A convergence acceleration operator for multiobjective optimisation

A novel multiobjective optimisation accelerator is introduced that uses direct manipulation in objective space together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions

Robotic synthesis using a hierarchical multi-objective evolutionary algorithm

This paper addresses the robotic manipulator synthesis problem considering multiple design criteria simultaneously. This is a complex problem suitable for the application of multi-objective genetic algorithms. Thus, an hierarchical multi-objective genetic algorithm is proposed to generate a robot structure and corresponding manipulating trajectories. The design aim is to minimize the trajectory space ripple, the initial and final torques while optimizing the mechanical structure. Simulation results are presented concerning the solution of a structure synthesis problem with the optimization of three objectives.N/

Research on Preference Polyhedron Model Based Evolutionary Multiobjective Optimization Method for Multilink Transmission Mechanism Conceptual Design

To make the optimal design of the multilink transmission mechanism applied in mechanical press, the intelligent optimization techniques are explored in this paper. A preference polyhedron model and new domination relationships evaluation methodology are proposed for the purpose of reaching balance among kinematic performance, dynamic performance, and other performances of the multilink transmission mechanism during the conceptual design phase. Based on the traditional evaluation index of single target of multicriteria design optimization, the robust metrics of the mechanism system and preference metrics of decision-maker are taken into consideration in this preference polyhedron model and reflected by geometrical characteristic of the model. At last, two optimized multilink transmission mechanisms are designed based on the proposed preference polyhedron model with different evolutionary algorithms, and the result verifies the validity of the proposed optimization method

BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

Many scientific and industrial applications require joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. We show a natural connection between non-dominated solutions and the highest multivariate rank, which coincides with the outermost level line of the joint cumulative distribution function (CDF). We propose the CDF indicator, a Pareto-compliant metric for evaluating the quality of approximate Pareto sets that complements the popular hypervolume indicator. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. Multi-objective acquisition functions that rely on box decomposition of the objective space, such as the expected hypervolume improvement (EHVI) and entropy search, scale poorly to a large number of objectives. We propose an acquisition function, called BOtied, based on the CDF indicator. BOtied can be implemented efficiently with copulas, a statistical tool for modeling complex, high-dimensional distributions. We benchmark BOtied against common acquisition functions, including EHVI and random scalarization (ParEGO), in a series of synthetic and real-data experiments. BOtied performs on par with the baselines across datasets and metrics while being computationally efficient.Comment: 10 pages (+5 appendix), 9 figures. Submitted to NeurIP

How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?

International audienceThis study provides a comprehensive assessment of state-of-the-art evolutionary multiobjective optimization (EMO) tools' relative effectiveness in calibrating hydrologic models. The relative computational efficiency, accuracy, and ease-of-use of the following EMO algorithms are tested: Epsilon Dominance Nondominated Sorted Genetic Algorithm-II (?-NSGAII), the Multiobjective Shuffled Complex Evolution Metropolis algorithm (MOSCEM-UA), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2). This study uses three test cases to compare the algorithms' performances: (1) a standardized test function suite from the computer science literature, (2) a benchmark hydrologic calibration test case for the Leaf River near Collins, Mississippi, and (3) a computationally intensive integrated surface-subsurface model application in the Shale Hills watershed in Pennsylvania. One challenge and contribution of this work is the development of a methodology for comprehensively comparing EMO algorithms that have different search operators and randomization techniques. Overall, SPEA2 attained competitive to superior results for most of the problems tested in this study. The primary strengths of the SPEA2 algorithm lie in its search reliability and its diversity preservation operator. The biggest challenge in maximizing the performance of SPEA2 lies in specifying an effective archive size without a priori knowledge of the Pareto set. In practice, this would require significant trial-and-error analysis, which is problematic for more complex, computationally intensive calibration applications. ?-NSGAII appears to be superior to MOSCEM-UA and competitive with SPEA2 for hydrologic model calibration. ?-NSGAII's primary strength lies in its ease-of-use due to its dynamic population sizing and archiving which lead to rapid convergence to very high quality solutions with minimal user input. MOSCEM-UA is best suited for hydrologic model calibration applications that have small parameter sets and small model evaluation times. In general, it would be expected that MOSCEM-UA's performance would be met or exceeded by either SPEA2 or ?-NSGAII

A Scalable Model for Design and Control of Turboprop Engines for Advanced Propulsion Systems

In this study, a methodology is proposed for designing turboprop engines and evaluating their off-design performance. It involves optimization steps for the choice of some of the system design parameters and adaptive scaling methods for the turbomachinery and propeller maps. Results show that it leads to a good estimation of the performance of the real architecture of the existing aircraft and is suitable to be used for innovative application such as the sizing of the engine for advanced propulsion systems like the hybrid-electric architectures with increasing hybridization factor

CES-485 Approximating the Set of Pareto Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Most existing multiobjective evolutionary algorithms aim at approximating the PF, the distribution of the Pareto optimal solutions in the objective space. In many real-life applications, however, a good approximation to the PS, the distribution of the Pareto optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of MOPs, in which the dimensionalities of the PS and PF are different so that a good approximation to the PF might not approximate the PS very well. It proposes a probabilistic model based multiobjective evolutionary algorithm, called MMEA, for approximating the PS and the PF simultaneously for a MOP in this class. In the modelling phase of MMEA, the population is clustered into a number of subpopulations based on their distribution in the objective space, the PCA technique is used to detect the dimensionality of the centroid of each subpopulation, and then a probabilistic model is built for modelling the distribution of the Pareto optimal solutions in the decision space. Such modelling procedure could promote the population diversity in both the decision and objective spaces. To ease the burden of setting the number of subpopulations, a dynamic strategy for periodically adjusting it has been adopted in MMEA. The experimental comparison between MMEA and the two other methods, KP1 and Omni-Optimizer on a set of test instances, some of which are proposed in this paper, have been made in this paper. It is clear from the experiments that MMEA has a big advantage over the two other methods in approximating both the PS and the PF of a MOP when the PS is a nonlinear manifold, although it might not be able to perform significantly better in the case when the PS is a linear manifold

Adaptive modelling strategy for continuous multi-objective optimization

The Pareto optimal set of a continuous multi-objective optimization problem is a piecewise continuous manifold under some mild conditions. We have recently developed several multi-objective evolutionary algorithms based on this property. However, the modelling methods used in these algorithms are rather costly. In this paper, a cheap and effective modelling strategy is proposed for building the probabilistic models of promising solutions. A new criterion is proposed for measuring the convergence of the algorithm. The locality degree of each local model is adjusted according to the proposed convergence criterion. Experimental results show that the algorithm with the proposed strategy is very promising. © 2007 IEEE