Shuffled Shepherd Optimization Algorithm (SSOA): To Find the Right Parameters for Each Problem

1. Introduction

In today’s extremely competitive world, everybody offers the maximum output or profit from a limited amount of available resources [1]. Optimization offers a suitable technique for finding maximum output or profit. That is why optimization techniques are becoming more popular. A new population-based meta-heuristic optimization algorithm of Shuffled shepherd optimization algorithm (SSOA) is developed by Kaveh and Zaerreza [2]. SSOA is the population based algorithm and the main purpose is to investigate the ability to developed multi-community [3].

2. Shuffled Shepherd Optimization Algorithm (SSOA)

 Each sheep is arranged by its objective function value, and then divided into herds. In each herd the sheep are selected in order, selected sheep are called shepherd and sheep with better objective function in a herd are called horses [4]. Therefore, there are some horses and sheep for each shepherd. A shepherd tries to guide the sheep to the horse; the new position of the shepherd is achieved by moving to one of the sheep and horse [5]. This is done for two purposes:

• Moving to worse agent causes exploration
• Moving to a better member results in exploitation

New position of shepherd update when new objective function is not worse than old objective function, this leads to elitism in the algorithm [6].

2. Inspiration of SSOA

The main inspiration of the SSOA is the herding behavior of shepherds. Humans have learned over time that they can use animal abilities to achieve their goals [7]. Shepherds try to steer their herds to the right direction.For this purpose, shepherds usually put animals like horses or herding dogs in their herds and use the herding instinct of these animals to direct the herd and guard it from predation and theft. This behavior is the basis info for obtaining the SSOA algorithm [8].

3. Numerical Implementation of SSOA

Step 1: Initialization

SSOA starts with a randomly generated initial member of community in the search space by the following equation

Where R is a random vector with each component being generated between 0 and 1;  and are, respectively, the lower and upper bounds of design variables, i is the number of communities, and j specifies number of members belonging to each community. In this way, the total number of member of communities is obtained as:

iSS = i * j                                                                     (3)

Step 2: Shuffling process

The members of each community so that members of the first column of SS are the best members in each community. This process is performed n time independently until SS matrix is formed as

Step 3: Movement of community member

A unique step size of movement for each community member is calculated based on two vectors known as the best and worse vectors. The mathematical formulation of the step size can be expressed as follows:

From this result shown that as iteration number t increases, ß and γ increase and decrease, respectively. As a result, exploration rate declines, while exploitation rate rises.

Step 4: Updating position of each community member

The new position is calculated. After that, the position will be updated if it is not worse than its old objective function value.

Step 5: Checking termination conditions

After a fixed number of iterations as stopping criterion, the optimization process will be terminated [9].

4. Pseudo code & Advantages of SSOA

5. Flowchart of SSOA

6. Applications of SSOA

As the results show, that it easy to apply the SSOA to the optimization problems. Thus the applications implemented in SSOA are as follows below;

• Optimal design problems [10].
• Engineering design problems [11].
• Hybrid clustering optimization problem [12].

Reference

[1] A. Kaveh, K. Biabani Hamedani and A. Zaerreza, “A set theoretical shuffled shepherd optimization algorithm for optimal design of cantilever retaining wall structures”, Engineering with Computers, 2020. Available: 10.1007/s00366-020-00999-9.

 [2] A. Kaveh, A. Zaerreza and S. Hosseini, “Shuffled Shepherd Optimization Method Simplified for Reducing the Parameter Dependency”, Iranian Journal of Science and Technology, Transactions of Civil Engineering, 2020. Available: 10.1007/s40996-020-00428-3.

[3] A. Kaveh and V. Mahdavi, “Colliding bodies optimization: A novel meta-heuristic method”, Computers & Structures, vol. 139, pp. 18-27, 2014. Available: 10.1016/j.compstruc.2014.04.005.

[4] U. Meyer, “Fire resistance assessment of masonry structures – Structural fire design of masonry buildings according to the Eurocodes”, Mauerwerk, vol. 17, no. 3, pp. 143-148, 2013. Available: 10.1002/dama.201300573.

[5] C. Camp and A. Akin, “Design of Retaining Walls Using Big Bang–Big Crunch Optimization”, Journal of Structural Engineering, vol. 138, no. 3, pp. 438-448, 2012. Available: 10.1061/ (asce) st.1943-541x.0000461.

[6] M. Khajehzadeh, M. Taha and M. Eslami, “Efficient gravitational search algorithm for optimum design of retaining walls”, Structural Engineering and Mechanics, vol. 45, no. 1, pp. 111-127, 2013. Available: 10.12989/sem.2013.45.1.111.

[7] A. Gandomi, A. Kashani, D. Roke and M. Mousavi, “Optimization of retaining wall design using recent swarm intelligence techniques”, Engineering Structures, vol. 103, pp. 72-84, 2015. Available: 10.1016/j.engstruct.2015.08.034.

[8] V. Yepes, J. Alcala, C. Perea and F. González-Vidosa, “A parametric study of optimum earth-retaining walls by simulated annealing”, Engineering Structures, vol. 30, no. 3, pp. 821-830, 2008. Available: 10.1016/j.engstruct.2007.05.023.

[9]  P. Mergos and F. Mantoglou, “Optimum design of reinforced concrete retaining walls with the flower pollination algorithm”, Structural and Multidisciplinary Optimization, vol. 61, no. 2, pp. 575-585, 2019. Available: 10.1007/s00158-019-02380-x.

[10] “Building Code Requirements for Reinforced Concrete (ACI 318-56)”, ACI Journal Proceedings, vol. 59, no. 12, 1962. Available: 10.14359/7970.

[11] A. Groenwold and N. Stander, “Optimal discrete sizing of truss structures subject to buckling constraints”, Structural Optimization, vol. 14, no. 2-3, pp. 71-80, 1997. Available: 10.1007/bf01812508.

[12] A. Kaveh and M. Zarandi, “Optimal Design of Steel-Concrete Composite I-girder Bridges Using Three Meta-Heuristic Algorithms”, Periodica Polytechnica Civil Engineering, 2018. Available: 10.3311/ppci.12769.