Aiming at the shortcomings of the basic whale optimization algorithm's slow convergence speed and easy to fall into local optimum, an improved whale optimization algorithm IGWOA is proposed, which uses the chaotic strategy to initialize the population, and the elite reverse learning strategy to increase the diversity of the population. factor and nonlinear convergence factor to speed up the global convergence; by adding an adaptive threshold, the global search capability is improved. Finally, the Gaussian mutation strategy is used to improve the convergence efficiency of the algorithm. Simulation experiments are carried out on 6 standard test functions, and the results show the effectiveness of the improved whale optimization algorithm.
1. Introduction 1 2. Algorithm Improvement 2.1. Improved The Whale Optimization Algorithm
The more evenly the initialized population is distributed in the search space, the more beneficial it is to improve the optimization efficiency and solution accuracy of the algorithm. The chaotic sequence generated by Tent map has good distribution and randomness, which can be used to significantly improve the optimization performance of the algorithm. The Tent formula is: = 2 ,
2(1 − ) , = + ( − ) (, ) =
( ) ∗ ∗ () − ( + 1) =
( ) ∗ ∗() + ( + 1) = ( ) ∗ (2) − ’ = 1 − (/
) The basic steps are as follows: 1) Tent mapping initializes the population S, and selects the first N/2 individuals with better fitness as the elite population E
3) Combine the population S and the reverse population OE to obtain a new population {S∪OE}, calculate the objective function value of the new population, and select the N individuals with the best fitness as the initial population. extent. However, when it comes to changing the strategy formula, the convergence factor alone cannot effectively balance global optimization and local search. To solve this problem, the adaptive weight is added at the time of change, and the formula is as follows: () = ( − ) + 0.5 ∗ (( − )/ )
Among them: t is the current number of iterations, Tmax is the maximum number of iterations, Winital and Wend are the initial and final values of the control parameter w, respectively, and φ is a constant coefficient. In summary, the position update formula defined in this paper is defined as: (1) (2) (3) (4) (5) (6) (7) (8) (9) •
Among them, μ is a constant variable. At the beginning of the iteration, P>P', the algorithm selects ( + 1) =
()(1 + ()) the spiral method to update the leader's position with high probability. The latter period decreases to 0 at a slow rate as the probability threshold decreases. By iterative adaptive threshold, the convergence accuracy of the algorithm is improved. a random variable that satisfies the Gaussian distribution. The global optimal position is updated as follows: ( + 1) = (), (
( + 1) , ℎ ( + 1 ) > ( ) < ∗ (10) (11)
Among them, rand represents a random variable between [0,1], p* is the selection probability of survival of the fittest, and f(x) is the fitness value of the individual. It can be seen from formula (11) that by performing mutation operation on the current global optimal solution Xbest(t), the population can evolve towards the optimal solution, and at the same time, the search efficiency of the algorithm can be effectively improved. 2.2. IGWOA Algorithm Process
If(|A|>=1) do Else if (p >= p') do End if
End for mutation
t=t+1
2.3. Simulation Experiments and Analysis •
F(2)，Schwefel 2.22
[-100,100] n
[-10,10] n [-5.12,5.12] n
[-32,32] n [-600,600] n
[-5,5] n
Parameter 0 0 7.8E-190 9.83E-84 0 0 1.2E-112 1.16E-48 0 0 0 0 8.88E-16 8.88E-16 7.99E-15 1.15E-14 0 0 1.4E-206 6.97E-88 0 0 1.2E-122 7.41E-50 0 0 0 0 8.88E-16 8.88E-16 8.88E-16 7.99E-15 • Parameter Setting and Analysis
Whale algorithm (WOA) and Gray Wolf algorithm (GWO) based on chaotic search strategy are simultaneously conducted 20 times of comparative experiments under the 6 benchmark test functions in Table 1. We selected F(1)-F(6), including F(1), F(2) a total of 2 unimodal functions and F(3, F(4),
0 0 0 0 0
The unimodal function is usually used to evaluate the development ability of the function. In F(1), F(2), IGWOA found the optimal value of 0.The function curve in Figure 1 shows that IGWOA has the fastest convergence rate.
Multimodal functions are often used to evaluate the search ability of a function. IGWOA found the optimal value 0 on the F(3) and F(4) functions, and showed the optimal mean and standard value in the test of the F(4) F(6) function. Fig. 1 It is proved that the initial population adjusted by the chaotic strategy converges faster than the traditional algorithm at the beginning of all the convergence curves. By comparing the numerical value and the curve as a whole, the IGWOA algorithm has better optimization performance than the CWOA, WOA and GWO functions.
3. Conclusion
In order to improve the performance of WOA, this paper firstly uses chaos Tent mapping to initialize the population to make the population more uniform, then solves the fitness value, and uses the elite reverse learning strategy to obtain the initialization population with higher fitness value, which effectively improves the diversification of the initialization population. In the search and predation stage of the algorithm, nonlinear convergence factor and adaptive weight are added to improve the global search ability of the population, so as to avoid the algorithm falling into the local optimal value too early. Moreover, by adding a custom threshold, the algorithm has a higher probability of searching prey in the early stage, so as to avoid falling into local extremum too early. Finally, Gaussian mutation is carried out on the optimal individual to accelerate the convergence performance of the algorithm and improve the local search ability to balance the global search and local search. Simulation results show that the improved algorithm in this paper has faster convergence speed and higher search accuracy. 4. References