Dominance-Based Pareto-Surrogate for Multi-Objective Optimization

Mainstream surrogate approaches for multi-objective problems build one approximation for each objective. Mono-surrogate approaches instead aim at characterizing the Pareto front with a single model. Such an approach has been recently introduced using a mixture of regression Support Vector Machine (SVM) to clamp the current Pareto front to a single value, and one-class SVM to ensure that all dominated points will be mapped on one side of this value. A new mono-surrogate EMO approach is introduced here, relaxing the previous approach and modelling Pareto dominance within the rank-SVM framework. The resulting surrogate model is then used as a filter for offspring generation in standard Evolutionary Multi-Objective Algorithms, and is comparatively validated on a set of benchmark problems

Scalarizing Functions in Bayesian Multiobjective Optimization

Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving (computationally) expensive multi- and many-objective optimization problems in Bayesian multiobjective optimization is scarce. Scalarizing functions can play a crucial role on the quality and number of evaluations required when doing the optimization. In this article, we study and review 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models (as surrogates, metamodels or emulators) on them. We use expected improvement as infill criterion (or acquisition function) to update the models. In particular, we compare different scalarizing functions and analyze their performance on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights when using and selecting a scalarizing function when using a Bayesian multiobjective optimization method

Multi-objective simulation optimization via kriging surrogate models applied to natural gas liquefaction process design

A surrogate-based multi-objective optimization framework is employed in the design of natural gas liquefaction processes using reliable, black-box process simulation. The conflicting objectives are minimizing both power consumption and heat exchanger area utilization. The Pareto solutions of the single-mixed refrigerant (SMR) and propane-precooled mixed refrigerant (C3MR) processes are compared to determine the suitability of each process in terms of energy consumption and heat exchanger area. Kriging models and the ɛ-constraint methodology are used to sequentially provide simple surrogate optimization subproblems, whose minimizers are promising feasible and non-dominated solutions to the original black-box problem. The surrogate-based ɛ-constrained optimization subproblems are solved in GAMS using CONOPT. The Pareto Fronts achieved with the surrogate-based framework dominate the results from the NSGA-II, a well-established meta-heuristics of multi-objective optimization. The objective functions of non-dominated solutions go as low as 1045 and 980.3 kJ/kg-LNG and specific UA values of 212.2 and 266.9 kJ/(°C kg-LNG) for SMR and C3MR, respectively. The trade-off solutions that present the minimum sum of relative objectives are analyzed as well as the dominance of C3MR over SMR at low power consumption values and conversely at low heat exchanger area utilization.The authors LFS, CBBC, and MASSR acknowledge the National Council for Scientific and Technological Development–CNPq (Brazil), processes 200305/2020-4, 148184/2019-7, 440047/2019-6, 311807/2018-6, 428650/2018-0, 307958/2021-3 and Coordination for the Improvement of Higher Education Personnel–CAPES (Brazil) for the financial support. The author JAC acknowledges financial support from the “Generalitat Valenciana” under project PROMETEO 2020/064 and the Ministerio de Ciencia e Innovación , under project PID2021-124139NB-C21

Multi-objective design of antenna structures using variable-fidelity EM simulations and co-kriging

A methodology for low-cost multi-objective design of antenna structures is proposed. To reduce the computational effort of the design process the initial Pareto front is obtained by optimizing the response surface approximation (RSA) model obtained from low-fidelity EM simulations of the antenna structure of interest. The front is further refined by iterative incorporation of a limited number of high-fidelity training points into the RSA surrogate using co-kriging. Our considerations are illustrated using two examples of antenna structure

An optimization method for nacelle design

A multi-objective optimiZation method is demonstrated using an evolutionary genetic algorithm. The applicability of this method to preliminary nacelle design is demonstrated by coupling it with a response surface model of a wide range of nacelle designs. These designs were modelled using computational fluid dynamics and a Kriging interpolation was carried out on the results. The NSGA-II algorithm was tested and verified on established multi-dimensional problems. Optimisation on the nacelle model provided 3-dimensional Pareto surfaces of optimal designs at both cruise and off-design conditions. In setting up this methodology several adaptations to the basic NSGA-II algorithm were tested including constraint handling, weighted objective functions and initial sample size. The influence of these operators is demonstrated in terms of the hyper volume of the determined Pareto set

Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm