Reporter : Mac Date : Multi-Start Method Rafael Marti

1.Introduction Search method based in local optimization need some type of diversification. Multi-Start method. Re-Start mechanisms

2.Oeveview Two phases Generation Search Pseudo-code

2.Overview Tabu Search Adaptive memory design. Use different memory function to design restarting mechanisms. Adaptive memory strategies Combinatorial optimization problems. Based on memory structure.

2.Overview Devoted to the Monte Carlo random re-start in the context of nonlinear unconstrained optimization. Combine Monte Carlo method with LS. Reduce the number of complete local search increase the probability that they start from points close to the global optimum

2.Overview Genetic Algorithms Use TSP for testing Generation, Combination, Local Search Stop Criteria Number of initial solutions generated Number of objective function evaluations

2.Overview 6 benchmark problem TSP, JSP, knapsack, bin packing, neural network weight optimization, numerical function optimization. Multiple restart stochastic hill-climbing(MRSH) solutions are represented with strings local search based on random flip of bits

2.Overview GRASP Unconstrained global optimization Quasirandom samples Inexpensive local search terminates when no new local minimum is found after several iterations

2.Overview Clustering Adaptive Multi Start method (CAMS) Solve VLSI. a set of random starting points and local search adaptive starting points that are central to the best local minimum solutions found so far

2.Overview Enhance multi-start approaches strongly determined and consistent variables Strongly determined variables Value can’t be changed without significantly eroding consistent variables receives a particular value in a significant portion of good solutions. Based on Tabu Search framework

2.Overview For Capacitated Minimum Spanning Tree Problem Adaptive Reasoning Techniques, proposed in the tabu search framework able to learn about, and modify the behavior of a primary greedy heuristic. Path Relinking within GRASP

3.Classification Memory identify elements that are common to good previously generated solutions Memory-less It is not as unreasonable as might be imagined since the construction of “unconnected” solutions may be interpreted as a means of strategically sampling the solution space.

3.Classification Randomized solutions are generated in a random way Systematic solutions are generated in a deterministic way Combine Randomized and Systematic GRASP

3.Classification Degree of Rebuild Rebuild Build

3.1 Diversity Measures 1. Calculate the median position of each element i in the solutions in P. 2. Calculate the dissimilarity of each solution in the population with respect to the median solution 3. Calculate d as the sum of all the individual dissimilarities.

3.1 Diversity Measures Cal 1 Case 2

3.1 Diversity Measures The notion of influence introduced by Glover (1990) in the context of Tabu Search The influence considers the potential and the structure of a solution in the search process. conclusion

4.Computational Experiments linear ordering problem (LOP) Matrix of weight : Maximize the sum of the weight in the upper triangle

4.Computational Experiments

G5, G4, G2, G1, DG, RND, G6, G3, MIX and FQ. The weight of quality and diversity is equivalent

5.Conclusion The objective of this study has been to extend and advance the knowledge associated to implementing multi-start procedures. It has not yet become widely implemented and tested as a metaheuristic itself for solving complex optimization problems