模擬退火法應用在離散型模擬最佳化問題上

邱容彬

doi:10.6840/cycu200400294

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模擬退火法應用在離散型模擬最佳化問題上

Simulated Annealing Algorithms for Discrete Simulation Optimization Problems

邱容彬 , Masters　　Advisor：陳慧芬　　

英文 DOI： 10.6840/cycu200400294

模擬退火法；回溯近似法；隨機搜尋法；隨機比較；離散型模擬最佳化； Discr ； Simulated Annealing ； Retrospective Approximation

Abstract │ Reference (151) │ Altmetrics

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We consider the discrete simulation optimization problem, finding the optimal
point (in a discrete set) that minimizes the objective function, where the function
value is difficult to compute but can be estimated by simulation experiments. Such
problems occur in system <a href="http://www.ntsearch.com/search.php?q=design&v=56">design</a>. The decision variables are system parameter values to be determined and the objective function value is the associate system cost. The optimization problem is to find the system parameter values that minimize the system cost under certain constraints. Applications of discrete stochastic optimization include the <a href="http://www.ntsearch.com/search.php?q=network&v=56">network</a> <a href="http://www.ntsearch.com/search.php?q=design&v=56">design</a>, supply chains <a href="http://www.ntsearch.com/search.php?q=design&v=56">design</a>, scheduling, and inventory control.
Several methods have been developed for discrete simulation optimization problems. Depending on the number of decision variables, there are two branches: (i)infinite or many, and (ii) finite but a few. This research considers only the first branch. Available algorithms include heuristic methods (e.g., simulated annealing, tabu <a href="http://www.ntsearch.com/search.php?q=search&v=56">search</a>, and genetic algorithm), random <a href="http://www.ntsearch.com/search.php?q=search&v=56">search</a> methods (e.g., pure random <a href="http://www.ntsearch.com/search.php?q=search&v=56">search</a> and stochastic ruler), and sample path methods. The existing methods usually use a big sample size to make the sample-path problem mimics the real problem. The disadvantage is that each function evaluation takes a long computation <a href="http://www.ntsearch.com/search.php?q=time&v=56">time</a> and hence decreases the algorithm efficiency.
We propose the SADRA algorithm for solving discrete simulation optimization
problems. SADRA uses the DRA (dependent retrospective approximation) idea to
iteratively solve a sequence of sample-path problems with increasing sample size. Each sample-path problem is then solved by the heuristic SA (simulated annealing) algorithm.
Simulation experiments are run to evaluate the performance of SADRA and compare it to four existing algorithms. The algorithm performance measures used are the mean square error MSEf in function values and the convergent path (i.e., the percentage of replications that converge). A smaller MSEf and a big CP are preferred. Our simulation results show that SADRA converges and converges faster than the four existing algorithms. The sensitivity analysis is also conducted to study the influence of algorithm parameters to the algorithm performance. Simulation results show that a smaller neighborhood structure (for simulated annealing) works better when the objective function is smooth and has only one optimal point. A random neighborhood strategy works better when many local optima exist.

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LIST OF REFERENCES
連結：
[1] Alander, J. T. (1992). On optimal population size of genetic algorithms. Proc.
連結：
with Constant Temperature for Discrete Stochastic Optimization. Management
連結：
Ruler Method for Discrete Stochastic Optimization. European Journal of Operation
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[4] Andrad’ottir, S. (1995). A Method for Discrete Stochastic Optimization. Management
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