Wolf Search Algorithm with Ephemeral Memory Rui Tang, Simon Fong Department of Computer and Information Science University of Macau Taipa, Macau SAR ccfong@umac.mo Xin-She Yang Mathematics and Scientific Computing National Physical Laboratory Teddington, UK xin-she.yang@npl.co.uk Suash Deb Department of Computer Science & Engineering C. V. Raman College of Engineering Bidyanagar, India suashdeb@gmail.com Abstract—In computer science, a computational challenge exists in finding a globally optimized solution from a tremendously large search space. Heuristic optimization methods have therefore been created that can search the very large spaces of candidate solutions. These methods have been extensively studied in the past, and progressively extended in order to suit a wide range of optimization problems. Researchers recently have invented a collection of heuristic optimization methods inspired by the movements of animals and insects (e.g., Firefly, Cuckoos, Bats and Accelerated PSO) with the advantages of efficient computation and easy implementation. This paper proposes a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA) that imitates the way wolves search for food and survive by avoiding their enemies. The contribution of the paper is twofold: 1. for verifying the efficacy of the WSA the algorithm is tested quantitatively and compared to other heuristic algorithms under a range of popular non-convex functions used as performance test problems for optimization algorithms; 2. The WSA is investigated with respective to its memory requirement. Superior results are observed in most tests. Index Terms—Metaheuristic; Bio-inspired Optimization; Wolf Search Algorithm I. INTRODUCTION An optimization problem generally aims to find x opt =    where   is the search space and f(x) is a fitness function measuring the goodness of the solution. The global optimum represents a best solution x opt that is assumed to exist in the problem space. In many real-life applications, the optimization functions may not behave well mathematically and it is a well-known challenge in searching for a global optimal solution. Fig. 1. Griewank Function with it local minima and a global minimum. Left: zoom-out, x=[-600, 600], Right: zoom-in, x=[-150, 150] For example, the Griewank function that is shown in Figure 1, has been commonly used to test the convergence of optimization algorithms because its number of local minima grows exponentially as its number of dimensions increases; while its single global minimum is located at x=0. In such cases where the global optimum is hard to find, especially when the data carry high dimensional variables, the optimization problems can be complex and the problem sizes may thwart efficient calculation. For instance, in the travelling salesman problem, the search-space of candidate solutions grows more than exponentially as the size of the problem increases, which makes an exhaustive search for the optimal solution infeasible. A heuristic optimization method is a heuristic strategy for searching the search space of an ultimately global optimum in a more or less intelligent way [1]. This is also known as a stochastic optimization. A stochastic optimization is grounded in the belief that a stochastic, high- quality approximation of a global optimum obtained at the best effort will probably be more valuable than a deterministic, poor-quality local minimum provided by a classical method or no solution at all. Incrementally, it optimizes a problem by attempting to improve the candidate solution with respect to a given measure of quality defined by a fitness function. It first generates a candidate solution x candidate and as long as the stopping criteria are not met, it checks its neighbors against the current solution (SELECT       ). The candidate solution is updated with its neighbor if it is better (IF f(x neighbor ) < f(x candidate ) THEN x candidate = x neighbor ), such that the global optimum at the end is x opt = x candidate . As such, heuristic optimization algorithms are often based on local search methods in which the solution space is not explored systematically or exhaustively, but rather a particular heuristic is characterized by the manner in which the exploration through the solution space is organized. The authors Yang and Deb have recently invented a collection of bio-inspired metaheuristic algorithms, including Firefly [2], Cuckoos [3], Bats [4] and Accelerated PSO [5]. These bio-inspired heuristic optimization algorithms have search methods both in breath and in depth that are largely based on the swarm movement patterns of animals and insects found in nature. Their performance in heuristic optimizations have proven superior to that of many classical metaheuristic methods [9, 10] (e.g. genetic algorithms, simulated annealing, Tabu search, etc). 978-1-4673-2430-4/12/$31.00 ©2012 IEEE 165