In this paper the problem of permutation flow shop scheduling with the objectives of minimizing the makespan and total flow time of jobs is considered. A Pareto-ranking based multi-objective genetic algorithm, called a Pareto genetic algorithm (GA) with an archive of non-dominated solutions subjected to a local search (PGA-ALS) is proposed. The proposed algorithm makes use of the principle of non-dominated sorting, coupled with the use of a metric for crowding distance being used as a secondary criterion. This approach is intended to alleviate the problem of genetic drift in GA methodology. In addition, the proposed genetic algorithm maintains an archive of non-dominated solutions that are being updated and improved through the implementation of local search techniques at the end of every generation. A relative evaluation of the proposed genetic algorithm and the existing best multi-objective algorithms for flow shop scheduling is carried by considering the benchmark flow shop scheduling problems. The non-dominated sets obtained from each of the existing algorithms and the proposed PGA-ALS algorithm are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by the proposed PGA-ALS.
Placement and routing of fluid power valves impact operational or manufacturing costs. Choosing the right placement that provides optimum routing configuration, and subsequently determining the optimum routing for a given placement, are both hard problems. Evolutionary algorithms, for two categories, are developed here to determine the placement of the valves, based on the optimal routing configuration that minimizes costs. The two categories we consider are a) the placement of conventional valves on a valve-stand and b) the placement of cartridge valves on a manifold block. Our results meet or exceed experienced designers’ solutions.
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