Improved sine algorithm for global optimization

Highlights

• A modified SCA algorithm is proposed.

• Improving the convergence speed and accuracy of the algorithm.

• The proposed algorithm is more stable than other benchmark algorithms.

Abstract

An improved sine cosine algorithm (abbreviated MSA) is presented to overcome the disadvantages of the sine cosine algorithm (SCA), such as its low accuracy, premature convergence, and slow local convergence. We changed the method for setting the conversion parameters of the SCA algorithm from a linear decline into a nonlinear decline in order to optimize the timing of global exploration and local exploration. In order to improve the convergence accuracy and to increase the convergence speed of the SCA, an inertia weight is introduced in the position update equation. Ten high-dimensional complex benchmark functions are simulated with five improved SCA algorithms, under the same particle numbers and maximum iteration times. According to our experiments, the MSA algorithm is not only much better than two of the improved SCA algorithms in optimization accuracy but also better than the other three improved SCA algorithms in terms of stability.

Introduction

The so-called optimization problem refers to finding the optimal solution or parameter value among many solutions or parameter values to optimize one or more functions under certain conditions (Fang, Wu, & You, 2020). The optimization problem has always been an important research topic in the fields of computer science and management. The swarm intelligence optimization algorithm mainly simulates the group behavior of insects, animals, birds, and fish. These organisms will form a group to find food in a cooperative way, and each member of the group will continuously change the direction of the search by learning from its own experience and the experience of other members.

The sine cosine algorithm (SCA) is a new type of swarm intelligence optimization algorithm proposed by Mirjalili (2016). The core idea of ​​the algorithm is to use the periodicity of the waves of the sine and cosine functions to explore the optimal solution globally and make the algorithm gradually converge. SCA requires only a few parameters and is easy to implement, as optimization is achieved by iterating the properties of the sine and cosine functions. Although SCA has been proven to be superior to particle swarm optimization (PSO), the genetic algorithm (GA), and the bat algorithm (BA) in terms of convergence accuracy and convergence speed, it still has several shortcomings, such as low solution accuracy, premature convergence, and slow local convergence in the later stage. Qu and He (2018) proposed a simplified sine cosine algorithm known as the sine algorithm (SA), which is based on the theoretical analysis of the sine cosine algorithm. The structure of the algorithm is simpler than that of SCA, and the operation efficiency is higher. In order to avoid the shortcomings in the convergence and accuracy of the SCA and SA algorithms, this paper introduced inertia weights based on SA and improved the conversion parameter $r_1$ as part of an improved sine algorithm (called the modified sine algorithm [MSA]) to solve complex high-dimensional global optimization problems. The simulation results of ten high-dimensional standard test functions showed that MSA had better optimization performance than SA and was an improvement over the improved sine cosine algorithm (ISCA), exponential sine cosine algorithm (ESCA), exponential sine algorithm (ESA), and exponential cosine algorithm (ECA).

The rest of this paper is organized as follows. Section 2 presents related works. Section 3 introduces the SCA algorithm and other improved algorithms used to compare the results. The proposed method is described in Section 3. The experimental results and analysis are provided in Section 4. Finally, brief conclusions are given in Section 5.