Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem. Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.

Theory and practice of uncertain programming

A problem-specific genetic algorithm (GA) is developed and demonstrated to analyze series-parallel systems and to determine the optimal design configuration when there are multiple component choices available for each of several k-out-of-n:G subsystems. The problem is to select components and redundancy-levels to optimize some objective function, given system-level constraints on reliability, cost, and/or weight. Previous formulations of the problem have implicit restrictions concerning the type of redundancy allowed, the number of available component choices, and whether mixing of components is allowed. GA is a robust evolutionary optimization search technique with very few restrictions concerning the type or size of the design problem. The solution approach was to solve the dual of a nonlinear optimization problem by using a dynamic penalty function. GA performs very well on two types of problems: (1) redundancy allocation originally proposed by Fyffe, Hines, Lee, and (2) randomly generated problem with more complex k-out-of-n:G configurations.

Reliability optimization of series-parallel systems using a genetic algorithm

Metaheuristics are the most exciting development in approximate optimization techniques of the last two decades. They have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas. This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics. Metaheuristics include but are not limited to constraint logic programming; greedy random adaptive search procedures; natural evolutionary computation; neural networks; non-monotonic search strategies; space-search methods; simulated annealing; tabu search; threshold algorithms and their hybrids. References are presented in alphabetical order under a number of subheadings.

Metaheuristics: A bibliography

This paper provides: an overview of the methods that have been developed since 1977 for solving various reliability optimization problems; applications of these methods to various types of design problems; and heuristics, metaheuristic algorithms, exact methods, reliability-redundancy allocation, multi-objective optimization and assignment of interchangeable components in reliability systems. Like other applications, exact solutions for reliability optimization problems are not necessarily desirable because exact solutions are difficult to obtain, and even when they are available, their utility is marginal. A majority of the work in this area is devoted to developing heuristic and metaheuristic algorithms for solving optimal redundancy-allocation problems.

An annotated overview of system-reliability optimization

Evolutionary algorithms in control systems engineering: a survey

After initial production, improvements are often made to components of a system, to upgrade system performance; for example, when designing a later version or release. This paper presents an optimization model that identifies the types of component improvements and the level of effort spent on those improvements to maximize one or more performance measures (e.g., system reliability or availability) subject to constraints (e.g., cost) in the presence of uncertainty about the component failure rates. For each component failure mode, some possible improvements are identified along with their cost and the resulting improvement in failure rates for that failure mode. The objective function is defined as a stochastic function of the performance measure of interest-in this case, 5/sup th/ percentile of the mean time-between-failure distribution. The problem formulation is combinatorial and stochastic. Genetic algorithms are used as the solution method. Our approach is demonstrated on a case study of a personal computer system. Results and comparison with enumeration of the configuration space show that genetic algorithms perform very favorably in the face of noise in the output: they are able to find the optimum over a complicated, high dimensional, nonlinear space in a tiny fraction of the time required for enumeration. The integration of genetic algorithm optimization capabilities with reliability analysis can provide a robust, powerful design-for-reliability tool. >

Genetic algorithms in optimization of system reliability

This paper examines a novel optimization technique called genetic algorithms and its application to the optimization of reliability allocation strategies. Reliability allocation should occur in the initial stages of design, when the objective is to determine an optimal breakdown or allocation of reliability to certain components or subassemblies in order to meet system specifications. The reliability allocation optimization is applied to the design of a cluster tool, a highly complex piece of equipment used in semiconductor manufacturing. The problem formulation is presented, including decision variables, performance measures and constraints, and genetic algorithm parameters. Piecewise ``effort curves`` specifying the amount of effort required to achieve a certain level of reliability for each component of subassembly are defined. The genetic algorithm evolves or picks those combinations of ``effort`` or reliability levels for each component which optimize the objective of maximizing Mean Time Between Failures while staying within a budget. The results show that the genetic algorithm is very efficient at finding a set of robust solutions. A time history of the optimization is presented, along with histograms or the solution space fitness, MTBF, and cost for comparative purposes.

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James Campbell

Papers

Genetic algorithms in optimization of system reliability

Optimization of reliability allocation strategies through use of genetic algorithms