Abstract
In this paper, we target the problems of finding a global minimum of nonlinear and stochastic programming problems. To solve this type of problem, we propose new approaches based on combining direct search methods with Evolution Strategies (ESs) and Scatter Search (SS) metaheuristics approaches. First, we suggest new designs of ESs and SS with a memory-based element called Gene Matrix (GM) to deal with those type of problems. These methods are called Directed Evolution Strategies (DES) and Directed Scatter Search (DSS), respectively, and they are able to search for a global minima. Moreover, a faster convergence can be achieved by accelerating the evolutionary search process using GM, and in the final stage we apply the Nelder-Mead algorithm to find the global minimum from the solutions found so far. Then, the variable-sample method is invoked in the DES and DSS to compose new stochastic programming techniques. Extensive numerical experiments have been applied on some well-known functions to test the performance of the proposed methods.
Highlights
IntroductionThere are many challenging applications which naturally require involving optimization techniques to have the best configurations, and find the optimal resources [1]
In the real world, there are many challenging applications which naturally require involving optimization techniques to have the best configurations, and find the optimal resources [1].In particular, these complex application problems are computationally expensive in a sense of resources and time and most of them contain noise
Algorithm compared to the other methods at a large number of function evaluation. These results demonstrate the standing of the Directed Scatter Search (DSS) method on the exploration process, which requests a high cost of function evaluations to guarantee good coverage to the search space
Summary
There are many challenging applications which naturally require involving optimization techniques to have the best configurations, and find the optimal resources [1] These complex application problems are computationally expensive in a sense of resources and time and most of them contain noise. Trials to compute the derivatives using finite differences methods mostly fail Such real complex systems are usually modeled using a series of simulation procedures to evaluate their output responses. They are integrated with an optimization algorithm to find their optimal parameters. The integration of the stochastic optimization methods into simulation software packages to meet their design requirements is crucial
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