Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems

This letter suggests an approach for decomposing a multiobjective optimization problem (MOP) into a set of simple multiobjective optimization subproblems. Using this approach, it proposes MOEA/D-M2M, a new version of multiobjective optimization evolutionary algorithm-based decomposition. This proposed algorithm solves these subproblems in a collaborative way. Each subproblem has its own population and receives computational effort at each generation. In such a way, population diversity can be maintained, which is critical for solving some MOPs. Experimental studies have been conducted to compare MOEA/D-M2M with classic MOEA/D and NSGA-II. This letter argues that population diversity is more important than convergence in multiobjective evolutionary algorithms for dealing with some MOPs. It also explains why MOEA/D-M2M performs better. © 2013 IEEE

qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling

Classical evolutionary approaches for multiobjective optimization are quite effective but incur a lot of queries to the objectives; this can be prohibitive when objectives are expensive oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates. This ``inner'' optimization can be hard due to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; the success of MOBO heavily relies on this inner optimization. We do away with this hard acquisition function optimization step and propose a simple, but effective, Thompson sampling based approach ($q\texttt{POTS}$) where new candidate(s) are chosen from the Pareto frontier of random GP posterior sample paths obtained by solving a much cheaper multiobjective optimization problem. To further improve computational tractability in higher dimensions we propose an automated active set of candidates selection combined with a Nystr\"{o}m approximation. Our approach applies to arbitrary GP prior assumptions and demonstrates strong empirical performance over the state of the art, both in terms of accuracy and computational efficiency, on synthetic as well as real-world experiments.Comment: 12 pages, 4 figure

Turbopump Performance Improved by Evolutionary Algorithms

The development of design optimization technology for turbomachinery has been initiated using the multiobjective evolutionary algorithm under NASA's Intelligent Synthesis Environment and Revolutionary Aeropropulsion Concepts programs. As an alternative to the traditional gradient-based methods, evolutionary algorithms (EA's) are emergent design-optimization algorithms modeled after the mechanisms found in natural evolution. EA's search from multiple points, instead of moving from a single point. In addition, they require no derivatives or gradients of the objective function, leading to robustness and simplicity in coupling any evaluation codes. Parallel efficiency also becomes very high by using a simple master-slave concept for function evaluations, since such evaluations often consume the most CPU time, such as computational fluid dynamics. Application of EA's to multiobjective design problems is also straightforward because EA's maintain a population of design candidates in parallel. Because of these advantages, EA's are a unique and attractive approach to real-world design optimization problems

Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

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

Effective and efficient algorithm for multiobjective optimization of hydrologic models

Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity

Multi-objective engineering shape optimization using differential evolution interfaced to the Nimrod/O tool

This paper presents an enhancement of the Nimrod/O optimization tool by interfacing DEMO, an external multiobjective optimization algorithm. DEMO is a variant of differential evolution – an algorithm that has attained much popularity in the research community, and this work represents the first time that true multiobjective optimizations have been performed with Nimrod/O. A modification to the DEMO code enables multiple objectives to be evaluated concurrently. With Nimrod/O’s support for parallelism, this can reduce the wall-clock time significantly for compute intensive objective function evaluations. We describe the usage and implementation of the interface and present two optimizations. The first is a two objective mathematical function in which the Pareto front is successfully found after only 30 generations. The second test case is the three-objective shape optimization of a rib-reinforced wall bracket using the Finite Element software, Code_Aster. The interfacing of the already successful packages of Nimrod/O and DEMO yields a solution that we believe can benefit a wide community, both industrial and academic

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