A New Multiple Objective Evolutionary Algorithm for Reliability Optimization of Series-Parallel Systems

A New Multiple Objective Evolutionary Algorithm for Reliability Optimization of Series-Parallel Systems

Heidi A. Taboada (The University of Texas at El Paso, USA) and David W. Coit (Rutgers, The State University of New Jersey, USA)
Copyright: © 2012 |Pages: 18
DOI: 10.4018/jaec.2012040101
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Abstract

A new multiple objective evolutionary algorithm is proposed for reliability optimization of series-parallel systems. This algorithm uses a genetic algorithm based on rank selection and elitist reinsertion and a modified constraint handling method. Because genetic algorithms are appropriate for high-dimensional stochastic problems with many nonlinearities or discontinuities, they are suited for solving reliability design problems. The developed algorithm mainly differs from other multiple objective evolutionary algorithms in the crossover operation performed and in the fitness assignment. In the crossover step, several offspring are created through multi-parent recombination. Thus, the mating pool contains a great amount of diverse solutions. The disruptive nature of the proposed type of crossover, called subsystem rotation crossover, encourages the exploration of the search space. The paper presents a multiple objective formulation of the redundancy allocation problem. The three objective functions that are simultaneously optimized are the maximization of system reliability, the minimization of system cost, and the minimization of system weight. The proposed algorithm was thoroughly tested and a performance comparison of the proposed algorithm against one well-known multiple objective evolutionary algorithms that currently exists shows that the algorithm has a better performance when solving multiple objective redundant allocation problems.
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Multiple Objective Optimization

Multiple objective optimization refers to the solution of problems with two or more objectives to be satisfied simultaneously. Often, such objectives are in conflict with each other and are expressed in different units. Because of their nature, multiple objective optimization problems normally have, not one, but a set of solutions, which are called Pareto-optimal solutions or nondominated solutions (Chankong & Haimes, 1983; Hans, 1988). When such solutions are represented in the objective function space, the graph produced is called the Pareto front or the Pareto-optimal set of the problem.

In general, there are two primary approaches for the solution of a multiple objective problem. The first approach involves determining the relative importance of the attributes, and aggregating the attributes into some kind of overall composite objective function (sometimes called a value or utility function); while the second approach involves populating a number of feasible solutions along a Pareto frontier and the final solution is a set of non-dominated solutions. MOEAs are the most notable methods from this second approach.

A general formulation of a multiple objective optimization problem consists of a number of objectives with a number of inequality and equality constraints. Mathematically, the problem can be written as in Equation 1 (Rao, 1991):minimize / maximize f(x) (1) subject to:j = 1, 2, …, Jk = 1, 2, …, Kwhere,

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