Peter J. Fleming

Evolutionary algorithms in control systems engineering: a survey

Abstract Challenging optimisation problems, which elude acceptable solution via conventional methods, arise regularly in control systems engineering. Evolutionary algorithms (EAs) permit flexible representation of decision variables and performance evaluation and are robust to difficult search environments, leading to their widespread uptake in the control community. Significant applications are discussed in parameter and structure optimisation for controller design and model identification, in addition to fault diagnosis, reliable systems, robustness analysis, and robot control. Hybrid neural and fuzzy control schemes are also described. The important role of EAs in multiobjective optimisation is highlighted. Evolutionary advances in adaptive control and multidisciplinary design are predicted.

On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers

This work proposes a quantitative, non-parametric interpretation of statistical performance of stochastic multiobjective optimizers, including, but not limited to, genetic algorithms. It is shown that, according to this interpretation, typical performance can be defined in terms analogous to the notion of median for ordinal data, as can other measures analogous to other quantiles.

Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example

For part I see ibid., 26-37. The evolutionary approach to multiple function optimization formulated in the first part of the paper is applied to the optimization of the low-pressure spool speed governor of a Pegasus gas turbine engine. This study illustrates how a technique such as the multiobjective genetic algorithm can be applied, and exemplifies how design requirements can be refined as the algorithm runs. Several objective functions and associated goals express design concerns in direct form, i.e., as the designer would state them. While such a designer-oriented formulation is very attractive, its practical usefulness depends heavily on the ability to search and optimize cost surfaces in a class much broader than usual, as already provided to a large extent by the genetic algorithm (GA). The two instances of the problem studied demonstrate the need for preference articulation in cases where many and highly competing objectives lead to a nondominated set too large for a finite population to sample effectively. It is shown that only a very small portion of the nondominated set is of practical relevance, which further substantiates the need to supply preference information to the GA. The paper concludes with a discussion of the results.

Stability analysis of the particle dynamics in particle swarm optimizer

Previous stability analysis of the particle swarm optimizer was restricted to the assumption that all parameters are nonrandom, in effect a deterministic particle swarm optimizer. We analyze the stability of the particle dynamics without this restrictive assumption using Lyapunov stability analysis and the concept of passive systems. Sufficient conditions for stability are derived, and an illustrative example is given. Simulation results confirm the prediction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced.

On the Evolutionary Optimization of Many Conflicting Objectives

This study explores the utility of multiobjective evolutionary algorithms (using standard Pareto ranking and diversity-promoting selection mechanisms) for solving optimization tasks with many conflicting objectives. Optimizer behavior is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal tradeoff surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behavior are offered via the concepts of dominance resistance and active diversity promotion.

Many-Objective optimization: an engineering design perspective

Evolutionary multicriteria optimization has traditionally concentrated on problems comprising 2 or 3 objectives. While engineering design problems can often be conveniently formulated as multiobjective optimization problems, these often comprise a relatively large number of objectives. Such problems pose new challenges for algorithm design, visualisation and implementation. Each of these three topics is addressed. Progressive articulation of design preferences is demonstrated to assist in reducing the region of interest for the search and, thereby, simplified the problem. Parallel coordinates have proved a useful tool for visualising many objectives in a two-dimensional graph and the computational grid and wireless Personal Digital Assistants offer technological solutions to implementation difficulties arising in complex system design.

Genetic Algorithms in Engineering Systems

From the Publisher: A broad survey of the current trends and techniques in genetic algorithms (GAs), which are general purpose search and optimisation methods applicable to a wide variety of problems. Theoretical innovations and practical applications in engineering systems are then discussed in the text.

Evolutionary many-objective optimisation: an exploratory analysis

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by NSGA-II, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance as the number of objectives is increased, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion.

Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization

The simultaneous optimization of many objectives (in excess of 3), in order to obtain a full and satisfactory set of tradeoff solutions to support a posteriori decision making, remains a challenging problem. The concept of coevolving a family of decision-maker preferences together with a population of candidate solutions is studied here and demonstrated to have promising performance characteristics for such problems. After introducing the concept of the preference-inspired coevolutionary algorithm (PICEA), a realization of this concept, PICEA-g, is systematically compared with four of the best-in-class evolutionary algorithms (EAs); random search is also studied as a baseline approach. The four EAs used in the comparison are a Pareto-dominance relation-based algorithm (NSGA-II), an ε-dominance relation-based algorithm [ ε-multiobjective evolutionary algorithm (MOEA)], a scalarizing function-based algorithm (MOEA/D), and an indicator-based algorithm [hypervolume-based algorithm (HypE)]. It is demonstrated that, for bi-objective problems, all of the multi-objective evolutionary algorithms perform competitively. As the number of objectives increases, PICEA-g and HypE, which have comparable performance, tend to outperform NSGA-II, ε-MOEA, and MOEA/D. All the algorithms outperformed random search.

Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimisation

This paper contributes a platform for the treatment of large numbers of criteria in evolutionary multi-criterion optimisation theory through consideration of the relationships between pairs of criteria. In a conflicting relationship, as performance in one criterion is improved, performance in the other is seen to deteriorate. If the relationship is harmonious, improvement in one criterion is rewarded with simultaneous improvement in the other. The criteria may be independent of each other, where adjustment to one never affects adjustment to the other. Increasing numbers of conflicting criteria pose a great challenge to obtaining a good representation of the global trade-off hypersurface, which can be countered using decision-maker preferences. Increasing numbers of harmonious criteria have no effect on convergence to the surface but difficulties may arise in achieving a good distribution. The identification of independence presents the opportunity for a divide-and-conquer strategy that can improve the quality of trade-off surface representations.