Perfectarial bird optimization algorithm based on swarm intelligence

Abstract

The invention provides a secretary bird optimization algorithm for swarm intelligent optimization, and relates to the field of optimization algorithms, the algorithm has excellent optimization ability, and is mainly divided into two key stages, namely an exploration stage and a development stage: in the exploration stage, the secretary bird optimization algorithm performs the processes of secretary bird prey search, prey physical exhaustion, prey attack and the like; and convergence of the algorithm is rapidly realized. In the development stage, the algorithm adopts two strategies that secretary birds escape from the predators, namely escape by means of environment camouflage and flying or running, so that the difficulty of falling into a local optimal solution is effectively avoided. The method is unique in that hunting and survival behavior processes of secretary birds are used for reference, so that the algorithm has the characteristic of easy understanding, and the optimization capacity is remarkably improved. The secretary bird optimization algorithm can be flexibly applied to different scenes, and a feasible and effective optimization scheme is provided for solving practical problems.

Description

Technical Field

[0001] The present invention relates to the field of intelligent optimization algorithms, in particular to a novel swarm intelligent optimization algorithm, namely, the secretary bird optimization algorithm. Background Art

[0002] Nature-inspired computing, a type of metaheuristic algorithm, draws inspiration from various natural phenomena, encompassing fields such as biology, physics, and chemistry. It is widely used in scientific research and engineering to solve complex optimization problems. Within nature-inspired computing, swarm intelligence is a crucial branch of this approach. The fundamental principle of swarm intelligence optimization algorithms is to achieve global optimization by simulating and leveraging the cooperation and information sharing among swarm members. Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), and Bird Swarm Algorithm (BSA) are typical and common examples. ACO simulates the pheromone release of ants during their food search, using pheromone evaporation and deposition to search and optimize the solution space. PSO simulates the coordinated behavior of individual particles in a flock of birds, adjusting their speed and position to find the optimal solution. BSA simulates the collective collaboration and adaptability of a flock of birds during flight to achieve a balance between global search and local optimization.

[0003] Swarm intelligence optimization algorithms are widely used in various fields. In engineering, particle swarm optimization (PSO) is used for power system scheduling and structural design. In traffic planning, ant colony optimization (ACO) is used for route planning to reduce traffic congestion. In finance, artificial bee colony optimization (ABC) excels in portfolio optimization and risk management. In medical image processing, swarm intelligence algorithms are used to improve image segmentation and diagnostic accuracy. In drone path planning, swarm intelligence algorithms in multi-agent systems are used for path planning and task optimization. Furthermore, algorithms such as swarm algorithms in network optimization have also achieved remarkable results, optimizing network topology and improving performance. These examples highlight the multi-domain applicability of swarm intelligence optimization algorithms in solving various practical problems.

[0004] The emergence of swarm intelligence algorithms has provided a powerful tool for optimizing complex problems. Over time, researchers have proposed a wide variety of swarm intelligence algorithms, such as particle swarm optimization (PSO), ant colony optimization (ACO), and artificial bee colony optimization (ABC). However, despite their promising performance in theory and practice, these algorithms face several challenges. Currently, many swarm intelligence algorithms have a large number of parameters that require adjustment, making their use quite cumbersome, especially for non-experts. Understanding and adjusting these parameters requires profound expertise, which can be frustrating for users. This complexity not only limits the widespread application of these algorithms in real-world problems but also reduces their practicality. Summary of the Invention

[0005] The purpose of the present invention is: the present invention proposes a secretary bird optimization algorithm based on swarm intelligence, the secretary bird optimization algorithm (Secretary Bird Optimization Algorithm, referred to as SBOA) is used for continuous function optimization problems, can achieve rapid convergence, and has high convergence accuracy.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a secretary bird optimization algorithm based on swarm intelligence, comprising the following steps:

[0007] Step 1: Initialize the parameters of the Secretary Bird optimization algorithm, set the total number of algorithm iterations, the number of individuals in each iteration, the dimension of the problem to be optimized, and the upper and lower bounds of the search space;

[0008] Step 2: Determine the exploration phase of the secretary bird, calculate the fitness value of the secretary bird's exploration process, and complete the exploration and search process for prey;

[0009] Step 3: Select the predator avoidance strategy in the development stage of the secretary bird, calculate the fitness value of the secretary bird's development process according to the strategy, and complete the process of avoiding predators;

[0010] Step 4: Perform boundary checks on the new solutions generated in the exploration and development phases to ensure they are within the solution space;

[0011] Step 5: Evaluate the fitness values of all secretary bird locations, and the location with the best fitness value will be retained for the next round of iterative information sharing.

[0012] Secretary birds typically engage in hunting and evading predators. SBOA's algorithm is divided into two phases: exploration and exploitation. During the search process, SBOA adjusts the secretary bird's search range based on its current fitness. The exploration phase aims to rapidly converge the algorithm to the optimal solution, while the exploitation phase searches for solutions within a larger search space, effectively leveraging global information to avoid local optimality. The Lévy flight function corresponds to the secretary bird's ability to fly, enabling it to quickly escape from a local optimum and obtain a better solution.

[0013] The Secretary Bird optimization algorithm specifically includes the following steps:

[0014] Step 1: Initialize SBOA parameters

[0015] The number of algorithm iterations is set to T, the number of individuals in the population is set to N, the dimension of the problem to be optimized is set to Dim, and the upper and lower bounds of the lock space are set to ub respectively. j lb j ,In the initialization process of the secretary bird optimization algorithm, the values of each dimension of the individual are random numbers between the upper and lower bounds. A total of N secretary birds will be generated, and the position of the individual with the best fitness value will be retained as the benchmark for the next round of iteration;

[0016] Step 2: Secretary Bird's Exploration and Search Process

[0017] The secretary bird exploration process uses equations (1), (2), (3) and (4) to update the secretary bird's position and update the individual fitness value:

[0018] when hour,

[0019]

[0020] when hour,

[0021]

[0022] when hour,

[0023]

[0024]

[0025] Among them, t represents the current number of iterations, T represents the maximum number of iterations, represents the new state of the i-th secretary bird in the first stage, x i,j represents the value of the j-th problem variable of the i-th secretary bird, and is the random candidate solution of the first stage iteration, R1 represents a randomly generated array of dimension 1×Dim from the interval [0,1], x best represents the best candidate solution obtained in the current iteration, rand(1, Dim) represents a 1×Dim array randomly generated from a normal distribution, and RL represents the Levy flight function, which is calculated by equations (5) and (6). represents the fitness value of the i-th secretary bird in the j-th dimension, Represents the fitness value of its objective function;

[0026]

[0027]

[0028] Where s is a fixed constant of 0.01, η is a fixed constant of 1.5, u and v are random numbers in the interval [0,1], σ represents a transition variable, and Γ represents a gamma function;

[0029] When the Secretary Bird's fitness value is less than the previous iteration, it means that a better solution has been found, and the Secretary Bird's location information is updated. When the Secretary Bird's fitness value is greater than or equal to the previous iteration, it means that the Secretary Bird has not found a more suitable area, and the location information of the previous iteration is retained.

[0030] Step 3. Developing a search process for Secretary Bird

[0031] In the development phase of the secretary bird optimization algorithm, formulas (7) and (8) are used to update the position of the secretary bird and update the individual fitness value.

[0032]

[0033]

[0034] Where r = 0.5, R2 means randomly generating an array of dimension (1×Dim) from a normal distribution, x random Indicates the random candidate solution of the current iteration, round(1+rand(1,1)) means randomly obtaining an integer 1 or 2, represents the new state of the i-th secretary bird in the second stage;

[0035] When encountering predators, secretary birds typically employ evasive strategies to protect themselves or their food. These strategies can be categorized into two main types: flight or running to escape, and camouflage. Secretary birds may employ camouflage techniques using the colors or structures of their surroundings, making them more difficult for predators to detect. When faced with a predator, if the surrounding environment is suitable for camouflage, the secretary bird will use it to evade the predator. Here, C1 in Equation (7) is used to update its position. Otherwise, the secretary bird will run or fly quickly to escape the predator. Here, C2 in Equation (7) is used to update its position.

[0036] Step 4: Check the boundaries of the new solutions generated in the SBOA exploration and development phases to ensure that they are within the solution space; if X i,j If the upper and lower limits are exceeded, [lb j ,ub j ] as the value of X i,j value.

[0037] In step 5, the algorithm evaluates the fitness of all secretary bird positions. The position of the secretary bird with the best fitness value is retained for the next iteration. At the beginning of the next iteration, all secretary bird positions are set to the positions with the best fitness values from the previous iteration. If the termination condition is met, the optimal solution is output; otherwise, the algorithm returns to step 2 and continues. The algorithm's termination condition can be set according to user requirements, such as the maximum number of iterations and the required accuracy.

[0038] The beneficial effects of this invention: Compared with existing technologies, this method, inspired by the hunting behavior of secretary birds and their ability to evade predators, exhibits superior search capabilities and efficient convergence. Compared with other algorithms, this algorithm requires fewer control parameters for function optimization, converges quickly, and demonstrates excellent optimization capabilities for both unimodal and multimodal optimization problems, achieving a high degree of convergence accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is the flowchart of the algorithm;

[0040] Figure 2 This is a comparison experiment diagram of multiple algorithms. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0042] Example 1: Figure 1As shown in Figure 1, a new swarm intelligence optimization algorithm, the Secretary Bird optimization algorithm, includes the following steps:

[0043] Step 1: Initialize SBOA parameters

[0044] The number of algorithm iterations is set to T, the number of individuals in the population is set to N, the dimension of the problem to be optimized is set to Dim, and the upper and lower bounds of the lock space are set to ub respectively. j lb j ,In the initialization process of the secretary bird optimization algorithm, the values of each dimension of the individual are random numbers between the upper and lower bounds.,A total of N secretary birds will be generated, among which the individual position with the best fitness value will be retained as the benchmark for the next round of iterative process;

[0045] Step 2: Secretary Bird's Exploration and Search Process

[0046] The secretary bird exploration process uses equations (1), (2), (3) and (4) to update the secretary bird's position and update the individual fitness value:

[0047] when hour,

[0048]

[0049] when hour,

[0050]

[0051] when hour,

[0052]

[0053]

[0054] Among them, t represents the current number of iterations, T represents the maximum number of iterations, represents the new state of the i-th secretary bird in the first stage, x i,j represents the value of the j-th problem variable of the i-th secretary bird, and is the random candidate solution of the first stage iteration, R1 represents a randomly generated array of dimension 1×Dim from the interval [0,1], x best represents the best candidate solution obtained in the current iteration, rand(1, Dim) represents a 1×Dim array randomly generated from a standard normal distribution, and RL represents the Levy flight function, which is calculated by equations (5) and (6). represents the fitness value of the i-th secretary bird in the j-th dimension, Represents the fitness value of its objective function;

[0055]

[0056]

[0057] Where s is a fixed constant of 0.01, η is a fixed constant of 1.5, u and v are random numbers in the interval [0,1], and σ represents a transition variable. represents the gamma function;

[0058] When the Secretary Bird's fitness value is less than the previous iteration, it means that a better solution has been found, and the Secretary Bird's location information is updated. When the Secretary Bird's fitness value is greater than or equal to the previous iteration, it means that the Secretary Bird has not found a more suitable area, and the location information of the previous iteration is retained.

[0059] Step 3. Developing a search process for Secretary Bird

[0060] In the development phase of the secretary bird optimization algorithm, formulas (7) and (8) are used to update the position of the secretary bird and update the individual fitness value.

[0061]

[0062]

[0063] Where r = 0.5, R2 means randomly generating an array of dimension (1×Dim) from a normal distribution, x random Indicates the random candidate solution of the current iteration, round(1+rand(1,1)) means randomly obtaining an integer 1 or 2, represents the new state of the i-th secretary bird in the second stage;

[0064] When encountering predators, secretary birds typically employ evasive strategies to protect themselves or their food. These strategies can be categorized into two main types: flight or running to escape, and camouflage. Secretary birds may employ camouflage techniques using the colors or structures of their surroundings, making them more difficult for predators to detect. When faced with a predator, if the surrounding environment is suitable for camouflage, the secretary bird will use it to evade the predator. Here, C1 in Equation (7) is used to update its position. Otherwise, the secretary bird will run or fly quickly to escape the predator. Here, C2 in Equation (7) is used to update its position.

[0065] Step 4: Check the boundaries of the new solutions generated in the SBOA exploration and development phases to ensure that they are within the solution space; if X i,j If the upper and lower limits are exceeded, [lb j ,ub j ] as the value of X i，j value.

[0066] In step 5, the algorithm evaluates the fitness of all secretary bird positions. The position of the secretary bird with the best fitness value is retained for the next iteration. At the beginning of the next iteration, all secretary bird positions are set to the positions with the best fitness values from the previous iteration. If the termination condition is met, the optimal solution is output; otherwise, the algorithm returns to step 2 and continues. The algorithm's termination condition can be set according to user requirements, such as the maximum number of iterations and the required accuracy.

[0067] In summary, SBOA execution can be described as shown in the pseudo code Algorithm 1.

[0068]

[0069]

[0070] To verify the performance of the SBOA algorithm, we selected the industry-recognized CEC 2017 test suite for testing and compared it with classic algorithms and efficient swarm intelligence algorithms proposed in recent years. Table 1 shows the 30 benchmark functions used to test SBOA performance, including the dimensions of the benchmark functions and the range of variation for each dimension.

[0071] Table 1. CEC 2017 test functions

[0072]

[0073] During the test, the benchmark function is used as the fitness value evaluation function, and the position of the secretary bird X i It will be brought into the benchmark function to obtain the fitness value, and various intelligent optimization algorithms will adjust the selection of positions in the next iteration according to the change in fitness value.

[0074] Figure 2 The paper presents comparative results between the SBOA algorithm and the particle swarm optimization algorithm (PSO), differential evolution algorithm (DE), Harris Hawk Optimizer (HHO), gray wolf optimization algorithm (GWO), and whale algorithm (WOA). PSO and DE are classic intelligent optimization algorithms, while GWO, WOA, and HHO are highly recognized intelligent optimization algorithms proposed in recent years. The parameters used in the comparative experiments are: 500 iterations and 30 populations. In addition, to eliminate the possibility of randomness when running the algorithm only once, each algorithm is independently run 30 times to average the results and plot the convergence curve.

[0075] The algorithm proposed in this invention is a new type of swarm intelligence algorithm that can be applied to complex optimization problems in various industries. For example, SBOA can be used to optimize the selection of parameters of artificial neural networks and improve their learning ability; it can also be used for load balancing problems in the network and improve the overall performance of the network.

[0076] In summary, the present invention has excellent optimization capabilities, which are mainly divided into two key stages: the exploration stage and the development stage. In the exploration stage, the secretary bird optimization algorithm quickly achieves algorithm convergence through the processes of secretary bird prey search, prey physical exertion and attack on prey. In the development stage, the algorithm adopts two strategies of secretary birds to escape from predators, namely, camouflage with the environment and escape by flying or running, which effectively avoids falling into the dilemma of local optimal solutions. The uniqueness of this invention is that it draws on the hunting and survival behavior process of secretary birds, making the algorithm easy to understand and significantly improving the optimization capability. The secretary bird optimization algorithm can be flexibly applied to different scenarios, providing a feasible and effective optimization solution for solving practical problems.

[0077] The above briefly describes the embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A secretary bird optimization algorithm based on swarm intelligence, characterized in that: The following steps are involved: Step 1: Initialize the parameters of the Secretary Bird optimization algorithm, set the total number of algorithm iterations, the number of individuals in each iteration, the dimension of the problem to be optimized, and the upper and lower bounds of the search space; Step 2: Determine the exploration phase of the secretary bird, calculate the fitness value of the secretary bird's exploration process, and complete the exploration and search process for prey; Step 3: Select the predator avoidance strategy in the development stage of the secretary bird, calculate the fitness value of the secretary bird's development process according to the strategy, and complete the process of avoiding predators; Step 4: Perform boundary checks on the new solutions generated in the exploration and development phases to ensure they are within the solution space; Step 5: Evaluate the fitness values of all secretary bird locations, and the location with the best fitness value will be retained for the next round of iterative information sharing.

2. The swarm intelligence-based secretary bird optimization algorithm according to claim 1, characterized in that: In step 1, the parameters of the secretary bird optimization algorithm are initialized, the total number of iterations of the algorithm is set to T, the number of individuals in the population in each iteration is set to N, and the dimension of the problem to be optimized is Dim, and the upper and lower bounds of the search space are ub respectively. j and lb j ; In the initialization process of the Secretary Bird algorithm, the values of each dimension of the individual are random numbers between the upper and lower bounds, and a total of N candidate solutions will be generated. Among them, the position of the individual with the best fitness value will be retained as the benchmark for the next round of iterative process.

3. The swarm intelligence-based secretary bird optimization algorithm according to claim 2 is characterized in that: In step 2, the exploration phase of the secretary bird, the fitness value of the secretary bird's exploration process is calculated, and the exploration and search process for prey is completed. Formulas (1)-(4) are used to update the position of the secretary bird and update the individual fitness value, that is, when hour, when hour, when hour, Among them, t represents the current number of iterations, T represents the maximum number of iterations, represents the new state of the i-th secretary bird in the first stage, x i,j represents the value of the j-th problem variable of the i-th secretary bird, and is the random candidate solution of the first stage iteration, R1 represents a randomly generated array of dimension 1×Dim from the interval [0,1], x best represents the best candidate solution obtained in the current iteration, rand(1, Dim) represents a 1×Dim array randomly generated from a standard normal distribution, and RL represents the Levy flight function, which is calculated by equations (5) and (6). represents the fitness value of the i-th secretary bird in the j-th dimension, Represents the fitness value of its objective function; Where s is a fixed constant of 0.01, η is a fixed constant of 1.5, u and v are random numbers in the interval [0,1], σ represents a transition variable, and Γ represents a gamma function.

4. The swarm intelligence-based secretary bird optimization algorithm according to claim 3 is characterized in that: In step 3, the development phase of the secretary bird optimization algorithm, equations (7) and (8) are used to update the position of the secretary bird and update the individual fitness value: Where r = 0.5, R2 means randomly generating an array of dimension (1×Dim) from a normal distribution, x random represents the random candidate solution of the current iteration, round(1+rand(1,1)) represents a random integer value of 1 or 2, Represents the new state of the i-th secretary bird in the second stage.

5. The swarm intelligence-based secretary bird optimization algorithm according to claim 4 is characterized in that: In step 4, boundary control is performed on the solutions obtained in steps 2 and 3 to ensure that all solutions obtained are within the solution space.

6. The swarm intelligence-based secretary bird optimization algorithm according to claim 5, characterized in that: In step 5, the fitness values of all secretary bird positions are evaluated. The position of the secretary bird with the best fitness value will be retained for the next iteration. At the beginning of the next iteration, the positions of all secretary birds are set to the positions with the best fitness values in the previous iteration. If the end condition is met, the optimal solution is output, otherwise return to step 2 to continue execution.

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