Let me make a statement first: the article is directly copied and pasted from the push in my personal official account, so friends who are interested in intelligent optimization algorithms can follow my personal official account: heuristic algorithm discussion . From time to time, I will share different intelligent optimization algorithms in the official account, classic ones, or new intelligent optimization algorithms proposed in recent years, with MATLAB code attached.

Professor Zhao Shijie and others started with the movement, predation and reproductive behavior of seahorses in nature, and proposed a meta-heuristic algorithm based on swarm intelligence: Sea-horse Optimizer (SHO). The performance of SHO is evaluated on 23 Benchmark functions and the CEC2014 test suite, and compared with 6 state-of-the-art algorithms. Finally, the authors validate the effectiveness of the method using five real engineering problems. Experimental results show that the algorithm is a high-performance optimizer and also has good adaptability to constrained optimization problems. The original reference for SHO is as follows:

“Zhao S, Zhang T, Ma S, et al. Sea-horse optimizer: a novel nature-inspired meta-heuristic for global optimization problems[J]. Applied Intelligence, 2023, 53(10): 11833-11860.”

01
Source of inspiration

Locomotion, predation and reproductive behavior are particularly important to the life of the seahorse, as described below:

In terms of locomotor behavior, seahorses sometimes curl their tails around algae stems (or leaves). Because the algae stems are floating around the algae roots under the action of the ocean vortex, the seahorse performs a spiral movement at this time. At other times, Brownian motion occurs when the seahorse hangs upside down on floating algae or other objects, moving randomly with the waves.

In terms of predation behavior, seahorses use the special shape of their heads to sneak up on prey, and then capture prey with a success rate of up to 90%.

In terms of reproductive behavior, male and female seahorses mate randomly to produce new offspring, which helps to inherit certain excellent information from father and mother.

Taken together, these three behaviors allow the hippocampus to better adapt to the environment and survive better. The SHO algorithm proposed by the author is mainly inspired by the above three behaviors. These behaviors are therefore the authors' motivation to develop this novel optimizer through mathematical modeling.

02
Algorithm design

The SHO algorithm proposed by the author consists of three key parts, namely movement, predation and reproduction. In order to balance the exploration and exploitation of SHO, local search and global search strategies were designed for the social behavior of locomotion and predation, respectively. The breeding behavior is performed after the first two behaviors have been completed. Their mathematical models will be expressed and discussed in detail as follows.

03
Calculation process

The calculation process of the SHO algorithm is a little more cumbersome, and the pseudocode is as follows:

04
Experimental simulation

Here is a simple test of the performance of the SHO algorithm. First, the SHO algorithm is used for function optimization, and the MATLAB program of the algorithm is coded strictly according to its original reference. In addition, the population size is set to N equal to 50, and the Benchmark function uses the CEC2005 test set, CEC2013 test set, CEC2014 test set, CEC2017 test set, CEC2020 optimization function test set and CEC2022 optimization function test set. The simulation results are briefly displayed here, and no further analysis will be made.

First, let's test the balance ability of SHO algorithm for global exploration and local development. As shown in Figure 4, it is the exploration and development ratio curve of the SHO algorithm on the CEC2005 test function f8.

Figure 4 The change curve of SHO's exploration and development percentages on CEC2005 f8

Secondly, taking the unimodal function Schwefel's 2.22 (f2) and the multimodal function Ackley (f10) of CEC2005 as examples, the convergence effect of the SHO algorithm in a 30-dimensional environment is shown, as shown in Figure 5.

(a) f2

(b) f10

Figure 5 Convergence curves of SHO on two test functions of CEC2005

Again, take the unimodal function F5 in the CEC2013 test set as an example to show the convergence effect of SHO in a 30-dimensional environment, as shown in Figure 6. (Note that the error curve is drawn)

Figure 6 The error convergence curve of SHO on CEC2013 F5

Next, taking the multimodal function F14 in the CEC2014 test set as an example, the convergence effect of SHO in a 30-dimensional environment is shown, as shown in Figure 7. (Note that the error curve is drawn)

Figure 7 The error convergence curve of SHO on CEC2014 F14

Then, taking the multimodal function F4 in the CEC2017 test set as an example, the convergence effect of SHO in the 30-dimensional environment is shown, as shown in Figure 8. (Note that the error curve is drawn)

Figure 8 The error convergence curve of SHO on CEC2017 F4

After that, take the compound function F9 in the CEC2020 optimization function test set as an example to demonstrate the convergence effect of SHO in a 10-dimensional environment, as shown in Figure 9. (Note that the error curve is drawn)

Figure 9 The error convergence curve of SHO on the CEC2020 optimization function F9

Finally, take the unimodal function F1 in the CEC2022 optimization function test set as an example to demonstrate the convergence effect of SHO in a 10-dimensional environment, as shown in Figure 10. (Note that the error curve is drawn)

Figure 10 The error convergence curve of SHO on the CEC2022 optimization function F1

Further, the SHO algorithm can be applied to complex engineering constrained optimization problems, such as the application content of the two algorithms previously pushed:

Algorithm Application: Engineering Optimization Design Based on DBO Algorithm (Phase 1) (including MATLAB code)

Algorithm Application: Engineering Optimal Design (Phase 2) (including MATLAB code)

Here, the Welded beam design problem is taken as an example to demonstrate the solution effect of the SHO algorithm. The convergence curve is shown in Figure 11.

Fig.11 Convergence curve of objective function of SHO on welded beam design problem

05
MATLAB code

The SHO algorithm runs the MATLAB of the CEC2005 test set is open source, you can copy the address below to extract:

Link: https://pan.baidu.com/s/1JM4l1sH_2w372Gq7FqCcdA

Extraction code: 8023

The SHO algorithm runs the CEC2013 test set: