# Parallel Improvements of the Jaya Optimization Algorithm
## 1 Introduction  
Optimization algorithms aim at finding an optimal value for a given function within a constrained domain. However, functions to be optimized can be highly complex and may present different numbers of parameters (or design variables). Indeed, many functions have local minima, so finding the absolute optimal value among the whole range of possibilities can be difficult. Optimization methods fall into two main categories: deterministic and heuristic approaches. Deterministic approaches take advantage of the problem's analytical properties to generate a sequence of points that converge toward a global optimal solution, these methods depend heavily on linear algebra, since they are commonly based on the computation of the gradient of the response variables. Deterministic approaches can provide general tools for solving optimization problems to obtain a global or an approximate global optimum (see [1]). Nonetheless, in the case of non-convex or large-scale optimization problems, the issues can be so complex that deterministic methods may not allow one to easily derive a globally optimal solution within a reasonable time frame. These methods are within the scope of mathematical programming, being the results of a deterministic optimization process that is unequivocable and replicable. Well known methods include the Newton method, the gradient descent method, and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Heuristic methods are proposed in order to speed the convergence up, to avoid local minimums, and to avoid restrictions in the functions to be optimized. Heuristic methods can be defined as guided (random) search techniquesthat are able to produce an acceptable problem solution, though its adequacy with respect to the target problem cannot be formally proven. Heuristic optimization algorithms are usually classified into two main groups: Evolutionary Algorithms (EA) and Swarm Intelligence (SI) algorithms. Among EA algorithms, worthy of mention are the Genetic Algorithm (GA), the Evolutionary Strategy (ES), Evolutionary Programming (EP), Genetic Programming (GP), Differential Evolution (DE), Bacteria Foraging Optimization (BFO), and the Artificial Immune Algorithm (AIA). Among SI algorithms, worthy of mention are Particle Swarm Optimization (PSO), Shuffled Frog Leaping (SFL), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), and the Fire Fly (FF) algorithm. Other algorithms based on phenomena in nature have been developed, and these include Harmony Search (HS), Lion Search (LS), the Gravitational Search Algorithm (GSA), Biogeography-Based Optimization (BBO), and the Grenade Explosion Method (GEM). The success of the vast majority of these algorithms is largely based on the parameters they use, which basically guide the search process and contribute chiefly to exploring the search space. The proper tuning of an algorithm-specific parameters represents a crucial success factor toward finding the global optimum. There are other algorithm-specific parameters. In PSO, these include population size, maximum number of generations, elite size, inertia weight, and acceleration rate; in ABC, these include onlooker bees, employed bees, and scout bees; in HS, harmony memory, number of improvisations, and pitch adjusting rate. Recently, two optimization algorithms, called TLBO (Teacher-Learner Based Optimization) [2] and Jaya [3], allowing one to dispense with specific parameter tuning have been put forward. In fact, only general parameters such as the number of iterations and population dimension are required. The TLBO and the Jaya algorithm are quite similar, the main difference being that TLBO uses two phases at every iteration (teacher and learner phases), while the Jaya algorithm performs only one. The Jaya algorithm in particular has sparked great interest that is growing within a range of diverse scientific areas, see [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] among others.