An exploratory research of elitist probability schema and its applications in evolutionary algorithms

• Published in: Applied intelligence (Dordrecht, Netherlands) Vol. 40; no. 4; pp. 695 - 709
• Main Authors: Zhang, Hong-Guang, Liu, Yuan-An, Tang, Bi-Hua, Liu, Kai-Ming
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.06.2014; Kluwer; Springer Nature B.V
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Artificial Intelligence; Classical and quantum physics: mechanics and fields; Computer Science; Computer science; control theory; systems; Elitism; EPS; Equipments and installations; Evolutionary algorithms; Exact sciences and technology; Genetic algorithms; Knapsack problem; Machines; Manufacturing; Mathematical models; Mechanical Engineering; Mobile radiocommunication systems; Optimization algorithms; Physics; Population; Probability distribution; Processes; Quantum computation; Quantum information; Radiocommunications; Similarity; Strings; Swarm intelligence; Telecommunications; Telecommunications and information theory; Theoretical computing; Coding similarity; Genetic algorithm; Evolutionary algorithm; Elitist probability schema; Estimation of distribution algorithm; Local search; Probabilistic approach; Internet protocol; Elitism; Modeling; Particle swarm optimization; Knapsack problem; Quantum computation; Innovation; Character string; Swarm intelligence
• ISSN: 0924-669X; 1573-7497
• DOI: 10.1007/s10489-013-0494-9

An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0–1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.