Penalty function approach in heuristic algorithms for constrained redundancy reliability optimization

To solve the problem of constrained redundancy reliability optimization, several heuristic algorithms have been developed in the literature. Most of these algorithms search for the solutions remaining within the feasible boundary e.g. [15], [20]. Perhaps the most interesting & efficient heuristic algorithm in terms of solution quality is that given by KYA [9], in which the search is made not only in the feasible region but also into the bounded infeasible region by making an excursion, which returns to the feasible region with a possibly improved solution. In this paper, a heuristic algorithm based on the penalty function approach is proposed to solve the constrained redundancy optimization problem for complex systems. An excursion is made into the infeasible region, but an adaptive penalty function helps the search not to go too far into the infeasible region. Thus, promising feasible & infeasible regions of the search space are explored efficiently & effectively to identify finally an optimal or near optimal solution. Computational experiments are conducted on 11 sets of problems (10 with linear constraints, and 1 with nonlinear constraints); each with 10 different randomly generated initial solutions. Comparison is made between the proposed algorithm P-Alg, N-N algorithm [15], Shi algorithm [20], and KYA [9]. It is observed that P-Alg performs consistently better than others, showing an overall improvement in various measures of performance. Besides, as P-Alg does not require any assumptions on the nature of the objective & constraint functions, it can solve a wide variety of problems.