Geoffrey T. Parks

a species conserving genetic algorithm for multimodal function optimization

This paper introduces a new technique called species conservation for evolving parallel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current generation are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.

A SIMULATED ANNEALING ALGORITHM FOR MULTIOBJECTIVE OPTIMIZATION

This paper describes a novel implementation of the Simulated Annealing algorithm designed to explore the trade-off between multiple objectives in optimization problems. During search, the algorithm maintains and updates an archive of non-dominated solutions between each of the competing objectives. At the end of search, the final archive corresponds to a number of optimal solutions from which the designer may choose a particular configuration. A new acceptance probability formulation based on an annealing schedule with multiple temperatures (one for each objective) is proposed along with a novel restart strategy. The performance of the algorithm is demonstrated on three examples. It is concluded that the proposed algorithm offers an effective and easily implemented method for exploring the trade-off in multiobjective optimization problems.

The development of a multi-objective Tabu Search algorithm for continuous optimisation problems

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.

Selective Breeding in a Multiobjective Genetic Algorithm

This paper describes an investigation of the efficacy of various elitist selection strategies in a multiobjective Genetic Algorithm implementation, with parents being selected both from the current population and from the archive record of nondominated solutions encountered during search. It is concluded that, because the multiobjective optimization process naturally maintains diversity in the population, it is possible to improve the performance of the algorithm through the use of strong elitism and high selection pressures without suffering the disadvantages of genetic convergence which such strategies would bring in single objective optimization.

An intelligent stochastic optimization routine for nuclear fuel cycle design

A simulated annealing (Metropolis algorithm) optimization routine named AMETROP, which has been developed for use on realistic nuclear fuel cycle problems, is introduced. Each stage of the algorithm is described and the means by which it overcomes or avoids the difficulties posed to conventional optimization routines by such problems are explained. Special attention is given to innovations that enhance AMETROPs performance both through artificial intelligence features, in which the routine uses the accumulation of data to influence its future actions, and through a family of simple performance aids, which allow the designer to use his heuristic knowledge to guide the routines essentially random search. Using examples from a typical fuel cycle optimization problem, the performance of the stochastic Metropolis algorithm is compared to that of the only suitable deterministic routine in a standard software library, showing AMETROP to have many advantages.

Robust Aerodynamic Design Optimization Using Polynomial Chaos

This paper investigates the potential of polynomial chaos methods, when used in conjunction with computational fluid dynamics, to quantify the effects of uncertainty in the computational aerodynamic design process. The technique is shown to be an efficient and accurate means of simulating the inherent uncertainty and variability in manufacturing and flow conditions and thus can provide the basis for computationally feasible robust optimization with computational fluid dynamics. This paper presents polynomial chaos theory and the nonintrusive spectral projection implementation, using this to demonstrate polynomial chaos as a basis for robust optimization, focusing on the problem of maximizing the lift-to-drag ratio of a two-dimensional airfoil while minimizing its sensitivity to uncertainty in the leading-edge thickness. The results demonstrate that the robustly optimized designs are significantly less sensitive to input variation, compared with nonrobustly optimized airfoils. The results also indicate that the inherent geometric uncertainty could degrade the on-design as well as the offdesign performance of the nonrobust airfoil. This leads to the further conclusion that the global optimum for some design problems is unreachable without accounting for uncertainty.

Biobjective Design Optimization for Axial Compressors Using Tabu Search

At present, optimization is an enabling technology in innovation. Multi-objective and multidisciplinary optimization tools are essential in the design process for real-world applications. In turbomachinery design, these approaches give insight into the design space and identify the tradeoffs between the competing performance measures. This paper describes the application of a novel multi-objective variant of the tabu search algorithm to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and eventually of the whole engine. The integrated system developed for this purpose is described. It combines the optimizer with an existing geometry parameterization scheme and a well-established computational fluid dynamics package. Its performance is illustrated through a case study in which the flow characteristics most important to the overall performance of turbomachinery blades are optimized.

Optimal design of functionally graded materials using a procedural model and particle swarm optimization

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples.

Engineering design optimization using species-conserving genetic algorithms

The species conservation technique described here, in which the population of a genetic algorithm is divided into several groups according to their similarity, is inspired by ecology. Each group with similar characteristics is called a species and is centred on a dominating individual, called the species seed. A genetic algorithm based on this species conservation technique, called the species-conserving genetic algorithm (SCGA), was established and has been proved to be effective in finding multiple solutions of multimodal optimization problems. In this article, the SCGA is used to solve engineering design optimization problems. Different distance measures (measures of similarity) are investigated to analyse the performance of the SCGA. It is shown that the Euclidean distance is not the only possible basis for defining a species and sometimes may not make sense in engineering applications. Two structural design problems are used to demonstrate how the choice of a meaningful measure of similarity will help the exploration for significant designs.

Multi-objective Parallel Tabu Search

This paper describes the implementation of a parallel Tabu Search algorithm for multi-objective continuous optimisation problems. We compare our new algorithm with a leading multi-objective Genetic Algorithm and find it exhibits comparable performance on standard benchmark problems. In addition, for certain problem types, we expect Tabu Search to outperform other algorithms and present preliminary results from an aerodynamic shape optimisation problem. This is a real-world, highly constrained, computationally demanding design problem which requires efficient optimisation algorithms that can be run on parallel computers: with this approach optimisation algorithms are able to play a part in the design cycle.