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Heterogeneous Objectives: State-of-the-Art and Future Research

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Many-Criteria Optimization and Decision Analysis

Part of the book series: Natural Computing Series ((NCS))

Abstract

Multiobjective optimization problems with heterogeneous objectives are defined as those that possess significantly different types of objective function components (not just incommensurable in units or scale). For example, in a heterogeneous problem the objective function components may differ in formal computational complexity, practical evaluation effort (time, costs, or resources), determinism (stochastic vs deterministic), or some combination of all three. A particularly challenging variety of heterogeneity may occur by the combination of a time-consuming laboratory-based objective with other objectives that are evaluated using faster computer-based calculations. Perhaps more commonly, all objectives may be evaluated computationally, but some may require a lengthy simulation process while others are computed from a relatively simple closed-form calculation. In this chapter, we motivate the need for more work on the topic of heterogeneous objectives (with reference to real-world examples), expand on a basic taxonomy of heterogeneity types, and review the state of the art in tackling these problems. We give special attention to heterogeneity in evaluation time (latency) as this requires sophisticated approaches. We also present original experimental work on estimating the amount of heterogeneity in evaluation time expected in many-objective problems, given reasonable assumptions, and survey related research threads that could contribute to this area in future.

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Notes

  1. 1.

    Solutions evaluated on the fast objective are considered for evaluation on the slow objective in the next generation if they outperform at least one of their parents on the fast objective.

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Author information

Authors and Affiliations

  1. Alliance Manchester Business School, The University of Manchester, Manchester, UK

    Richard Allmendinger & Joshua Knowles

  2. Schlumberger Cambridge Research, Madingley Road, Cambridge, UK

    Joshua Knowles

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  1. Richard Allmendinger
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Correspondence to Richard Allmendinger .

Editor information

Editors and Affiliations

  1. Inria Saclay-Île-de-France and CMAP, École Polytechnique, Palaiseau, France

    Dimo Brockhoff

  2. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Michael Emmerich

  3. Informatik und Ingenieurwissenschaften, TH Köln, Gummersbach, Germany

    Boris Naujoks

  4. Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Robin Purshouse

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Allmendinger, R., Knowles, J. (2023). Heterogeneous Objectives: State-of-the-Art and Future Research. In: Brockhoff, D., Emmerich, M., Naujoks, B., Purshouse, R. (eds) Many-Criteria Optimization and Decision Analysis. Natural Computing Series. Springer, Cham. https://doi.org/10.1007/978-3-031-25263-1_12

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  • DOI: https://doi.org/10.1007/978-3-031-25263-1_12

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