Towards Solving Large-scale Expensive Optimization Problems Efficiently Using Coordinate Descent Algorithm

Abstract

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their convergence, which is not affordable for practical applications since the most of them are computationally expensive. In other words, these problems are not only large-scale but also computationally expensive, that makes them very difficult to solve. There is no efficient surrogate model to support large-scale expensive global optimization (LSEGO) problems. As a result, the algorithms should address LSEGO problems using a limited computational budget to be applicable in real-world applications. Coordinate Descent (CD) algorithm is an optimization strategy based on the decomposition of a n-dimensional problem into n one-dimensional problem. To the best our knowledge, there is no significant study to assess benchmark functions with various dimensions and landscape properties to investigate CD algorithm. In this paper, we propose a modified Coordinate Descent algorithm (MCD) to tackle LSEGO problems with a limited computational budget. Our proposed algorithm benefits from two leading steps, namely, finding the region of interest and then shrinkage of the search space by folding it into the half with exponential speed. One of the main advantages of the proposed algorithm is being free of any control parameters, which makes it far from the intricacies of the tuning process. The proposed algorithm is compared with cooperative co-evolution with delta grouping on 20 benchmark functions with dimension 1000. Also, we conducted some experiments on CEC-2017, D=10, 30, 50, and 100, to investigate the behavior of MCD algorithm in lower dimensions. The results show that MCD is beneficial not only in large-scale problems, but also in low-scale optimization problems.