A computational algorithm for solving 0‐1 goal programming with GUB structures and its application for optimization problems in system reliability

Abstract

Upon to now, system optimal allocation problems such as system reliability and system availability problems have been formulated as single‐objective problems and solved through the use of various well‐developed optimization techniques. However, in this field, there are many problems that cannot be solved without applying MODM (multiple‐objective decision making) methods. These methods deal with multiple objectives that conflict with each other instead of formulating the problem as a single objective programming problem which optimizes only the reliability of the cost function, as is done in previous methods. GP (goal programming) is one of the most powerful MODM tools in this field. In practical MODM problems, many GP problems involve a large number of 0‐1 decision variables and a special type of 0‐1 variable, which arises during the transformation of non‐linear integer programming into 0‐1 linear programming. In this paper, we propose an efficient and specific algorithm for solving large‐scale 0‐1 GP problems in particular structures, which are termed GUB structures. Furthermore, to illustrate the effectiveness of the algorithm proposed here, we introduce two numerical examples from among the problems of system reliability, and compare the algorithm proposed with previous methods.

A note on a reliability redundancy allocation problem using a tuned parameter genetic algorithm

“…There are several methods to optimize NP-hard problems such as dynamic programming [26], integer programming [27], and meta-heuristics like GA [20,[28][29][30], particle swarm optimization [31][32][33], the cuckoo search (CS) algorithm [34], the bee algorithm [35]. Thus, we employ an improved meta-heuristic to optimize the model.…”

Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review

“…Gen et al (1989) develop computational algorithms for solving zero-one GP for optimization problem of system reliability for allocating redundant units. By extending this work, Gen et al (1990Gen et al ( 1993 propose an efficient algorithm for solving large scale zero-one problems with generalized upper bounding applied to problems in system reliability. Schniederjans and Karuppan (1995) propose a zero-one type GP model to select quality control attributes for data collection in service organizations.…”

Genetic algorithm for chance constrained reliability stochastic optimisation problems

“…Traditionally, many researchers have been using exact optimisation approaches to solve RAP which include dynamic programming (Nakagawa and Miyazaki, 1981), integer programming (Gen et al, 1990), mixed integer and non-linear programming. Two most familiar methods of improving system reliability are to increase the reliability of the components and/or add redundancy.…”