Memory-Based Evolutionary Algorithms for Nonlinear and Stochastic Programming Problems

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.

Simulation-Based EDAs for Stochastic Programming Problems

“…The heuristic solution x is said to be optimal in case of the gap defined in Equation (6) being less than or equal to 0.001. Table 6 reported the average f Gap for 25 independent runs of EDA method for each function, and it is compared with the Directed Scatter Search (DSS) method, which is introduced in [51] with 5000 maximum number of function evaluations for each method. The results shown in Table 6 that the performance of the EDA-D code show promising performance, and its f Gap values show its ability of obtaining global minima for 6 of 10 test problems.…”

“…The proposed method has been compared with another metahuristic method to demonstrate its performance in terms of simulation optimization. The EDA-MMSS method has been compared with Evolution Strategies and Scatter Search for a simulation-based global optimization problem, which is introduced in [51]. Table 10 shows the comparison among the proposed method, Directed Evolution Strategies for Simulation-based (DESSP), and Scatter Search for Simulation-Based Optimization (DSSSP).…”

“…For simulation-based optimization, two different benchmark test sets are used. The first one (SBO-Set A) consists of four well-known classical test functions; Goldstein and Price, Rosenbrock, Griewank, and Pinter functions that are used to compose seven test problems ( f 1 -f 7 ) [49][50][51]. The details of these seven test functions are shown in Table 2.…”

Evolutionary Algorithms Enhanced with Quadratic Coding and Sensing Search for Global Optimization

“…First, an exploration and exploitation strategy is proposed to provide the search process with accelerated automatic termination criteria. Specifically, matrices called Gene Matrix (GM) are constructed to sample the search space [1,39,40]. The role of the GM is to aid the exploration process.…”

“…Evolutionary Algorithms (EAs) are considered to be one of the core methods applied in the area of computational intelligence [1]. Generally, EAs constitute a class of the main global search tools which can be adapted to deal with many forms of nonlinear and hard optimization problems.…”