Keywords: sonar inspired optimization, Nature-Inspired Intelligent (NII) algorithm, population based

1. Introduction

In the last twenty (20) years, a growth on Nature Inspired Intelligent (NII) methods [1,2,3] is observed. Applications [4] and new challenges [5] are presented, underlying the major contribution of these algorithms on the field of optimization. Except for swarm based techniques [6], there are many others that are inspired by physical phenomena [7] and laws of science [8]. Recently the authors have extensively searched and collected all the algorithms that are based in the above mentioned categories and extracted some useful conclusions. The overwhelming majority is population based schemes. A detail that highlights the need of multiple agents to achieve high exploration, while many of these algorithms are based also on attraction between their agents through equations that model the main idea inspired from nature.
The most used schemes are based on the gravitational law (Gravitational Search Algorithm [9]) or in attraction-based laws, e.g. Charged System Search [10], Electromagnetism-like optimization [11]. Based on these phenomena, the best solution attracts all the others towards it. On the proposed scheme, introduced in this paper, each agent doesn’t interact with the others and thus, performs its independent search. The only information shared between all agents is the best-so-far fitness achieved. That’s a very useful feature, because all better solutions are contributing to find the best one and the algorithm cannot be trapped in local optima. So, a good balance between exploration and exploitation is achieved.
What is more, in recent works, a major point of interest is the need for parameter tuning of the metaheuristic for different kinds of problems [12,13,14]. Our goal here is to provide a new self-tuning algorithm, which overcomes the problem of setting the exact number of agents to solve a problem. Keeping the number of agents constant in the proposed algorithm, does not limit the area searched. Also, the self-tuning mechanism is based on the value of the solution; the worse that a solution is, the bigger will be the step for the current agent.
Similar concepts like the one of the proposed algorithm are used in Dolphin Echolocation algorithm [15] and Bat-inspired algorithm [16]. In Dolphin Echolocation algorithm, the authors use also a probability generator for alternative solutions. And they state that their algorithm performs no movement to the best answer, but works only with possibilities. On the other hand, Yang [16] built his algorithm on the logic of swarm models. So movement is done with vectors in the solution space area, whereas in our proposed scheme there is only replacement of solutions that each agent discovers. Our goal was to build an equally effective tool, aiming at increasing the exploration grade without decreasing the corresponding exploitation. Bat-inspired algorithm is a swarm method, in which each agent performs one step in each iteration of the algorithmic process. On the other hand, the proposed algorithm is based on the search of multiple points around each agent during each iteration.
Furthermore, a significant detail is that our algorithm needs less parameterization. However, experimentation around parameter tuning of the proposed algorithm will be performed in future research on various real world problems. The values of the parameters presented in this work were carefully set by the authors and are in tune the literature findings on similar optimization algorithms. The concept we propose is based on the auto-tuning of the intensity parameter that determines how big search steps in the solution space the algorithm performs.
Finally, recent reviews of the nature inspired algorithms [17, 18] show that even more schemes are presented every year. The importance of a new algorithm can be shown by its effectiveness in a specific application or the usage as a hybrid component. The authors are working towards this direction, by applying the proposed algorithm in various optimization problems and also hybridizing with other schemes.
The rest of the paper is organized as follows; in section 2 the actual sonar mechanism is briefly presented, in section 3 the algorithm is explained analytically, in section 4 the experimental results are presented and explained and in section 5 there are further research recommendations and conclusion.

2. The actual sonar mechanism

The mechanism that provides inspiration in the proposed algorithm is the sonar that the Navy uses for war ships’ exploration for submarines. The basic idea behind the sonar application was to send an ultrasound and based on the sound level that the radio receives the size of an object or an obstacle can be estimated. So the ship can identify the position of possible targets (Fig. 1).