Introduction

Regarding an optimization problem, it can be understood that echolocation is like optimization in some respects; the process of foraging preys using echolocation in dolphins is similar to finding the optimum answer of a problem. Dolphins initially search all around the search space to find the prey. As soon as a dolphin approaches the target, the animal restricts its search, and incrementally increases its clicks to concentrate on the location.

The method simulates dolphin echolocation by limiting its exploration proportional to the distance from the target. For making the relationship much clear, consider an optimization problem. Two stages can be identified: in the first stage the algorithm explores all around the search space to perform a global search, therefore it should look for unexplored regions. This task is carried out by exploring some random locations in the search space, and in the second stage it concentrates on investigation around better results achieved from the previous stage. These are obvious inherent characteristics of all meta-heuristic algorithms.

Algorithm

Before starting optimization, search space should be sorted using the following rule: Search Space Ordering: For each variable to be optimized during the process, sort alternatives of the search space in an ascending or descending order. If alternatives include more than one characteristic, perform ordering according to the most important one. Using this method, for 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑗, 𝑉𝑒𝑐𝑡𝑜𝑟 𝐴𝑗 of length 𝐿𝐴𝑗 is created which contains all possible alternatives for the 𝑗 𝑡ℎ variable putting these vectors next to each other, as the columns of a matrix, the Matrix 𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒𝑠𝑀𝐴×𝑁𝑉 is created, in which 𝑀𝐴 is 𝑀𝑎𝑥(𝐿𝐴𝑗)𝑗=1:𝑁𝑉 ; with 𝑁𝑉 being the number of variables.

Application of Dolphin Echolocation (DE) Algorithm

By applying Dolphin Echolocation (DE) algorithm, the user would be able to change the ratio of answers produced in phase 1 to the answers produces in phase 2 according to a predefined curve. In other words, global search, changes to a local one gradually in a user defined style. The user defines a curve on which the optimization convergence should be performed, and then the algorithm sets its parameters to be able to follow the curve.

The method works with the likelihood of occurrence of the best answer in comparison to the others. In other words, for each variable there are different alternatives in the feasible region, in each loop the algorithm defines the possibility of choosing the best so far achieved alternative according to the user determined convergence curve. By using this curve, the convergence criterion is dictated to the algorithm, and then the convergence of the algorithm becomes less parameter dependent. The curve can be any smooth ascending curve but there are some recommendations for it

The main steps of Dolphin Echolocation (DE) for optimization are as follows: 1- Initiate 𝑁𝐿 locations for a dolphin randomly. This step contains creating 𝐿𝑁𝐿×𝑁𝑉 matrix, in which 𝑁𝐿 is the number of locations and 𝑁𝑉 is the number of variables

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