A Suite of Computationally Expensive Shape Optimisation Problems Using Computational Fluid Dynamics

Abstract

In many product design and development applications, Computational Fluid Dynamics (CFD) has become a useful tool for analysis. This is particularly because of the accuracy of CFD simulations in predicting the important flow attributes for a given design. On occasions when design optimisation is applied to real-world engineering problems using CFD, the implementation may not be available for examination. As such, in both the CFD and optimisation communities, there is a need for a set of computationally expensive benchmark test problems for design optimisation using CFD. In this paper, we present a suite of three computationally expensive real-world problems observed in different fields of engineering. We have developed Python software capable of automatically constructing geometries from a given decision vector, running appropriate simulations using the CFD code OpenFOAM, and returning the computed objective values. Thus, users may easily evaluate a decision vector and perform optimisation of these design problems using their optimisation methods without developing custom CFD code. For comparison, we provide the objective values for the base geometries and typical computation times for the test cases presented here.

Uncertainty Handling in Surrogate Assisted Optimisation of Games

“…Simulations become necessary in cases where the actual fitness function is either (1) too expensive to compute or (2) carries a safety or security risk. For shape optimisation problems, for example, simulations using cheaper computational fluid dynamics models are often employed [28]. The need for simulations becomes especially prevalent when the problem involves the need to predict or react to human behaviour, as it is difficult to obtain data to train a model on.…”

“…We chose to add game optimisation problems specifically for several reasons: 1. Games describe highly complex systems, but their true state is always completely observable. This is a contrast to problems that rely on real-world measurements such as described in [28]. 2.…”

“…This results in a lack of appropriate benchmarks for algorithms specifically designed for expensive fitness function, such as surrogate-assisted evolutionary algorithms (see section 3.2). According to [28], these benchmarks are rare because real-world problems in relevant publications are mostly proprietary in nature. This claim is made despite the existence of the Black Box Optimization Competition (BBComp) 3 , which includes expensive as well as bi-objective problems, but is set up as a competition rather than a benchmark.…”

“…Recently, efforts have been made to tackle these issues. For example, in [28], three real-world problems involving computational fluid dynamics (CFD) are compiled into a benchmark for computationally expensive optimisation available on BitBucket 4 . Two of these problems are single-objective and one is bi-objective, and all rely on a CFD simulation for the computation of a fitness function.…”

“…We would consider these results sufficient to claim that the benchmark is indeed practical in terms of computational resources required. This is based on the average execution times reported for a comparable benchmark [28]. For their CFD-based benchmark, the authors report average execution times of 40.35, 947.37 and 34.44, respectively, for the three functions included in the benchmark.…”