Applied Soft Computing Journal 85 (2019) 105734 Contents lists available at ScienceDirect Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc The spherical search algorithm for bound-constrained global optimization problems Abhishek Kumar a , Rakesh Kumar Misra a , Devender Singh a , Sujeet Mishra b , Swagatam Das c ,∗ a Department of Electrical Engineering, Indian Institute of Technology (BHU), Varanasi, Varanasi, 221005, India b Chief Design Engineer (Electrical), Diesel Locomotive Works, Varanasi, India c Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India article info Article history: Received 17 February 2019 Received in revised form 22 July 2019 Accepted 25 August 2019 Available online 14 September 2019 Keywords: Spherical search algorithm Real-life optimization problems Bound constrained optimization problem Optimization algorithm Global optimization abstract In this paper, a new optimization algorithm called Spherical Search (SS) is proposed to solve the bound- constrained non-linear global optimization problems. The main operations of SS are the calculation of spherical boundary and generation of new trial solution on the surface of the spherical boundary. These operations are mathematically modeled with some more basic level operators: Initialization of solution, greedy selection and parameter adaptation, and are employed on the 30 black-box bound constrained global optimization problems. This study also analyzes the applicability of the proposed algorithm on a set of real-life optimization problems. Meanwhile, to show the robustness and proficiency of SS, the obtained results of the proposed algorithm are compared with the results of other well-known optimization algorithms and their advanced variants: Particle Swarm Optimization (PSO), Differential Evolution (DE), and Covariance Matrix Adapted Evolution Strategy (CMA-ES). The comparative analysis reveals that the performance of SS is quite competitive with respect to the other peer algorithms. © 2019 Published by Elsevier B.V. 1. Introduction For over the last few decades, complexity of real-life optimiza- tion problems has been rapidly increasing with the advent of latest technologies. Solving these optimization problems is an es- sential component of any engineering design problem. So far nu- merous optimization techniques have been proposed and adapted to provide the optimal solutions for different optimization prob- lems. According to the nature of operators, these algorithms can be classified into two classes: Deterministic techniques and Meta-heuristics. In deterministic techniques, the solution of the previous iteration is used to determine the updated solution for the current iteration. Therefore, in the case of deterministic techniques, the choice of the initial solution influences the final solution. Furthermore, the solutions can be a victim of easily getting trapped into the local optima. Consequently, deterministic techniques are less efficient and less effective tools for solving multi-modal, highly complex, and high-dimensional optimiza- tion problems. As an alternate technique, meta-heuristics have been preferred for solving global optimization problems. A lot of theoretical work on these algorithms have been published in various popular journals thereby mainstreaming meta-heuristics. ∗ Corresponding author. E-mail address: swagatam.das@isical.ac.in (S. Das). Principal reasons for the popularity of the said algorithms over deterministic techniques are as follows: Simplicity- Foremost characteristic of meta-heuristics is the simplicity of theories and techniques. Meta-heuristics are ba- sically inspired by the simple concepts of some biological or physical phenomena. Flexibility- Meta-heuristics can easily be applied to the differ- ent optimization problems with no change or minor changes in the basic structure of the technique. Most of the techniques of meta-heuristics assume the problem as a black box requiring only input and output. Derivative free- The most important characteristic of these algorithms is a derivative-free mechanism. This means that there is no need for derivatives to solve the real-life optimization prob- lems having complex search space with multiple local minima. Local optima avoidance- Meta-heuristics have an in-built ca- pability for local optima avoidance. Local optima avoidance is required in the optimization of multi-modal problems. Meta- heuristics hence are preferred over conventional techniques for finding global optima of multi-modal problems. Researchers have introduced many meta-heuristics. Some of them are popular because of showing good efficiency for most of the real-life optimization problems. The No-Free-Lunch theo- rem [1] logically proved that there is no universal method, which solves all type of problems efficiently. A particular method may https://doi.org/10.1016/j.asoc.2019.105734 1568-4946/© 2019 Published by Elsevier B.V.