Abstract
A novel algorithm, called restricted Boltzmann machine-assisted estimation of distribution algorithm, is proposed for solving computationally expensive optimization problems with discrete variables. First, the individuals are evaluated using expensive fitness functions of the complex problems, and some dominant solutions are selected to construct the surrogate model. The restricted Boltzmann machine (RBM) is built and trained with the dominant solutions to implicitly extract the distributed representative information of the decision variables in the promising subset. The visible layer’s probability of the RBM is designed as the sampling probability model of the estimation of distribution algorithm (EDA) and is updated dynamically along with the update of the dominant subsets. Second, according to the energy function of the RBM, a fitness surrogate is developed to approximate the expensive individual fitness evaluations and participates in the evolutionary process to reduce the computational cost. Finally, model management is developed to train and update the RBM model with newly dominant solutions. A comparison of the proposed algorithm with several state-of-the-art surrogate-assisted evolutionary algorithms demonstrates that the proposed algorithm effectively and efficiently solves complex optimization problems with smaller computational cost.
Highlights
Evolutionary computation (EC) has attracted considerable research attention in recent decades because of its ability to handle optimization problems [1]
We propose a surrogate based on restricted Boltzmann machine (RBM) that can learn the distribution of the input data to implicitly describe the interactions among the variables and present an energy function to represent the relationships between the dependent and independent variables
One evolutionary process of RBM-assisted EDA (RBMAEDA) for the Griewank function with 10 dimensions is recorded, and the results show that RBMAEDA finds the optimal solution in the 11th generation, where γth = 0 6
Summary
Evolutionary computation (EC) has attracted considerable research attention in recent decades because of its ability to handle optimization problems [1]. EC methods, e.g., genetic algorithms (GAs), estimation of distribution algorithm (EDA), particle swarm optimization (PSO), ant colony optimization (ACO), and differential evolution (DE), have been empirically shown to perform well for a wide variety of real-world applications including load scheduling [2], energy management systems [3, 4], robotics [5], parameter control [6, 7], classification [8], and community detection [9] These optimization problems usually have different types of decision variables, e.g., binary, integer, real, and mixed integer, and do not assume any convexity or differentiability of the objective functions and/or constraints involved. (1) An improved EDA based on an RBM is designed to generate new potential better individuals with discrete variables for guiding the evolutionary progress in the search space (2) The surrogate model based on an RBM is proposed to partly replace FEs to estimate the individual fitness and reduce the computational cost (3) The model management is presented to further enhance the effectiveness of the RBMAEDA by considering the relative rank of the promising individuals.
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