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Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches

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Abstract

The generalised assignment problem (GAP) is the problem of finding a minimum cost assignment of a set of jobs to a set of agents. Each job is assigned to exactly one agent. The total demands of all jobs assigned to any agent can not exceed the total resources available to that agent. A review of exact and heuristic methods is presented. Aλ-generation mechanism is introduced. Different search strategies and parameter settings are investigated for theλ-generation descent, hybrid simulated annealing/tabu search and tabu search heuristic methods. The developed methods incorporate a number of features that have proven useful for obtaining optimal and near optimal solutions. The effectiveness of our approaches is established by comparing their performance in terms of solution quality and computional requirement to other specialized branch-and-bound tree search, simulated annealing and set partitioning heuristics on a set of standard problems from the literature.

Zusammenfassung

Das verallgemeinerte Zuordnungsproblem (GAP) besteht darin, eine Menge von Aufträgen einer Menge von Agenten kostenminimal zuzuordnen. Jeder Auftrag wird genau einem Agenten zugeordnet; die Summe der Anforderungen der einem Agenten zugeordneten Aufträge ist durch die diesem zur Verfügung stehenden Ressourcen begrenzt. Die Arbeit gibt eine Übersicht über exakte und heuristische Lösungsverfahren zum GAP. Es wird einλ-Generierungs-Mechanismus beschrieben, wobei verschiedene Suchstrategien (ein Hybridverfahren aus Simulated Annealing und Tabu Search sowie reine Tabu Search-Verfahren) sowie Parameterkonstellationen untersucht werden. Die entwickelten Methoden beinhalten eine Anzahl von Eigenschaften, die sich für die Erzielung von optimalen Lösungen sowie guten Näherungen als geeignet erwiesen haben. Die Effektivität der Ansätze wird über den Vergleich hinsichtlich Lösungsqualität und Berechnungsanforderungen mit anderen speziellen Verfahren wie Branch und Bound, Simulated Annealing sowie Partitionierungs-Heuristiken bei Anwendung auf Standardprobleme aus der Literatur gezeigt.

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  1. Institute of Mathematics and Statistics, University of Kent, CT2 7NF, Canterbury, Kent, UK

    Ibrahim H. Osman

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Osman, I.H. Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches. OR Spektrum 17, 211–225 (1995). https://doi.org/10.1007/BF01720977

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