Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

An evolutionary algorithm with double-level archives for multiobjective optimization

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problemlevel and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed

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 worst case optimization by means of evolutionary algorithms

Many real-world optimization problems are subject to uncertainty. A possible goal is then to find a solution which is robust in the sense that it has the best worst-case performance over all possible scenarios. However, if the problem also involves mul- tiple objectives, which scenario is “best” or “worst” depends on the user’s weighting of the different criteria, which is generally difficult to specify before alternatives are known. Evolutionary multi-objective optimization avoids this problem by searching for the whole front of Pareto optimal solutions. This paper extends the concept of Pareto dominance to worst case optimization problems and demonstrates how evolu- tionary algorithms can be used for worst case optimization in a multi-objective setting

Comparison of Geometric Optimization Methods with Multiobjective Genetic Algorithms for Solving Integrated Optimal Design Problems

In this paper, system design methodologies for optimizing heterogenous power devices in electrical engineering are investigated. The concept of Integrated Optimal Design (IOD) is presented and a simplified but typical example is given. It consists in finding Pareto-optimal configurations for the motor drive of an electric vehicle. For that purpose, a geometric optimization method (i.e the Hooke and Jeeves minimization procedure) associated with an objective weighting sum and a Multiobjective Genetic Algorithm (i.e. the NSGA-II) are compared. Several performance issues are discussed such as the accuracy in the determination of Pareto-optimal configurations and the capability to well spread these solutions in the objective space