• Title/Summary/Keyword: Hill climbing method

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Evaluating Reverse Logistics Networks with Centralized Centers : Hybrid Genetic Algorithm Approach (집중형센터를 가진 역물류네트워크 평가 : 혼합형 유전알고리즘 접근법)

  • Yun, YoungSu
    • Journal of Intelligence and Information Systems
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    • v.19 no.4
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    • pp.55-79
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    • 2013
  • In this paper, we propose a hybrid genetic algorithm (HGA) approach to effectively solve the reverse logistics network with centralized centers (RLNCC). For the proposed HGA approach, genetic algorithm (GA) is used as a main algorithm. For implementing GA, a new bit-string representation scheme using 0 and 1 values is suggested, which can easily make initial population of GA. As genetic operators, the elitist strategy in enlarged sampling space developed by Gen and Chang (1997), a new two-point crossover operator, and a new random mutation operator are used for selection, crossover and mutation, respectively. For hybrid concept of GA, an iterative hill climbing method (IHCM) developed by Michalewicz (1994) is inserted into HGA search loop. The IHCM is one of local search techniques and precisely explores the space converged by GA search. The RLNCC is composed of collection centers, remanufacturing centers, redistribution centers, and secondary markets in reverse logistics networks. Of the centers and secondary markets, only one collection center, remanufacturing center, redistribution center, and secondary market should be opened in reverse logistics networks. Some assumptions are considered for effectively implementing the RLNCC The RLNCC is represented by a mixed integer programming (MIP) model using indexes, parameters and decision variables. The objective function of the MIP model is to minimize the total cost which is consisted of transportation cost, fixed cost, and handling cost. The transportation cost is obtained by transporting the returned products between each centers and secondary markets. The fixed cost is calculated by opening or closing decision at each center and secondary markets. That is, if there are three collection centers (the opening costs of collection center 1 2, and 3 are 10.5, 12.1, 8.9, respectively), and the collection center 1 is opened and the remainders are all closed, then the fixed cost is 10.5. The handling cost means the cost of treating the products returned from customers at each center and secondary markets which are opened at each RLNCC stage. The RLNCC is solved by the proposed HGA approach. In numerical experiment, the proposed HGA and a conventional competing approach is compared with each other using various measures of performance. For the conventional competing approach, the GA approach by Yun (2013) is used. The GA approach has not any local search technique such as the IHCM proposed the HGA approach. As measures of performance, CPU time, optimal solution, and optimal setting are used. Two types of the RLNCC with different numbers of customers, collection centers, remanufacturing centers, redistribution centers and secondary markets are presented for comparing the performances of the HGA and GA approaches. The MIP models using the two types of the RLNCC are programmed by Visual Basic Version 6.0, and the computer implementing environment is the IBM compatible PC with 3.06Ghz CPU speed and 1GB RAM on Windows XP. The parameters used in the HGA and GA approaches are that the total number of generations is 10,000, population size 20, crossover rate 0.5, mutation rate 0.1, and the search range for the IHCM is 2.0. Total 20 iterations are made for eliminating the randomness of the searches of the HGA and GA approaches. With performance comparisons, network representations by opening/closing decision, and convergence processes using two types of the RLNCCs, the experimental result shows that the HGA has significantly better performance in terms of the optimal solution than the GA, though the GA is slightly quicker than the HGA in terms of the CPU time. Finally, it has been proved that the proposed HGA approach is more efficient than conventional GA approach in two types of the RLNCC since the former has a GA search process as well as a local search process for additional search scheme, while the latter has a GA search process alone. For a future study, much more large-sized RLNCCs will be tested for robustness of our approach.

Optimal Design for Marker-assisted Gene Pyramiding in Cross Population

  • Xu, L.Y.;Zhao, F.P.;Sheng, X.H.;Ren, H.X.;Zhang, L.;Wei, C.H.;Du, L.X.
    • Asian-Australasian Journal of Animal Sciences
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    • v.25 no.6
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    • pp.772-784
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    • 2012
  • Marker-assisted gene pyramiding aims to produce individuals with superior economic traits according to the optimal breeding scheme which involves selecting a series of favorite target alleles after cross of base populations and pyramiding them into a single genotype. Inspired by the science of evolutionary computation, we used the metaphor of hill-climbing to model the dynamic behavior of gene pyramiding. In consideration of the traditional cross program of animals along with the features of animal segregating populations, four types of cross programs and two types of selection strategies for gene pyramiding are performed from a practical perspective. Two population cross for pyramiding two genes (denoted II), three population cascading cross for pyramiding three genes(denoted III), four population symmetry (denoted IIII-S) and cascading cross for pyramiding four genes (denoted IIII-C), and various schemes (denoted cross program-A-E) are designed for each cross program given different levels of initial favorite allele frequencies, base population sizes and trait heritabilities. The process of gene pyramiding breeding for various schemes are simulated and compared based on the population hamming distance, average superior genotype frequencies and average phenotypic values. By simulation, the results show that the larger base population size and the higher the initial favorite allele frequency the higher the efficiency of gene pyramiding. Parents cross order is shown to be the most important factor in a cascading cross, but has no significant influence on the symmetric cross. The results also show that genotypic selection strategy is superior to phenotypic selection in accelerating gene pyramiding. Moreover, the method and corresponding software was used to compare different cross schemes and selection strategies.