# Chaotic Java Approaches to Solving Electromagnetic Optimization Benchmark Problems
## 1 Introduction  
The Jaya algorithm, which was introduced by [PERSON] [1], is a simple, flexible, and powerful population-based stochastic algorithm for handling problems with discontinuous and non-differentiable objective functions and has been successfully applied to different kinds of global optimization problems. The Jaya algorithm is an emerging metaheuristic based on the concept that the candidate solution obtained for a given global optimization problem should change its position toward the best solution by updating its values and avoiding the worst solution in the current population. The major advantage of the Jaya algorithm is that it does not require any control parameter settings. Thus, the algorithmmay easily search to find the global or near-global solution of the optimization problem in the continuous domain. It only needs the essential population size and stopping condition (maximum number of iterations) for optimization. The other main characteristics of the Jaya algorithm are its simple structure in terms of formulation and fast convergence behavior. Despite its simplicity and efficiency features, the standard Jaya algorithm suffers from some of the same shortcomings as other metaheuristic algorithms applied to global optimization. The Jaya algorithm can present premature convergence to a local optimum solution and has the possibility of being trapped into local optima solutions when dealing with complex multimodal optimization problems due to weak exploration ability and insufficient population diversity. In general, balancing between the exploration (diversification) and exploitation (intensification) capabilities is a challenging task in metaheuristics design during the global optimization process. To overcome these drawbacks, different variants to improve the performance of the standard Jaya optimizer have been proposed in the literature, such as self-adaptive Jaya [2], Jaya with Levy flight [3], and shuffled Jaya [4]. To improve the global convergence ability of metaheuristics, chaotic sequences can be useful. Chaos is a nonlinear phenomenon characterized by a lack of periodicity, randomness, and ergodicity. Moreover, chaotic maps are sensitive to the initial conditions. Given the ergodicity and randomness of chaos, it can be an effective mechanism when employed for exploratory and exploitative purposes to avoid premature convergence for local optima during the searching process and enhance the convergence rate in metaheuristics in global optimization. From the recent literature [5; 6; 7; 8], there are methods of integration of one-dimensional chaotic maps with optimizers. The main contribution of our work is to introduce a modified version of Jaya using chaos sequences generated by chaotic maps (evolution function) that are discrete-time parametrized instead of uniformly distributed. Thus, by using the chaotic maps, we have been able to strengthen the original Jaya features and obtain robust and globally optimal solutions. The proposed chaotic Jaya (CJ) approaches combine exploitative local search and explorative global search processes efficiently by utilization of a chaotic map, introducing more diversity to produce candidate solutions. The proposed CJ approaches can lead to improving the acceleration capability toward the global solution in global optimization problems. Numerical results to the [PERSON]'s solenoid benchmark problem [9; 10] and a brushless direct current (DC) motor benchmark problem [11] are provided which demonstrate the usage and efficiency of the proposed CJ approaches. The rest of the paper is organized into the following sections. Section 2 briefly describes the [PERSON]'s solenoid, while Section 3 describes the brushless DC motor benchmark. After that, Section 4 covers the background information on the Jaya algorithm and the proposed CJ approaches. The performance of the Jaya approaches is evaluated on the optimization benchmarks and is compared to other metaheuristics in Section 5. Finally, we give the concluding remarks and the discussion for future works in Section 6.