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However, remote access to EBSCO's databases from non-subscribing institutions is not allowed if the purpose of the use is for commercial gain through cost reduction or avoidance for a non-subscribing institution. Author s : Kaur, Jaspreet; Goyal, Sonia. Abstract: Antenna array is defined as a collection of multiple radiating elements antennas which are placed in space in uniform or non- uniform manner to get a directional radiation pattern that a single antenna generally not adequate to achieve it.

In antenna array pattern side lobe level and deep nulls are major problems which cause wastage of energy. Thus, it just needs to recalculate the affected products and the affected periods of the setup cost and inventory holding cost after a mutation operation. By taking this advantage, the computing efficiency of IVND algorithm can be significantly improved since the recalculation of the objective function--the most time-consuming part of IVND algorithm, are avoided.

The above six implemental techniques are all used in our proposed IVND algorithm to mutate the incumbent solution into its neighborhood. Steps of implementing these techniques on neighborhood search, e. Although the new solutions from N k x may has a greater than k unit distance from the incumbent solution x after implemented with these six implemental techniques, it is still considered as a member of N k x.

These implemental techniques are only deemed as additional actions implemented on the new solution toward better solution. Moreover, benefiting from these actions, higher efficiency of VNS algorithm could be consequently anticipated, which has been confirmed in the experiments of Section 4.

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It starts from initiating a solution as the incumbent solution, and then launches a VND search. The VND search repeatedly tries of finding a better solution in the nearby neighborhood of the incumbent solution and moves to the better solution found; if a better solution cannot be found in current neighborhood, then go to explore a father neighborhood until the farthest neighborhood is reached. Once the VND process is stopped characterized by the farthest neighborhood been explored , another initial solution is randomly generated and restarts the VND search again.

This simply iterated search process loops until the stop condition is met. The stop condition can be a user-specified computing time or a maximum span between two restarts without improvement on the best solution found. In our experiments of the next section, we use the later one, i. There are three parameters, i. The first parameter P is a positive number which serves as a stop condition indicating the maximum span between two restarts without improvement on best solution found. The second parameter N is the maximum number of explorations between two improvements within a neighborhood.

The third parameter K max is the traditional parameter for VND search indicating the farthest neighborhood that the algorithm will go. The first set consists of 96 small-sized MLLS problems involving 5-item assembly structure over a period planning horizon, which was developed by Coleman and McKnew on the basis of work by Veral and LaForge and Benton and Srivastava , and also used by Dellaert and Jeunet a. In the 96 small-sized problems, four typical product structures with an one-to-one production ratio are considered, and the lead times of all items are zero.

For each product structure, four cost combinations are considered, which assign each individual item with different setup costs and different unit holding costs. Six independent demand patterns with variations to reflect low, medium and high demand are considered over a period planning horizon. The optimal solutions of 96 benchmark problem are previously known so that can serve as benchmark for testing against the optimality of the new algorithm. In the 40 medium-sized problems, four product structures with an one-to-one production ratio are constructed. Two of them are item assembly structures with 5 and 9 levels, respectively.

The other two are item general structure with 8 and 6 levels, respectively. All lead times were set to zero. Two planning horizons were used: 12 and 24 periods.

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There are 20 different product structures with one-to-one production ratio and different commonality indices [1] -. The first 5 instances are pure assembly structures with one end-product. The instances from 6 to 20 are all general structure with five end-products and different communality indices ranges from 1. The first 20 instances are all over a period planning horizon; the second 20 instances are of the same product structures of the first 20 instances but over a period planning horizon. The demands are different for each instances and only on end-products.

Since the hybrid GA algorithm developed by Dellaert and Jeunet a is the first meta-heuristic algorithm for solving the MLLS problem, it was always selected as a benchmark algorithm for comparison with newly proposed algorithm. Therefore, we compared the performance of our IVND algorithm with the hybrid GA algorithm on the all instances of three different scales. We fixed the parameter K max to be 5 for all experiments, and let the parameter P and N changeable to fit for the different size of problem.

The effect of individual parameter on the quality of solution was tested in section 5. We repeatedly ran IVND 50 on the 96 small-sized MLLS problems for 10 times and got results among which were the optimal results so the optimality was The column average time s indicates the average computing time in second of one run for each problem. After that, we adjust the parameter P from 50 to and repeatedly ran IVND on the 96 problems for 10 times again. We summarize the results and compare them with the existing algorithms in Table 5.

More detailed results of 40 problems are listed in Table 6 where the previous best known solutions summarized by Homberger are also listed for comparison. After that, we repeatedly ran IVND algorithm for several times and updated the best solutions for these 40 medium-sized problems which are listed in column new best solution in Table 6. Furthermore, by taking account into consideration of hardware advantage of the PGAC algorithm multiple processors and higher CPU speed , we can say that the IVND algorithm performances at least as best as the PGAC algorithm on medium-sized problems, if not better than.

We summarize the results and compare them with the existing algorithms in Table 7 , and show detailed results of 40 problems in Table 8. The average computing time for each problem used by IVND algorithm was relatively low. However, four problems, i.

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The column Inter D. Finally, we used the 40 medium-sized problems to test parameters, i. We did three experiments by varying one parameter while fixing other two parameters. The average costs gotten by the three experiments against varied parameters are shown in Table 9. A general trend can be observed that increases parameter P , N or K max will all lead to better solutions been found but at the price of more computing time.

However, all the parameter may contribute less to the quality of solution when they are increased large enough.

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Obviously, the best effectiveness-cost combination of these parameters exists for the IVND algorithm which is a worthwhile work to do in future works, but we just set these parameters manually in our experiments. The consideration of meta-heuristic is widly used in a lot of fields. Deffirent meta-heuristic algorithms are developed for solving deffirent problems, especially combinational optimization problems.

In this chapter, we discussed a special case of MLLS problem. First, the general definition of MLLS problem was described. We shown its solution structure and explained its NP completeness. Second, we reviewed the meta-heuristic algorithms which have been use to solve the MLLS problem and pointed their merits and demerits. Based on the recognition, third, we investigated those implement techniques used in the meta-heuristic algorithms for solving the MLLS problems. And two criteria of distance and range were firstly defined to evaluate the effective of those techniques. We brifly discussed the mechanisms and characteristics of the techniques by using these two criteria, and provided simulation experiments to prove the correctness of the two criteria and to explain the performance and utility of them.

This is one of our contributions. The IVND algorithm was evaluated by using benchmark problems of different scales small, medium and large from literatures. Experiments on other two sets of benchmark problems 40 medium-sized problems and 40 large-sized problems showed it good efficiency and effectiveness on solving MLLS problem with product structure complex. For the 40 large-sized problems, the IVND algorithm delivered even more exciting results on the quality of solution. Comparison of the best solutions achieved with the new method and those established by previous methods including HGA, MMAS, and PGA shows that the IVND algorithm with the six implemental techniques are till now among the best methods for solving MLLS problem with product structure complexity considered, not only because it is easier to be understood and implemented in practice, but more importantly, it also provides quite good solutions in very acceptable time.

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This chapter is distributed under the terms of the Creative Commons Attribution 3. Help us write another book on this subject and reach those readers. Login to your personal dashboard for more detailed statistics on your publications. Edited by Javier Del Ser Lorente. We are IntechOpen, the world's leading publisher of Open Access books.

Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. Downloaded: Meta-heuristic algorithms used to solve MLLS problems The meta-heuristic algorithms are widely used to refer to simple, hybrid and population-based stochastic local searching Hoos and Thomas Particle swarm optimization Particle swarm optimization PSO is also a meta-heuristic algorithm formally introduced Han et al, , Table 1.

The implement techniques used in various algorithms. Distance Better solutions Ratio 1 Table 2. Table 3. Implemental techniques Here six implemental techniques are used in the IVND algorithm which are integrated together to deliver good performance in the computing experiments. Computational experiments and the results 5. Method Avg. Of 10 Table 4. Comparing IVND with existing algorithms on 96 small-sized problems. Table 5. Comparing IVND with existing algorithms on 40 medium-sized problems.

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Table 6. Results of 40 medium-sized problems and the new best solutions. Cost Optimality on prev. Table 7. Comparing IVND with existing algorithms on 40 large-sized problems. Table 8. Results of 40 large-sized problems and the new best solutions. The effectiveness of individual parameter of VIND Finally, we used the 40 medium-sized problems to test parameters, i.

P N Kmax Avg. Cost of 10 runs Comp. Table 9. Experimental results of different parameters for medium-sized problem. Summarization The consideration of meta-heuristic is widly used in a lot of fields. Notes Commonality index is the average number of successors of all items in a product structure. More Print chapter. How to cite and reference Link to this chapter Copy to clipboard.

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