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African Vultures Optimization Algorithm (AVOA) is a new meta-heuristic algorithm proposed by Abdollahzadeh et al. in 2021, which has been applied in many practical engineering projects. AVOA simulates the foraging and navigation behavior of African vultures. To evaluate the performance of AVOA, tests are carried out on 36 standard benchmark functions, and the results demonstrate the superiority of the proposed algorithm compared with several state-of-the-art algorithms. Its original reference is as follows:
“Abdollahzadeh B, Gharehchopogh F S, Mirjalili S. African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems[J]. Computers & Industrial Engineering, 2021, 158: 107408.”
01
Source of inspiration
Vultures are a kind of raptor in nature. They have almost no natural enemies and mainly feed on the rotting carcasses of animals. They are known as "cleaners on the grassland". Most vultures are bald and have no regular feathers on top of their heads, a biological trait that allows vultures to protect themselves from contamination when feeding on carcasses. Plus, research shows that exposed skin plays a vital role in regulating body temperature. For example, in cold weather, the vulture will immerse its head in the feathers of its wings, and in hot weather, it will expose its neck and head. There are a large number of vultures living in the African continent, but most of them have similar living habits. They often move alone, and occasionally form small groups. They often fight for food when they encounter each other.
There are roughly three types of vultures that live in Africa, each with some unique physical characteristics. The first is an exceptionally strong vulture, which tends to have easier access to food, such as the wattled vulture; the second is a slightly weaker vulture than the first type, such as the African white-backed vulture; the last is strength and Vultures that are weaker than the previous two types in stature, such as the scarf-crested vulture. In their natural environment, vultures are constantly making long-distance flights in search of food, and the most common form of flight for vultures is rotational flight. During the foraging process, sometimes several species of vultures will move to the same food source and conflict with each other. Weak vultures in hunger will become more aggressive. By surrounding and attacking strong vultures, they will consume their energy and become Fatigue to increase your chances of getting food yourself. The swarm intelligence algorithm is generally divided into two stages of exploration and development, which are related to the long-distance flight of African vultures to find food, hovering near food, and conflicting biological activities.
Abdollahzadeh et al. simulated the population behavior of vultures through a mathematical model, and transformed the individual position movement of the population into the optimization process of each dimension component of the target solution variable, thus proposing AVOA.
02
Algorithm design
The population initialization method of AVOA is the same as that of most intelligent optimization algorithms, that is, several candidate solutions in the search space are randomly generated as initial individuals. For details, please refer to previous pushes, so I won’t go into details here.
AVOA was proposed by simulating and modeling the foraging behavior and living habits of African vultures. In AVOA, the living habits and foraging behavior of African vultures mainly include the following stages.
Phase 1: Determining the Best of the Group
Phase 2: Calculating population starvation rate
The third stage: exploration stage
Phase Four: Development Phase
03
Calculation process
The calculation flow chart of AVOA is shown in Figure 1:
Figure 1 AVOA flow chart
04
Experimental simulation
Here is a simple test of the performance of AVOA. Using AVOA for function optimization, the MATLAB program for the algorithm is coded strictly in accordance with its original reference. In addition, the population size is 50, and the Benchmark function uses the CEC2005 test set, CEC2013 test set, CEC2014 test set, CEC2017 test set and CEC2020 optimization function test set. The simulation results are briefly displayed here, and no further analysis will be made.
First, let's examine AVOA's ability to balance global exploration and local development. As shown in Figure 2, it is the exploration and development ratio curve of AVOA on the CEC2005 test function f7.
Fig. 2 The change curve of AVOA's exploration and development percentages on CEC2005 f7
Next, take the unimodal function f2 and multimodal function f10 in the CEC2005 test set as examples to demonstrate the convergence effect of AVOA in a 30-dimensional environment, as shown in Figure 3. Comparison of algorithm choices: gray wolf optimization ( GWO ), whale optimization ( WOA ), Harris eagle optimization ( HHO ), dung beetle optimization ( DBO ) and golden jackal optimization ( GJO ).
(a) f2
(b) f10
Figure 3 Convergence curves of six evolutionary algorithms on two test functions of CEC2005
Again, take the unimodal function F1 in the CEC2013 test set as an example to show the convergence effect of AVOA in a 30-dimensional environment, as shown in Figure 4. Comparison of algorithm choices: gray wolf optimization ( GWO ), whale optimization ( WOA ), raccoon optimization ( COA ), sandcat swarm optimization ( SCSO ) and fire hawk optimization ( FHO ).
(Note that the error curve is drawn)
Figure 4 Error convergence curves of six evolutionary algorithms on CEC2013 F1
Next, take the unimodal function F3 in the CEC2014 test set as an example to show the convergence effect of AVOA in a 30-dimensional environment, as shown in Figure 5. Comparison of algorithm choices: gray wolf optimization ( GWO ), whale optimization ( WOA ), raccoon optimization ( COA ), sandcat swarm optimization ( SCSO ) and fire hawk optimization ( FHO ). (Note that the error curve is drawn)
Figure 5 Error convergence curves of six evolutionary algorithms on CEC2014 F3
Then, taking the mixing function F14 in the CEC2017 test set as an example, the convergence effect of AVOA in the 30-dimensional environment is shown, as shown in Figure 6. Comparison of algorithm choices: gray wolf optimization ( GWO ), whale optimization ( WOA ), Harris Hawk optimization ( HHO ), dung beetle optimization ( DBO ), raccoon optimization ( COA ). (Note that the error curve is drawn)
Figure 6 Error convergence curves of six evolutionary algorithms on CEC2017 F14
Finally, taking the mixing function F5 in the CEC2020 optimization function test set as an example, the convergence effect of the AVOA algorithm in a 10-dimensional environment is shown, as shown in Figure 7. Comparison of algorithm choices: gray wolf optimization ( GWO ), whale optimization ( WOA ), Harris Hawk optimization ( HHO ), dung beetle optimization ( DBO ), raccoon optimization ( COA ). (Note that the error curve is drawn)
Figure 7 Error convergence curves of six evolutionary algorithms on CEC2020 F5
Further, AVOA can be applied to complex engineering constraint optimization problems, such as the two-phase algorithm application content previously pushed:
Algorithm Application: Engineering Optimal Design (Phase 2) (including MATLAB code)
Here, the problem of pressure vessel design is taken as an example to show the solution effect. In this design problem, the objective function is the total cost of the pressure vessel, including material, forming, and welding costs. As shown in Figure 8, both ends of the pressure vessel are capped, and the cap at the head end is hemispherical. The optimization problem includes four decision variables: the thickness of the vessel wall ( Ts ), the thickness of the hemispherical head ( Th ), the inner radius ( R ), and the length of the cylindrical section ( L ).
Figure 8 Pressure Vessel Design
Its mathematical model is as follows:
Apply AVOA to the pressure vessel design problem, and use the penalty function introduced in the previous " Algorithm Application: Engineering Optimization Design Based on DBO Algorithm (Phase 1) (including MATLAB code) " to deal with constraints. Comparison of algorithm selection: gray wolf optimization ( GWO ), Harris eagle optimization ( HHO ), sand cat swarm optimization ( SCSO ), dung beetle optimization ( DBO ), raccoon optimization ( COA ). The convergence curve is shown in Figure 9.
Fig.9 Convergence curves of objective functions of six evolutionary algorithms on pressure vessel design problems
05
MATLAB code
There are in the official account, pay attention to: heuristic algorithm discussion