PCIA: A Path Construction Imitation Algorithm for Global Optimization

Abstract— In this paper, a new metaheuristic optimization algorithm, called Path Construction Imitation Algorithm (PCIA), is proposed. PCIA is inspired by how humans construct new paths and use them. Typically, humans prefer popular transportation routes. In the event of a path closure, a new route is built by mixing the existing paths intelligently. Also, humans select different pathways on a random basis to reach unknown destinations. PCIA generates a random population to find the best route toward the destination, similar to swarm-based algorithms. Each particle represents a path toward the destination. PCIA has been tested with 53 mathematical optimization problems and 13 constrained optimization problems. The results showed that the PCIA is highly competitive compared to both popular and the latest metaheuristic algorithms.
Index Terms— Structural optimization; heuristic algorithm; optimization. I. INTRODUCTION Recently, several metaheuristic algorithms have been proposed to solve hard optimization problems [1,2]. These algorithms have interesting features such as bypassing local optima, high scalability, ease of implementation, and applicability to a wide variety of engineering problems. In general, metaheuristic algorithms can be divided into five categories (see Fig. 1) based on their source of inspiration: 1- natural evolution, 2-physical phenomena of the universe, 3-the social behavior of groups of animals, 4-biological processes and structures, and 5-the social behavior of the human community. Evolution-based algorithms are inspired by natural selection in the evolution of species. In these algorithms, the next generation is derived from the intelligent or random combination of the best individuals in the current generation. Genetic Algorithm (GA) [3], Evolution Strategy (ES) [4], Differential Evolution (DE) [5], and Genetic Programming (GP) [6] are popular examples of evolutionary algorithms. Physical-based algorithms mimic the physical principles ruling the universe. The most famous methods of this category are simulated annealing (SA) [7], Gravitational Search Algorithm (GSA) [8], Big-Bang Big-Crunch (BBBC) [9] and Memetic Algorithm (MA) [10]. The third group is based on the social behavior of a group of animals. The most famous representative of this group is Particle Swarm Optimization

• Corresponding author: Mozafar Bag-Mohammadi, mozafar@ilam.ac.ir (PSO) [11], which mimics the social behavior of birds’ flock. Other noticeable examples of this category are Ant Colony Optimization (ACO) [12], Artificial Bee Colony (ABC) [13], and Fish-Swarm Algorithm (FSA) [14].
  The biological behavior of living organisms has inspired the fourth category. It includes algorithms such as Artificial Immune System (AIS) [15], Bacteria Foraging Optimization (BFO) [16], Dendritic Cell Algorithm (DCA) [17], and Krill Herd Algorithm (KHA) [18]. Finally, some methods imitate the human behavior in solving real-life problems. For example, the Imperialist Competitive Algorithm (ICA) [19] models the colonial rivalry to seize and expand their colonies. Teaching-Learning-Based Optimization (TLBO) [20] has implemented the teacher and learners learning model. Harmony Search (HS) [21] and Tabu Search (TS) [22, 23] imitate the musicians’ improvisation of the harmony and neighborhood search procedure respectively. In this paper, we have imitated the human behavior in constructing new paths to reach various destinations. We introduced a new method, called Path Construction Imitation Algorithm (PCIA), which uses the following key ideas. First, humans usually walk along frequently used pathways. Second, if an existing route is not functional, he tries to access the destination via an alternative path by modifying some parts of the route. In addition, human naturally combines local and partial paths with new paths to reach an unknown destination.
  In PCIA, each particle models the human behavior searching the solution space for the optimum path. The particle represents a path toward the destination. The initial population is generated randomly. Then, PCIA constructs a new generation using the similarities and dissimilarities between short and long routes in the current iteration. Therefore, PCIA is a hybrid method that imitates the social behavior of humans (modeled by particles’ behavior) in finding the best path to the destination. Hence, it is similar to both human-inspired and swarm-based methods. It also could be categorized as an evolutionary algorithm since it mixes existing paths to construct a better route. PCIA makes new routes by merging existing paths cleverly. For example, consider two similar paths P1 and P2. Also, assume that P1 is a short path and P2 is a long path. Probably, the goodness of P1 is due to its differences with P2. Hence, the different parts of P1 and P2 must be preserved and their similar parts must be