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The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

A basic overview of optimization techniques is provided. The standard form of the general non-linear, constrained optimization problem is presented, and various techniques for solving the resulting optimization problem are discussed. The techniques are classified as either local (typically gradient-based) or global (typically nongradient based or evolutionary) algorithms. A great many optimization techniques exist and it is not possible to provide a complete review in the limited space available here. Instead, an effort is made to concentrate on techniques that are commonly used in engineering optimization applications. The review is kept general in nature, without considering special cases like linear programming, convex problems, multi-objective optimization, multidisciplinary optimization, etc. The advantages and disadvantages of the different techniques are highlighted, and suggestions are made to aid the designer in selecting an appropriate technique for a specific problem at hand. Where possible, a short overview of a representative method is presented to aid the discussion of that particular class of algorithms.

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel efficiency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example. Keywords: Particle Swarm Optimization, PSO, asynchronous parallel computing IntroductionParticle Swarm Optimization (PSO) is a fairly recent, but rapidly growing, addition to an expanding collection of non-gradient based, probabilistic search algorithms. Some widely used algorithms that fall into this category are genetic algorithms [1] that model Darwin's principle of survival of the fittest and simulated annealing algorithms [2] that model the equilibrium of large numbers of atoms during an annealing process. This class of optimization algorithms provides the designer with several attractive characteristics. For example, these algorithms are generally easy to implement, can efficiently make use of large numbers of parallel processors, do not require continuity in response functions and are better suited for finding global or near global solutions. Although these non-gradient based algorithms provide the designer with several advantages, they should be applied with care. Due to their high computational cost, these algorithms should only be used when a gradient-based algorithm is not a viable alternative, such as integer/discrete and discontinuous problems.Many non-gradient based search algorithms are based on some natural phenomena, and PSO is no exception. Particle swarm optimization is based on a simplified social model that is closely tied to swarming theory and was first introduced by Kennedy and Eberhart [3,4]. A physical analogy might be a school of fish that is adapting to its environment. In this analogy, each fish adapts to its environment by making use of its own memory as well as knowledge gained by the school as a whole.Although PSO is a fairly recent algorithm, it is quickly gaining momentum in the engineering research community. For example Fourie and Groenwold applied the algorithm to structu...

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