A new meta-heuristic optimizer: Pathfinder algorithm

Highlights

• A new heuristic algorithm has been proposed.

• The method is a swarm-based algorithm and different in mathematical model.

• The proposed method has been tested on some test beds.

• The proposed method showed a superior performance to find global optima.

• Also, it has been applied to a real engineering problem and found good results.

Abstract

This paper proposes a new meta-heuristic algorithm called Pathfinder Algorithm (PFA) to solve optimization problems with different structure. This method is inspired by collective movement of animal group and mimics the leadership hierarchy of swarms to find best food area or prey. The proposed method is tested on some optimization problems to show and confirm the performance on test beds. It can be observed on benchmark test functions that PFA is able to converge global optimum and avoid the local optima effectively. Also, PFA is designed for multi-objective problems (MOPFA). The results obtained show that it can approximate to true Pareto optimal solutions. The proposed PFA and MPFA are implemented to some design problems and a multi-objective engineering problem which is time consuming and computationally expensive. The results of final case study verify the superiority of the algorithms proposed in solving challenging real-world problems with unknown search spaces. Furthermore, the method provides very competitive solutions compared to well-known meta-heuristics in literature, such as particle swarm optimization, artificial bee colony, firefly and grey wolf optimizer.

Introduction

The swarm based meta-heuristic optimization algorithms have an important role to optimize the modern engineering problems. This is due to their flexibility, derivation-free mechanisms and local optima avoidance. First of all, it can be mentioned that a heuristic method is simple. Generally, these methods have been based on simple concepts of physical phenomena in nature. Also, this helps the researchers to implement easily meta-heuristic methods to their problems. Furthermore, heuristic methods can be modified for different areas without any major modifications in their structures. This makes them flexible. Moreover, these methods are concerned only with the inputs and outputs of a problem. So that, these methods become derivative-free. Also, in contrast of gradient-based methods, meta-heuristics optimize a problem stochastically, say, the process starts with random initial solution or solutions and they improve these solutions using the random operators during the process. This allows them to be able to avoid local optimums. According to this ability, the meta-heuristics can be implemented to many research areas.

The meta-heuristic methods can be taken into account in three classes: evolutionary based [1], physical-based [2] and swarm intelligence based [3]. Evolutionary based methods start with random population and then evaluate this initial population using one or several operators such as crossover, mutation and selection during the optimization process. In particular, these methods do not care with the information of previous population. The second class is physical-based, which is inspired by physical rules in universe. The search agents in these methods explore the search space in accordance with specific rules of physic. The last class is, generally speaking, based on behaviors of swarm of animals in nature. The methods in this class use the collective movement intelligence of animals. These methods can save the information about optimization problem over the process. On the other side, they have less operators to be adjusted, and thus, they are easy adapted with minor revisions to different areas.

Independently of the differences of algorithms, a general characteristic is that meta-heuristic algorithms divide the optimization process as exploration and exploitation [4]. In the exploration phase, an algorithm performs the searching a possible solution area, where the algorithm needs stochastic operators for the global search and also randomly search abilities. Conversely, in the part of the exploitation, the ability of the algorithm is shaped around local search capability in the promising areas obtained in the exploration [5].

Additionally, a meta-heuristic algorithm is not suitable for solving all optimization problems. Precisely at this time it is worth to mentioning the NFL (No Free Lunch) theorem [6]. This theorem has proved that a meta-heuristic algorithm can give very promising solutions on some optimization problems, but cannot show good performance on all optimization problems. For this reason, the NFL theory causes new meta-heuristic algorithms to be proposed or existing algorithms to be improved. Therefore, in this study, it is the motivation of this study to improve a new meta-heuristic algorithm inspired by the hunting behavior of animals leaded by a leader individual. Despite the use of leadership hierarchy in the literature, there is no a simple model of searching a feeding area or a hunt and directing a swarm by an individual or a pathfinder. For this reason, in this study, a new meta-heuristic algorithm, called Pathfinder (PFA), inspired by the behavior of searching a hunt or feeding area with the leadership of an individual in the animal herds, is presented. In contrast to the algorithms in the literature, in the proposed method there is a leader and the other members follow it. However, the motion of all particles is not orderly, all of them move randomly. Also, the proposed method is completely different in terms of mathematical model and inspiration.

We mentioned in previous section, the most important aspect of heuristic algorithms is that they are inspired by evolutionary, physical systems, swarm intelligence. Evolutionary based methods mimic the evolution concepts. It can be mentioned that the Genetic Algorithm (GA) [7] is well-known method in literature. This algorithm based on theory of Darwin for evolution. GAs have some operators to evaluate its initial population generated randomly which are crossover, mutation and selection. Some of the other famous methods are Differential Evolution (DE) [8] and Evolutionary Programming (EP) [9].

The other branch of algorithms is physics-based. They are based on physical systems. These methods use the physical rules of gravitational force, ray casting inertia force and etc. Some of them are big-bang big-crunch (BBBC) [10], gravitational search algorithm (GSA) [11], charged system search (CSS) [12], central force optimization (CFO) [13], artificial chemical reaction optimization algorithm (ACROA) [14], black hole (BH) [15] algorithm, ray optimization algorithm (RO) [16], small-world optimization algorithm (SWOA) [17], galaxy-based search algorithm (GBSA) [18], and curved space optimization (CSO) [19].

The other class is swarm intelligence-based methods. These methods use the concepts of behavior animals. So that, particle swarm optimization (PSO) [20] and artificial bee colony algorithm (ABC) [21] have been inspired from the behavior of the fish and bird schooling and the food foraging behavior of honey bees in nature, respectively. Another one is ACO [22], inspired by the behavior of ants which is based on finding the shortest path from the nest to the food. Since the development of heuristic algorithms, the interest on this area has been increased. Some recently developed algorithms are firefly algorithm (FA) [23]. The krill herd algorithm (KH) [24]. The bat algorithm (BA) [25], the cuckoo search (CS) [26], artificial algae algorithm (AAA) [27], tree seed algorithm (TSA) [28], the grey wolf optimizer algorithm (GWO), presented in [29], the social spider algorithm (SSA) [30], the moth-flame algorithm (MFA) [31], the salp swarm optimizer (SSO) [32], the whale optimization algorithm (WOA) [33], the dolphin echolocation algorithm (DEA) [34], cat swarm optimizer (CSO) [35] and lion optimization algorithm (LOA) [36].

The paper is organized as follows. Section 2 presents the inspiration and model of Pathfinder algorithm (PFA). Versions of single-objective and multi-objective PFA are introduced in this section. Two metric experiments have been carried out in Section 3 on variety of classical benchmark functions, composite functions and multi-objective functions. In Section 4, several design problems have been handled. Section 5 contains an experiment of challenging problem of multi-objective optimization problem. Finally, Section 6 concludes the study together with some recommends.