Two Population-Based Heuristic Search Algorithms and Their Applications

Search is one of the most frequently used problem solving methods in artificial intelligence (AI) [1], and search methods are gaining interest with the increase in activities related to modeling complex systems [2, 3]. Since most practical applications involve objective functions which cannot be expressed in explicit mathematical forms and their derivatives cannot be easily computed, a better choice for these applications may be the direct search methods as defined below: A direct search method for numerical optimization is any algorithm that depends on the objective function only through ranking a countable set of function values. Direct search methods do not compute or approximate values of derivatives and remain popular because of their simplicity, flexibility, and reliability [4]. Among the direct search methods, hill climbing methods often suffer from local minima, ridges and plateaus. Hence, random restarts in search process can be used and are often helpful. However, high-dimensional continuous spaces are big places in which it is easy to get lost for random search. Resultantly, augmenting hill climbing with memory is applied and turns out to be effective [5]. In addition, for many real-world problems, an exhaustive search for solutions is not a practical proposition. It is common then to resort to some kind of heuristic approach as defined below: heuristic search algorithm for tackling optimization problems is any algorithm that applies a heuristic to search through promising solutions in order to find a good solution. This heuristic search allows the bypass of the “combinatorial explosion” problem [6]. Those techniques discussed above are all classified into heuristics involved with random move, population, memory and probability model [7]. Some of the best-known heuristic search methods are genetic algorithm (GA), tabu search and simulated annealing, etc.. A standard GA has two drawbacks: premature convergence and lack of good local search ability [8]. In order to overcome these disadvantages of GA in numerical optimization problems, differential evolution (DE) algorithm has been introduced by Storn and Price [9]. In the past 20 years, swarm intelligence computation [10] has been attracting more and more attention of researchers, and has a special connection with the evolution strategy and the genetic algorithm [11]. Swarm intelligence is an algorithm or a device and illumined by the social behavior of gregarious insects and other animals, which is designed for solving distributed problems. There is no central controller directing the behavior of the swarm; rather, these systems are self-organizing. This means that the complex and constructive collective behavior emerges from the individuals (agents) who follow some simple rules and