SBOA: A Novel Heuristic Optimization Algorithm

two categories

Heuristic algorithms provide footing stone for metaheuristic algorithms, and metaheuristic algorithms are included in heuristic algorithms.The commonness of metaheuristic algorithms and heuristic algorithms lies in obtaining the optimal solution, the difference is the degree of greed, namely heuristic algorithm is easy to fall into local solution.

SBOA
This section includes the inspiration and the mathematical model of SBOA.

Inspiration source
The layout of snooker is shown in Error!Reference source not found..As everyone knows, if any player wants to win, he/she must make a good score.The highest score is 147, namely player must get 74 points at least.In a word, the number of cue balls contacting object balls must be more.It is said that one careless move loses the whole game.Therefore, players must maintain the initiative throughout the game.On one hand, players get score by offensive strategy.On the other hand, the player stops the opponent from scoring by defensive strategy, namely the cue ball is reasonably controlled by player, and create chances for score.can see from above; offensive strategy is an overall thinking and defensive strategy is a local thinking.
The aim is to make a good score whether offensive strategy or defensive strategy.Thus, the play rules can be used to solve optimization problems.

Mathematical model
The thought about SBOA is simple, the structure is also simple.In the beginning of the search, the first kickoff result is produced by using Eq.1.
First, SBOA starts by generating a random population in uniform distribution to begin, including the cue ball and other balls.Based on this idea, the cue ball is considered as the best individual, its position that contacting object balls is very important.The initial population can be obtained using Eq.1.
=  min +  * ( max −  min ) 1 Where Xi is the position of all balls, rand is a random number between 0 and 1, and Xmin, Xmax are the lower and upper bounds of the problem respectively.
The best solution is shown using Eq.2.
Where N is the number of the first retrieval result.
Snooker as a sport with two players, is divided into two phases as follow: (1) Attack phase In the attack phase, the cue ball is contacted by other balls, a red ball then a colored ball.
Alternating like this until a player wins.Therefore, the process is what the cue ball contacts other balls so that has a good score.The process of Learning from colleagues is calculated using Eq. 3.
Where X best is the position of the cue ball, rand (0, 1) is random vectors in intervals [-1, 1].A present's offensive ability that adapting to the game.
(2) Defensive phase In defensive phase, the cue ball can be docked two balls, cushion, or around snookered ball/balls.The aim is to prevent the opponent from winning or scoring when a player has no scoring advantage.Thus, the process is simulated using Eq.4.
In the process, players usually have snooker according to the remaining balls on the billiard table.Therefore, searching for the best one (ball) using Eq.5.
The pseudo-code of SBOA is shown in Error!Reference source not found..

Experiment and Result
In this subsection, the performance of the SBOA Test is divided into three parts and has different benchmark functions obtained from CEC 2019 and CEC 2022.Each algorithm is performed 30 times, and parameter settings are shown in Table 2.

Engineering Problems
Engineering design optimization problems involve many inequalities constraints, are used to search maximum or minimum 19 .Their essences are known as mathematical problems, so many algorithms can be used to get the best value.To prove efficiency, SBOA is used solving 4 constrained problems in this subsection.Welded Beam Design 20 , Pressure Vessel Design 21 , Gear Train Design 22 , and Three Bar Truss Design 23 .

Pressure vessel design problem
Pressure vessel design problem has 4 design variables(x 1 -x 4 ), the goal of this problem finds minimum.The equations as follow: The objective function: Subject to: Results of SBOA and other algorithms are given in Table 9, Error!Reference source not found..
Table 9 shows the best solution x= [0.9559055314 0.4725024408 49.52835701 116.4764305] and where f(x)= 5920.777474.From Error! Reference source not found.and Figure 1 the SBOA outperform another algorithm.

Welded beam design problem
Welded beam design problem has 4 decision variables(x 1 -x 4 ), the goal is to find the minimum because of cost savings.The equations of Welded beam design problem are shown below: The objective function:

Gear train design problem
This problem has 2 design variables(x 1 -x 4 ), the goal is to find minimum gear ratios.The equation of the problem is shown below: The objective function:

Three Bar Truss Design problem
This problem has 2 design variables(x 1 -x 2 ), the goal is to find minimum volume.The equation of the problem is shown below: The objective function:

Figure 1 .
Figure 1.The layout of snooker.

Table 3
shows the Wilcoxon rank sum test results for SBOA against other algorithms.From this table, can see that most P values are less than 0.05, and the smaller of the values, the better of these algorithms.

Table 3 . Wilcoxon rank sum test results for SBOA against other algorithms CEC2019
Error! Reference source not found.show 10 convergence curves.From these convergence curves of all functions, it is seen that SBOA has obvious superiority than other algorithms in 7 functions, the second-best of 1 other function whereas it ranked fifth in other 2 functions.https://doi.org/10.21123/bsj.2024.9766P-ISSN: 2078-8665 -E-ISSN: 2411-7986 Baghdad Science Journal Figure 2.

Convergence curve of some functions from F1-F10 for all algorithms CEC2019. Result on CEC 2022 In
this subsection, have used 12 objective benchmark functions obtained from CEC 2022.

Table 4 .
Summary of the CEC 2022 test functions shows the CEC 2022 summary of test functions.

Table 5 , Error! Reference source not found
. show the results of SBOA and other seven comparative algorithms (DE, SCA, WOA, LSO, SSA, GJO and BOA) in terms of mean (average), best (min), worst (max), median, and std CEC 2022 and Dim=10.And Dim=20.It is seen that SBOA has the best Mean results in 11 functions from all functions at least.So it has obvious superiority to other algorithms.

Table 7 ,
Table 8 show two the wilcoxon rank sum test results for SBOA against other algorithms CEC 2022 Dim = 10 and Dim=20.From these tables, the phenomenon that most values less than 0.05 is confirmed that SBOA is the best algorithm in all algorithms.

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SBOA algorithm is better than other algorithms, and convergence rate is best.

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SBOA outperforms another algorithm.