Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables—both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem—the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems

Liger : a cross-platform open-source integrated optimization and decision-making environment

Real-world optimization problems involving multiple conflicting objectives are commonly best solved using multi-objective optimization as this provides decision-makers with a family of trade-off solutions. However, the complexity of using multi-objective optimization algorithms often impedes the optimization process. Knowing which optimization algorithm is the most suitable for the given problem, or even which setup parameters to pick, requires someone to be an optimization specialist. The lack of supporting software that is readily available, easy to use and transparent can lead to increased design times and increased cost. To address these challenges, Liger is presented. Liger has been designed for ease of use in industry by non-specialists in optimization. The user interacts with Liger via a visual programming language to create an optimization workflow, enabling the user to solve an optimization problem. Liger contains a novel optimization library known as Tigon. The library utilizes the concept of design patterns to enable the composition of optimization algorithms by making use of simple reusable operator nodes. The library offers a varied range of multi-objective evolutionary algorithms which cover different paradigms in evolutionary computation; and supports a wide variety of problem types, including support for using more than one programming language at a time to implement the optimization model. Additionally, Liger functionality can be easily extended by plugins that provide access to state-of-the-art visualization tools and are responsible for managing the graphical user interface. Lastly, new user-driven interactive capabilities are shown to facilitate the decision-making process and are demonstrated on a control engineering optimization problem