Swarm intelligence optimization algorithm based on Wild seal habits

Abstract

The invention provides a swarm intelligence optimization algorithm based on the habits of Wild seal. The optimization algorithm is constructed in combination with the biological habits of South Pole Wild seal. For the problem that population diversity is insufficient and depends on population initialization in the later stage of algorithm iteration, a chaotic optimization strategy and a premature convergence judgment mechanism are introduced, and the situation that a population falls into a local optimal value is avoided; meanwhile, the Levy flight strategy balances the exploration and development capability of the algorithm, effectively improves the operation efficiency of the system, reduces the energy consumption, and promotes the reasonable utilization of resources.

Description

Technical Field

[0001] The present invention relates to a swarm intelligence optimization algorithm based on the habits of Weddell seals. As an emerging evolutionary computing technology, the swarm intelligence optimization algorithm has received extensive attention from scholars in recent years and has shown excellent results in many fields. According to the biological habits of Antarctic Weddell seals, a Weddell seal optimization algorithm is constructed, and in view of the problem of insufficient population diversity and dependence on population initialization in the late iteration of the algorithm, a chaotic optimization strategy and a premature convergence judgment mechanism are introduced to avoid the group from falling into a local optimal value. Through the Levy flight strategy, the exploration and development capabilities of the algorithm are balanced. The optimization algorithm effectively improves the operating efficiency of the system, reduces energy consumption, and promotes the rational use of resources. Background Art

[0002] The optimization problem aims to select the best solution or parameter value from many possible solutions or parameter values ​​under the premise of meeting specific conditions. Its purpose is to make one or more functional indicators reach the optimal state, or to make the specific performance indicators of the system achieve the optimization goal of maximum or minimum value. The optimization method is an application technology based on mathematical principles, which is specially used to solve various optimization problems. This technology has been widely used in many fields such as signal processing, image processing, production scheduling and task allocation, and has achieved significant economic and social benefits. Through practical application verification, the optimization method can not only effectively improve the operating efficiency of the system, reduce energy consumption, but also promote the rational use of resources. More importantly, as the scale of the processing object gradually expands, this optimization effect will become more and more significant, bringing greater impetus to the development of all walks of life. However, with the complexity of society, more and more complex combinatorial optimization problems have emerged. For large-scale optimization problems, traditional optimization methods cannot complete the search in a short time, and it is easy to produce a "combinatorial explosion" of search. For example, in engineering optimization problems, it is usually necessary to find the optimal solution or quasi-optimal solution in a large and complex search space. Given the complexity, constraints and modeling difficulties of actual engineering problems, relevant experts have been seeking efficient optimization algorithms.

[0003] The study of swarm intelligence was formed in the 1990s. In 1999, Bonabeau, Dorigo and Theraulaz discussed and analyzed swarm intelligence in detail in their book Swarm Intelligence: From natural to artificial systems, and gave a loose definition of swarm intelligence, that is, any algorithm designed based on the social behavior mechanism of insect colonies or other animals, or a distributed problem-solving strategy belongs to swarm intelligence.

[0004] The swarm intelligence method is not only simple and fast to implement, but its core algorithm is mainly based on basic mathematical operations, so in terms of computing resources, the demand for CPU and memory is relatively low. When processing data, this method only requires the output value of the objective function, without complex gradient information, which makes its application more extensive and flexible. A large number of theories and studies have fully proved that the swarm intelligence method has shown excellent performance in dealing with global optimization problems. Its unique parallelism and distributed characteristics provide solid technical support for processing massive database data. From the perspective of theoretical research and practical application, swarm intelligence theory and related research have far-reaching academic influence and important practical application value.

[0005] The swarm intelligence optimization algorithm originates from the simulation of biological evolution or foraging behavior in nature. It simulates the search and optimization process into the evolution or foraging process of individuals, and uses points in the search space to simulate biological individuals in nature; measures the objective function of solving the problem into the individual's ability to adapt to the environment; and compares the individual's survival of the fittest or foraging process to the iterative process of replacing bad feasible solutions with better feasible solutions in the search and optimization process. Thus, an iterative search algorithm with the characteristics of "generation + verification" is formed, which is an adaptive artificial intelligence technology for solving extreme value problems. All kinds of optimization algorithms are essentially to establish the objective function of the problem and find the optimal solution of the objective function. Therefore, actual engineering optimization problems can be transformed into function optimization problems. Summary of the invention

[0006] Inspired by the natural foraging and hunting behaviors of seals, and combined with the biological characteristics and group intelligence of seals, the present invention proposes a new intelligent optimization algorithm - the seal optimization algorithm. According to the characteristics of predation division of labor, the group is divided into three modules: cooperators, scavengers and wanderers. The three modules cooperate with each other to form the Weddell seal algorithm.

[0007] Its content mainly consists of the following steps:

[0008] (1) Initialization phase

[0009] Set the seal population size N and the maximum number of iterations t max , spatial dimension D, fitness function f, upper bound a of solution space, lower bound b of solution space and other parameters;

[0010] Randomly generate the initial positions of N seals Seal i , and randomly assign the cooperators and wanderers in a ratio of 8:2, and calculate the individual fitness value f of the current population i ;

[0011] (2) Iteration process (for t = 1 to t max )

[0012] Collaborators:

[0013] Select Seal * As a leader;

[0014] Assign the head steering angle α and compare it with the updated f i , Update Seal * ;

[0015] The rest act as searchers and update the vibration frequency v′;

[0016] Scavenger:

[0017] Calculate the average particle distance D(t) and fitness variance σ of the current population 2 ;

[0018] If D(t) or σ 2 If it is less than a given threshold, the population converges prematurely and chaos optimization is performed;

[0019] Randomly select a population individual X′, map the domain to (0,1), and use the logical self-mapping function z n+1 =4z n (1-z n ) is iterated to generate the chaotic sequence X n , inversely map back to the original solution space, and compare f i , select X n The individual with the best fitness value randomly replaces an individual in the original solution space;

[0020] Wanderer:

[0021] Calculate the step size dynamic control amount α;

[0022] Update the random search path s;

[0023] Update Seal by position formula i ;

[0024] Calculate f by f i ;

[0025] (3) Record the optimal solution

[0026] In each iteration, the optimal position found by all seal individuals is recorded as the current optimal solution;

[0027] After the iteration is completed, the global optimal solution is output, that is, the best value found in all iterations;

[0028] (4) Termination conditions

[0029] The algorithm usually sets a maximum number of iterations as the termination condition. When the number of iterations is reached, the algorithm stops running and outputs the optimal solution. In addition, other termination conditions can be set according to the change in the quality of the solution, such as stopping the algorithm when the optimal solution has not improved after multiple consecutive iterations. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the present invention is further described below in conjunction with the accompanying drawings and specific implementation plans:

[0031] Figure 1 Flowchart of the swarm intelligence optimization algorithm for Weddell seal behavior. DETAILED DESCRIPTION

[0032] The present invention is further described in detail below in conjunction with the content of the invention. The present invention mainly includes the following steps:

[0033] (1) Algorithm definition

[0034] 1) Seal

[0035] Based on the idea of ​​swarm intelligence, the present invention sets a certain number of seals to simulate the biological characteristics and living habits of seals in the actual hunting process. In the optimization problem, each seal represents a feasible solution. Since the expressions of feasible solutions of different optimization problems are different, for better understanding, the seal is defined as Seal i =(seal i1 ,seal i2 ,…,seal iD ),i=1,2,…,N, N represents the number of seals, and D represents the dimension of feasible solutions.

[0036] 2) Individual extreme values ​​and global extreme values

[0037] The individual extreme value is defined as the optimal position searched by each seal up to the current iteration, denoted as Seal best =(Seal besti1, Seal besti2 ,…,Seal bestiD ),i=1,2,…,N; define the global extreme value as the optimal position currently searched by the entire group, denoted as

[0038] 3) Team strategy

[0039] The hunting strategies of seals are mainly divided into group pursuit predation and ambush predation:

[0040] Group pursuit hunting: Seals hunt in groups to increase their chances of successful hunting through collaboration. Specifically, when a seal senses the presence of prey, it increases the information transmission between each other by making sounds or flapping its flippers, and cooperates with other seals to surround the prey, gradually narrowing the distance between them and the prey, forcing the prey into a situation where it cannot escape, making it easier to capture the prey.

[0041] Ambush hunting: In shallow water areas, seals may lurk underwater, using the surrounding water environment as cover to hide themselves from prey. Once the prey approaches, they will quickly attack, thereby accurately and quickly capturing the prey. This strategy is a highly flexible and efficient hunting method.

[0042] When seal groups are hunting, they also need to pay attention to the invasion of natural enemies or human interference. Seals have excellent hearing, vision, and smell perception abilities, and can keenly perceive changes in the surrounding environment. When hunting, the group will have special patrols to prevent invasion by foreign enemies. When sensing danger, they can quickly escape or take other defensive measures to protect the safety of the group, but at the same time they will also participate in the hunting operation.

[0043] The algorithm design of the present invention adopts three modules: cooperators, scavengers, and wanderers. Among them, cooperators refer to individuals that adopt a group hunting strategy, scavengers refer to some individuals that adopt an ambush hunting strategy, and wanderers are individuals responsible for patrolling during the hunting process.

[0044] (2) Partner Module

[0045] In each iteration, the individual with the best current fitness value is selected from all collaborators as the leader, and the rest are searchers, executing different strategies respectively.

[0046] 1) Leaders

[0047] The algorithm of the present invention assigns a head rotation angle to the leader and a unit vector The relationship between the two can be obtained by the following changes:

[0048]

[0049] In the iteration, the leader, as the pioneer of the population, can choose to move in five directions: forward, left, right, up, and down. Set the leader's head turning angle to α and the maximum field of view angle to

[0050] Because of the Snell window phenomenon, light entering the water is affected by the law of refraction. When the leader looks up from underwater, the light does not expand 180° from horizontal to horizontal as seen above the water surface, but is compressed into a light cone of about 96°. When the leader moves forward, the head turning angle α is 0, and the position update formula is as follows:

[0051]

[0052] When the leader turns to the remaining four directions, its position update formula is as follows:

[0053]

[0054] Where r1 is a normally distributed random number with a mean of 0 and a standard deviation of 1; r2 is a random sequence uniformly distributed in the range of (0,1). If the fitness value in a certain direction is better than the current fitness value, the leader moves to that point, otherwise it does not move.

[0055] 2) Searcher

[0056] The vibration of the whiskers of seals is an important tactile perception mechanism. Existing studies have shown that seals use whisker vibrations to perceive the surrounding environment and the location of prey. The relationship between whisker vibration and perception distance is indirectly related, depending on the properties of the vibration source and the propagation medium. When the vibration source is a point source, the vibration exhibits radial attenuation during the propagation process. According to physical principles, the energy of the vibration during the propagation process will gradually weaken as the distance increases, and the vibration speed will decrease as the distance increases. Specifically, when the vibration propagates in the form of a spherical wave, the relationship between the vibration speed and the perception distance is shown in formula (5):

[0057] v′~1 / r(5)

[0058] Where, the whisker vibration velocity v′=A*sin(2πft); A is the maximum displacement generated during the vibration process, that is, the vibration amplitude; f∈(f min ,f max ) is the vibration frequency of the whisker.

[0059] Assign each individual velocity vector in the searcher to v i =(v i1 ,v i2 ,…,v iD ), i = 1, 2, ..., N, the searcher updates its speed and position according to formula (6) and formula (7) respectively:

[0060]

[0061] Where c1 and c2 are learning factors, also known as acceleration constants; r1 and r2 are uniform random numbers between (0,1); is the speed of the individual at the tth iteration; v max is a constant, and the present invention limits it to 10% of the upper and lower bounds of the position; ω is the inertia factor, and its value is non-negative. The larger the value, the stronger the global search capability and the weaker the local development capability; conversely, the smaller the value, the weaker the global search capability and the stronger the local development capability. The present invention adopts a dynamically changing inertia factor, and has the following five strategies:

[0062] 1) Basic improvement methods

[0063]

[0064] 2) Parabolic form opening downward

[0065]

[0066] 3) Parabolic form opening upwards

[0067]

[0068] 4) Exponential curve form

[0069]

[0070] 5) Parabolic form opening to the left

[0071]

[0072] In the formula, ω start is the initial inertia weight; ω end is the inertia weight when the iteration reaches the maximum number.

[0073] (3) Scavenger module

[0074] Chaos, as a common manifestation of nonlinear systems, is widely present in natural and social phenomena, and its behavior is highly complex and random. However, although the chaotic state appears to be in chaos on the surface, its change process is not completely disordered, but contains subtle internal regularities. This regularity makes the study of chaotic states of great significance for understanding the behavior of complex systems. In view of the problem that the algorithm has insufficient population diversity and relies on population initialization in the late iteration, considering that chaos is sensitive to initial values, has high calculation accuracy, is easy to jump out of local minimum values, and has global asymptotic convergence, a premature convergence judgment mechanism is introduced into the algorithm to enrich the population position information, improve its convergence speed, and avoid late oscillations.

[0075] The present invention uses average seed distance and fitness variance as conditions for early maturity convergence judgment, and the formulas are as follows:

[0076]

[0077] Where D(t) represents the average distance between individuals; N is the number of populations; L is the maximum length of the spatial diagonal; ρ id is the d-th dimension coordinate of the ith individual; is the average value of all d-dimensional coordinates; σ 2 represents the fitness variance; f i is the fitness value of the ith individual; f avg is the average value of all current individual fitness values; f max is the maximum value of individual fitness.

[0078] Both the average particle distance and the fitness variance reflect the degree of “aggregation” of all individuals in the population. 2 The smaller it is, the smaller it is than the given threshold, which means the greater the degree of "clustering" of individuals and the denser the group. If the algorithm does not meet the termination conditions at this time, the group will fall into the local optimal value and enter a premature state.

[0079] When the population falls into premature maturity, an individual in the population is randomly selected as a scavenger to perform chaotic optimization.

[0080] For the scavenger position X′, the domain is mapped to (0,1) according to formula (15), and x′0 is used as the initial value of the chaotic search. According to the logical self-mapping function z n+1 =4z n (1-z n ) is iterated to generate the chaotic sequence X n , and then X n According to formula (16), the original solution space is inversely mapped back to the original solution space, the fitness value of each solution is compared, the best individual is retained, and an individual is randomly selected in the original solution space, and the random individual is replaced by the best individual in chaotic optimization.

[0081]

[0082] X′=a i +(b i -a i )X n (16)

[0083] In the formula, a i and b i are the upper and lower bounds of the original solution space.

[0084] (4) Wanderer Module

[0085] When a seal group hunts, some individuals not only participate in the hunt but also take on the task of vigilance to prevent foreign invasion. The present invention sets these seals as wanderers in the algorithm and adopts the Levy flight strategy. The position update formula is as follows:

[0086]

[0087] In the formula, is the position of the i-th individual in the t-th iteration; is point-to-point multiplication; α is the step length control amount. The present invention sets α to be dynamically changed, and the formula is as follows:

[0088]

Claims

1. A swarm intelligence optimization algorithm based on the habits of Weddell seals, characterized in that The following steps are involved: a. Initialization stage, set the seal population size N and the maximum number of iterations t max , spatial dimension D, fitness function f, solution space upper bound a, solution space lower bound b and other parameters, randomly generate the initial position Seal of N seals i , and randomly assign the cooperators and wanderers in a ratio of 8:2, and calculate the individual fitness value f of the current population i ; b. Iteration process (for t = 1 to t max ) Partner, choose Seal * As the leader, assign the head steering angle α and compare it with the updated f i , Update Seal * , the rest act as searchers and update the vibration frequency v'; c. Iteration process (for t = 1 to t max ) scavenger, calculate the average particle distance D(t) and fitness variance σ of the current population 2 , if D(t) or σ 2 If the value is less than the given threshold, the population converges prematurely, and chaotic optimization is performed. A population individual X' is randomly selected, and the domain is mapped to (0,1). According to the logical self-mapping function z n+1 =4z n (1-z n ) is iterated to generate the chaotic sequence X n , inversely map back to the original solution space, and compare f i , select X n The individual with the best fitness value randomly replaces an individual in the original solution space; d. Iteration process (for t = 1 to t max )Wanderer, calculate the step size dynamic control amount α, update the random search path s, and update Seal through the position formula i , calculate f through f i ; e. Record the optimal solution. In each iteration, record the optimal position found by all seal individuals as the current optimal solution. After the iteration is completed, output the global optimal solution, that is, the best value found in all iterations; f. Termination condition. The algorithm usually sets a maximum number of iterations as the termination condition. When the number of iterations is reached, the algorithm stops running and outputs the optimal solution. Other termination conditions can also be set according to the change in the quality of the solution, such as stopping the algorithm when there is no improvement in the optimal solution after multiple consecutive iterations.

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