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Reporter : Mac Date : 2012.01.03 Multi-Start Method Rafael
Marti
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1.Introduction Search method based in local optimization need
some type of diversification. Multi-Start method. Re-Start
mechanisms
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2.Oeveview Two phases Generation Search Pseudo-code
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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.
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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
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2.Overview Genetic Algorithms Use TSP for testing Generation,
Combination, Local Search Stop Criteria Number of initial solutions
generated Number of objective function evaluations
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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
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2.Overview GRASP Unconstrained global optimization Quasirandom
samples Inexpensive local search terminates when no new local
minimum is found after several iterations
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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
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2.Overview Enhance multi-start approaches strongly determined
and consistent variables Strongly determined variables Value cant
be changed without significantly eroding consistent variables
receives a particular value in a significant portion of good
solutions. Based on Tabu Search framework
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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
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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.
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3.Classification Randomized solutions are generated in a random
way Systematic solutions are generated in a deterministic way
Combine Randomized and Systematic GRASP
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3.Classification Degree of Rebuild Rebuild Build
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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.
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3.1 Diversity Measures Cal 1 Case 2
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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
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4.Computational Experiments linear ordering problem (LOP)
Matrix of weight : Maximize the sum of the weight in the upper
triangle
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4.Computational Experiments
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G5, G4, G2, G1, DG, RND, G6, G3, MIX and FQ. The weight of
quality and diversity is equivalent
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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