. Andreas Ernst & Houyuan Jiang & Mohan Krishnamoorthy, 2006. "Exact Solutions to Task Allocation Problems," Management Science, INFORMS, vol. 52(10), pages 1634-1646, October.
    3. Bernard Roy & Roman Słowiński, 2006. "Multi-criteria assignment problem with incompatibility and capacity constraints," Annals of Operations Research, Springer, vol. 147(1), pages 287-316, October.
    4. Lucci, Mauro & Nasini, Graciela & Severín, Daniel, 2024. "Solving the List Coloring Problem through a branch-and-price algorithm," European Journal of Operational Research, Elsevier, vol. 315(3), pages 899-912.
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