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Combining Local Search and Elicitation for Multi-Objective Combinatorial Optimization

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Algorithmic Decision Theory (ADT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11834))

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Abstract

In this paper, we propose a general approach based on local search and incremental preference elicitation for solving multi-objective combinatorial optimization problems with imprecise preferences. We assume that the decision maker’s preferences over solutions can be represented by a parameterized scalarizing function but the parameters are initially not known. In our approach, the parameter imprecision is progressively reduced by iteratively asking preference queries to the decision maker (1) before the local search in order to identify a promising starting solution and (2) during the local search but only when preference information are needed to discriminate between the solutions within a neighborhood. This new approach is general in the sense that it can be applied to any multi-objective combinatorial optimization problem provided that the scalarizing function is linear in its parameters (e.g., a weighted sum, an OWA aggregator, a Choquet integral) and that a (near-)optimal solution can be efficiently determined when preferences are precisely known. For the multi-objective traveling salesman problem, we provide numerical results obtained with different query generation strategies to show the practical efficiency of our approach in terms of number of queries, computation time and gap to optimality.

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Notes

  1. 1.

    Note that \(PMR(x,x',\varOmega _\varTheta )\) values can be computed using a LP solver since \(\varOmega _\varTheta \) is described by linear constraints and \(f_\omega \) is linear in its parameters \(\omega \).

  2. 2.

    https://eden.dei.uc.pt/~paquete/tsp/.

  3. 3.

    PMRs values are computed using CPLEX Optimizer (https://www.ibm.com/analytics/cplex-optimizer) and the optimization part of Select&Optimize is performed by the exact TSP solver Concorde (http://www.math.uwaterloo.ca/tsp/concorde).

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Authors and Affiliations

  1. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Nawal Benabbou, Cassandre Leroy, Thibaut Lust & Patrice Perny

Authors
  1. Nawal Benabbou
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  2. Cassandre Leroy
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  3. Thibaut Lust
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  4. Patrice Perny
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Correspondence to Thibaut Lust .

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Editors and Affiliations

  1. Fuqua School of Business, Duke University, Durham, NC, USA

    Saša Pekeč

  2. Florida Institute for Human and Machine Cognition (IHMC), Pensacola, FL, USA

    Kristen Brent Venable

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Benabbou, N., Leroy, C., Lust, T., Perny, P. (2019). Combining Local Search and Elicitation for Multi-Objective Combinatorial Optimization. In: Pekeč, S., Venable, K.B. (eds) Algorithmic Decision Theory. ADT 2019. Lecture Notes in Computer Science(), vol 11834. Springer, Cham. https://doi.org/10.1007/978-3-030-31489-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-31489-7_1

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