Improvement criteria for constraint handling and multiobjective optimization

Abstract

In engineering design, it is common to predict performance based on complex computer codes with long run times. These expensive evaluations can make automated and wide ranging design optimization a difficult task. This becomes even more challenging in the presence of constraints or conflicting objectives.

When the design process involves expensive analysis, surrogate (response surface or meta) models can be adapted in different ways to efficiently converge towards global solutions. A popular approach involves constructing a surrogate based on some initial sample evaluated using the expensive analysis. Next, some statistical improvement criterion is searched inexpensively to find model update points that offer some design improvement or model refinement. These update points are evaluated, added to the set of initial designs and the process is repeated with the aim of converging towards the global optimum.

In constrained problems, the improvement criterion is required to update the surrogate models in regions that offer both objective and constraint improvement whilst converging toward the best feasible optimum. In multiobjective problems, the aim is to update the surrogates in such a way that the evaluated points converge towards a spaced out set of Pareto solutions.

This thesis investigates efficient improvement criteria to address both of these situations. This leads to the development of an improvement criterion that better balances improvement of the objective and all the constraint approximations. A goal-based approach is also developed suitable for expensive multiobjective problems. In all cases, improvement criteria are encouraged to select multiple updates, enabling designs to be evaluated in parallel, further accelerating the optimization process.

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Identifiers

ORCID for A.J. Keane: orcid.org/0000-0001-7993-1569

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