Multi-strategy improved sea gull optimization algorithm

Abstract

The invention discloses a multi-strategy improved sea gull optimization algorithm, which adopts a mode of combining Logistic and Cubic chaotic mapping to realize population initialization, performs nonlinear change on a control factor in a sea gull migration stage, introduces Brownian motion to update a sea gull position, and introduces a Metropolis criterion to perform elimination selection on a final sea gull updated position. The randomness of position updating is increased, and the capabilities of global search and local search are fully balanced. According to the multi-strategy improved sea gull optimization algorithm, the convergence of the algorithm is effectively improved, and the algorithm is prevented from being caught in a local optimal solution too early.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, specifically to a multi-strategy improved Seagull optimization algorithm. Background Art

[0002] With the rapid development of modern engineering technology, optimization problems have become increasingly prevalent in engineering and research fields, requiring the solution of numerous multidimensional, complex, and computationally intensive optimization problems. Consequently, several new optimization algorithms have emerged in recent years, with swarm intelligence algorithms being representative. Common swarm intelligence algorithms include particle swarm optimization, sparrow optimization, and whale optimization. These algorithms are designed by simulating the population habits of animals in nature, possessing advantages such as global search, robustness, and feasibility. The algorithms themselves employ distributed computing, fully utilizing the advantages of cluster systems and multiprocessors to improve computational speed, thus gaining widespread attention from scholars and being applied in numerous fields to provide solutions to practical problems. The Seagull optimization algorithm (SOA) is a biomimetic swarm intelligence optimization algorithm inspired by the foraging behavior of seagulls. The optimization process of the Seagull algorithm mainly includes two stages: migration (global search) and attack (local search). The algorithm itself is characterized by simple structure, strong adaptability, and few parameters, and has wide applications in engineering optimization, feature selection, and other fields. However, it still suffers from problems such as being prone to getting trapped in local optima and slow convergence speed in global search. Summary of the Invention

[0003] The technical problem to be solved by this invention is to propose a multi-strategy improved Seagull optimization algorithm to address the shortcomings of the basic Seagull algorithm, which is prone to getting trapped in local optima.

[0004] The technical solution adopted in this invention is as follows:

[0005] A multi-strategy improved seagull optimization algorithm is proposed. The algorithm uses a combination of Logistic and Cubic chaotic mapping to initialize the population, performs nonlinear changes on the control factors during the seagull migration stage, introduces Brownian motion to update the seagull positions, and uses the Metropolis criterion to select the final updated positions of the seagulls, thereby improving the convergence of the algorithm and helping to avoid the trap of local convergence.

[0006] A multi-strategy improved Seagull optimization algorithm is mainly implemented by the following steps:

[0007] Step 1: Based on the Seagull algorithm, the population is initialized by combining Logistic and Cubic chaotic mapping.

[0008] Step 2: Apply nonlinear changes to the control factors during the seagull migration phase;

[0009] Step 3: During the seagull attack phase, Brownian motion is introduced to update the seagull positions;

[0010] Step 4: Use the Metropolis criterion to eliminate candidates from the final updated positions of the seagulls;

[0011] A multi-strategy improved Seagull optimization algorithm, wherein step 1 uses a combination of Logistic and Cubic chaotic mapping to initialize the population:

[0012] Assuming the size of the seagull population is N and the search space dimension is dim, then the position corresponding to the i-th seagull is HS. i =(HS) i,1 HS i,2 , ...,HS i,dim ), i = 1, 2, ..., N, and the specific dimension of the position component HS corresponding to the i-th seagull. i,j The random initialization is achieved through a uniform distribution, and the specific formula is as follows:

[0013] HS i,j =Lb j +rand×(Ub j -Lb j )

[0014] Ub j Lb j represents the upper and lower bounds of the j-th dimension, respectively, and rand is a random number that follows a uniform distribution within the range [0, 1].

[0015] Random sequences are generated using a combination of Logistic and Cubic chaotic mappings:

[0016] X n+1 =X n ×μ×(1-X n )

[0017] X′ n+1 =ρ×X′ n ×(1-X′ n 2 )

[0018] Where, X n+1 Represents the Logistic chaotic mapping, X′ n+1 This represents the Cubic chaotic mapping.

[0019] Add a random number α that follows a uniform distribution in the range [0, 1], and combine the two chaotic mappings, as shown in the following formula:

[0020] X_new n+1 =α×Xn+1 +(1-α)×X′ n+1

[0021] Initialize the seagull position HS based on the generated random number. i,j :

[0022] HS i,j =Lb j +X_new n+1 ×(Ub j -Lb j )

[0023] A multi-strategy improved seagull optimization algorithm, wherein step 2 involves nonlinearly varying the control factor during the seagull migration phase:

[0024] During migration, seagull populations seek new locations where they do not collide with neighboring seagulls. The algorithm primarily uses a control factor f... c To achieve:

[0025] C s (t)=f c ×HS(t)

[0026] In the formula, C s HS(t) represents a new position that does not conflict with other seagulls, HS(t) represents the position of the seagull before migration, and t is the current iteration number.

[0027] Control factor f c Not only can it avoid collisions, but it can also play a role in balancing global and local searches to some extent. The calculation formula is as follows:

[0028]

[0029] In the formula, MaxT represents the maximum number of iterations of the algorithm. It can be seen that f c The change is linearly decreasing during the iteration process.

[0030] Apply nonlinear changes to the control factors:

[0031]

[0032] Where, f c f represents the control factor. c，max with f c，min These represent the maximum and minimum values ​​of the control factor, respectively. rand represents a random number that follows a uniform distribution within the range [0, 1]. t is the current iteration number, and MaxT is the maximum iteration number.

[0033] Once the conditions for avoiding collisions are met, each seagull will determine the direction of the best seagull and then move towards it.

[0034] M s (t)=f b ×[HS best (t)-HS(t)]

[0035] Where M s (t) represents the optimal direction for the seagull; HS best (t) represents the optimal position of the seagull; parameter f b It is the search balance factor.

[0036] f b =2×f c 2 ×r d

[0037] r d It is a random number that follows a uniform distribution within the range [0, 1].

[0038] Approaching the optimal position: Determining the distance between the seagull and the optimal seagull

[0039] D s (t)=|C s (t)+M s (t)|

[0040] In the formula, D s (t) represents the distance between an individual seagull and the best seagull.

[0041] A multi-strategy improved seagull optimization algorithm, wherein step 3, introducing Brownian motion into the seagull position update during the seagull attack phase, includes:

[0042] The seagull's attack phase is a local search phase. During this phase, the seagull adjusts its attack angle and speed according to the prey's location, approaching the prey in a spiral motion in the air. The seagull's spiral motion is described in the x, y, z plane as follows:

[0043] x = r × cosθ

[0044] y = r × sinθ

[0045] z = r × θ

[0046] r = u × e θv

[0047] In the formula, r is the radius of the seagull's spiral flight in the air; θ is a random number that follows a uniform distribution within the range of [0, 2π], representing the seagull's attack angle; u and v are the spiral coefficients.

[0048] The seagulls' attack positions are as follows:

[0049] HS(t+1)=D s (t)×x×y×z+HS best (t)

[0050] Introducing Brownian motion into the seagull's attack position:

[0051] X s+t -X s ~N(0,c) 2 t)

[0052] HS(t+1)=D s (t)×x×y×z+HS best (t)+BM

[0053] In the formula, BM represents the stochastic process {X} t : t≥0} satisfies: X t It is an independent incremental process with stationary increments and follows a normal expectation of 0 and a variance of c. 2 t follows a normal distribution. HS(t+1) represents the attack position of the seagull, and D s (t) represents the distance between an individual seagull and the optimal seagull, HS best (t) represents the optimal position of the seagull, and x, y, z represent the coordinate descriptions of the seagull's spiral motion.

[0054] A multi-strategy improved seagull optimization algorithm, wherein step 4 uses the Metropolis criterion to select the final updated position of the seagull:

[0055] The Metropolis criterion is defined as follows: the probability that a solid object at temperature T transitions from state i to state j.

[0056]

[0057] Where E(i) and E(j) represent the internal energy of the object in state i and state j, respectively, and K is the Boltzmann constant.

[0058] According to the Metropolis criterion, if the newly generated solution HS(t+1) is better than HS(t), the updated solution replaces the original solution. If HS(t+1) is worse than HS(t), a random number γ in the [0, 1] range is generated. If γ < exp(d f / tem) then accepts the new solution. Where d f It is the difference between the fitness values ​​of HS(t+1) and HS(t), while tem is the current temperature.

[0059] The beneficial effects of this invention are as follows: The multi-strategy improved seagull optimization algorithm of this invention uses a combination of Logistic and Cubic chaotic mapping for population initialization, resulting in a more uniform initial position distribution of individuals and helping to avoid premature convergence in the early stages. During the seagull migration phase, the control factor is nonlinearly varied, making the initial f... c The value drops sharply, and the seagulls quickly move towards the optimal position; later, f c The value decreases slowly, gradually slowing down the pace, which fully balances the capabilities of global search and local search; Brownian motion is introduced to update the seagull's position, increasing the randomness of the position update and effectively avoiding premature entrapment in local optima; the Metropolis criterion is used to eliminate and select the final updated position of the seagull, making the simulation closer to the real situation and helping to escape the trap of local convergence. Attached Figure Description

[0060] Figure 1 The flowchart below shows a multi-strategy improved Seagull optimization algorithm according to the present invention. Detailed Implementation

[0061] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0062] A multi-strategy improved seagull optimization algorithm is proposed. The algorithm uses a combination of Logistic and Cubic chaotic mapping to initialize the population, performs nonlinear changes on the control factors during the seagull migration stage, introduces Brownian motion to update the seagull positions, and uses the Metropolis criterion to select the final updated positions of the seagulls, thereby improving the convergence of the algorithm and helping to avoid the trap of local convergence.

[0063] A multi-strategy improved Seagull optimization algorithm is implemented through the following steps:

[0064] Step 1: Based on the Seagull algorithm, the population is initialized by combining Logistic and Cubic chaotic mapping.

[0065] Step 2: Apply nonlinear changes to the control factors during the seagull migration phase;

[0066] Step 3: During the seagull attack phase, Brownian motion is introduced to update the seagull positions;

[0067] Step 4: Use the Metropolis criterion to eliminate candidates from the final updated positions of the seagulls;

[0068] A multi-strategy improved Seagull optimization algorithm, wherein step 1 uses a combination of Logistic and Cubic chaotic mapping to initialize the population:

[0069] Assuming the size of the seagull population is N and the search space dimension is dim, then the position corresponding to the i-th seagull is HS. i =(HS) i,1 HS i,2 , ...,HS i,dim ), i = 1, 2, ..., N, and the specific dimension of the position component HS corresponding to the i-th seagull. i,j The random initialization is achieved through a uniform distribution, and the specific formula is as follows:

[0070] HS i,j =Lb j +rand×(Ub j -Lb j )

[0071] Ub j Lb j represents the upper and lower bounds of the j-th dimension, respectively, and rand is a random number that follows a uniform distribution within the range [0, 1].

[0072] After initialization, the seagull population can change its location in any dimension. The specific distribution of the seagull population is as follows:

[0073]

[0074] During initialization, a combination of Logistic and Cubic chaotic mappings is used to generate random sequences.

[0075] X n+1 =X n ×μ×(1-X n )

[0076] X′ n+1 =ρ×X′ n ×(1-X′ n 2 )

[0077] Where, X n+1 Represents the Logistic chaotic mapping, X′ n+1 Denotes the Cubic chaotic mapping, μ∈[0,4], X n ∈(0,1). The Logistic mapping only has chaotic properties when 3.5699456<μ≤4.

[0078] Add a random number α that follows a uniform distribution in the range [0, 1], and combine the two chaotic mappings, as shown in the following formula:

[0079] X_new n+1 =α×X n+1 +(1-α)×X′ n+1

[0080] The seagull position HS is initialized based on the generated random number. i,j :

[0081] HS i,j =Lb j +X_new n+1 ×(Ub j -Lb j )

[0082] A multi-strategy improved seagull optimization algorithm, wherein step 2 involves nonlinearly varying the control factor during the seagull migration phase:

[0083] During migration, seagull populations seek new locations where they do not collide with neighboring seagulls. The algorithm primarily uses a control factor f... c To achieve:

[0084] C s (t)=f c ×HS(t)

[0085] In the formula, C s HS(t) represents a new position that does not conflict with other seagulls, HS(t) represents the position of the seagull before migration, and t is the current iteration number.

[0086] Control factor f c Not only can it avoid collisions, but it can also play a role in balancing global and local searches to some extent. The calculation formula is as follows:

[0087]

[0088] In the formula, MaxT represents the maximum number of iterations of the algorithm. It can be seen that f c The change is linearly decreasing during the iteration process.

[0089] To balance the control factors, a nonlinear transformation is performed on them:

[0090]

[0091] Where, f c f represents the control factor. c，max with f c，min These represent the maximum and minimum values ​​of the control factor, respectively. rand represents a random number that follows a uniform distribution within the range [0, 1]. t is the current iteration number, and MaxT is the maximum iteration number.

[0092] Once the conditions for avoiding collisions are met, each seagull will determine the direction of the optimal seagull and then move towards it, using the following formula:

[0093] M s (t)=f b ×[HS best (t)-HS(t)]

[0094] Where M s (t) represents the optimal direction for the seagull; HS best (t) represents the optimal position of the seagull; parameter f b It is the search balance factor.

[0095] f b =2×f c 2 ×r d

[0096] r d It is a random number that follows a uniform distribution within the range [0, 1].

[0097] Once the optimal direction for the seagulls is determined, the remaining seagulls move closer to the optimal position. The specific formula for calculating the distance between the seagulls and the optimal seagull is as follows:

[0098] D s (t)=|C s (t)+M s (t)|

[0099] In the formula, D s (t) represents the distance between an individual seagull and the best seagull.

[0100] A multi-strategy improved seagull optimization algorithm, wherein step 3, introducing Brownian motion into the seagull position update during the seagull attack phase, includes:

[0101] The seagull's attack phase belongs to the local search phase of the algorithm. In this phase, the seagull adjusts its attack angle and speed according to the prey's location, thus approaching the prey in a spiral motion in the air. The seagull's spiral motion is described in the x, y, z plane as follows:

[0102] x = r × cosθ

[0103] y = r × sinθ

[0104] z = r × θ

[0105] r = u × e θv

[0106] In the formula, r is the radius of the seagull's spiral flight in the air; θ is a random number that follows a uniform distribution within the range of [0, 2π], representing the seagull's attack angle; u and v are the spiral coefficients.

[0107] The seagulls' attack positions are as follows:

[0108] HS(t+1)=D s (t)×x×y×z+HS best (t)

[0109] Brownian motion is introduced during the seagull attack position update process to increase the randomness of the position update:

[0110] X s+t -X s ~N(0,c) 2 t)

[0111] HS(t+1)=D s (t)×x×y×z+HS best (t)+BM

[0112] In the formula, BM represents the stochastic process {X} t : t≥0} satisfies: X t It is an independent incremental process with stationary increments and follows a normal expectation of 0 and a variance of c. 2 t follows a normal distribution. HS(t+1) represents the attack position of the seagull, and D s (t) represents the distance between an individual seagull and the optimal seagull, HS best (t) represents the optimal position of the seagull, and x, y, z represent the coordinate descriptions of the seagull's spiral motion.

[0113] A multi-strategy improved seagull optimization algorithm, wherein step 4 uses the Metropolis criterion to select the final updated position of the seagull:

[0114] The Metropolis criterion is based on the physical annealing principle of a fixed material. As the temperature gradually decreases, the internal particles release internal energy and gradually tend to an ordered state, eventually reaching a stable ground state at room temperature. The Metropolis criterion allows even the worst solution to become a new solution.

[0115] The Metropolis criterion is defined as follows: the probability that a solid object at temperature T transitions from state i to state j.

[0116]

[0117] Where E(i) and E(j) represent the internal energy of the object in state i and state j, respectively, and K is the Boltzmann constant.

[0118] According to the Metropolis criterion, if the newly generated solution HS(t+1) is better than HS(t), the updated solution replaces the original solution. If HS(t+1) is worse than HS(t), a random number γ in the [0, 1] range is generated. If γ < exp(d f / tem) then accepts the new solution. Where d f It is the difference between the fitness values ​​of HS(t+1) and HS(t), while tem is the current temperature.

[0119] like Figure 1 As shown, a multi-strategy improved seagull optimization algorithm initializes the population by combining Logistic and Cubic chaotic mapping in the initial stage. During the seagull migration process, the control factor is nonlinearized, Brownian motion is introduced into the seagull attack behavior, and then the newly generated solutions are eliminated according to the Metropolis criterion. Finally, the optimal seagull position and fitness value are output.

[0120] The above examples are used to illustrate the present invention, not to limit it. Any modifications and changes made to the present invention within the spirit and scope of the claims fall within the protection scope of the present invention.

Claims

1. A multi-strategy improved Seagull optimization algorithm, whose features include Follow these steps: Step 1: Based on the Seagull algorithm, the population is initialized by combining Logistic and Cubic chaotic mapping; Step 2: nonlinearly change the control factors during the seagull migration stage; Step 3: In the seagull attack phase, Brownian motion is introduced to update the seagull position; Step 4: Use the Metropolis criterion to select the final seagull update position.

2. The multi-strategy improved seagull optimization algorithm according to claim 1, characterized in that: In step 1, the population is initialized by combining Logistic and Cubic chaotic mapping, which includes the following steps: Assuming the size of the seagull population is N and the dimension of the search space is dim, the position corresponding to the i-th seagull is HS i =(HS i,1 ,HS i,2 ,...,HS i,dim ), i = 1, 2, ..., N, and the position component HS of the specific dimension corresponding to the i-th seagull i,j , randomly initialized by uniform distribution, the specific formula is as follows: HS i，j =Lb j +rand×(Ub j -Lb j ) Among them Ub j , Lb j They represent the upper and lower bounds of the j-th dimension respectively, and rand is a random number in the range [0,1] that follows a uniform distribution; The random sequence is generated by combining Logistic and Cubic chaotic mapping: X n+1 =X n ×μ×(1-X n ) In the formula, X n+1 represents the Logistic chaotic map, X′ n+1 Represents Cubic chaotic map; Add a random number α in the range [0,1] that follows a uniform distribution and combine the two chaotic maps. The specific formula is as follows: X_new n+1 =α×X n+1 +(1-α)×X′ n+1 Initialize the seagull position HS according to the generated random number i,j : HS i，j =Lb j +X_new n+1 ×(Ub j -Lb j )。 3. The multi-strategy improved Seagull optimization algorithm according to claim 1, characterized in that: In step 2, nonlinear changes are made to the control factors during the seagull migration stage, including the following steps: In order to avoid collisions with neighboring seagulls during migration, seagull populations will first look for a new location that does not conflict with other seagulls. The algorithm mainly controls the factor f c To achieve: C s (t)=f c ×HS(t) In the formula, C s (t) represents the new position that does not conflict with other seagulls, HS(t) represents the position of the seagull before migration, and t is the current iteration number; Control factor f c It can not only avoid collisions, but also balance global search and local search to a certain extent. The calculation formula is as follows: Where MaxT is the maximum number of iterations of the algorithm. c It changes linearly in the iterative process; Make nonlinear changes to the control factors: In the formula, f c,max With f c,min They represent the maximum and minimum values ​​of the control factor, respectively; rand represents a random number that obeys a uniform distribution in the range [0,1]; t is the current number of iterations; and MaxT is the maximum number of iterations; After the conditions for avoiding collision are met, each seagull will determine the direction of the optimal seagull and then move towards it. M s (t)=f b ×[HS best (t)-HS(t)] Where M s (t) represents the direction of the optimal seagull; HS best (t) represents the optimal position of the seagull; the parameter f b is the search balance factor; f b =2×f c 2 ×r d r d It is a random number in the range [0,1] that follows a uniform distribution; Close to the best position: The distance between the seagull and the optimal seagull is determined; D s (t)=|C s (t)+M s (t)| Where D s (t) represents the distance between the individual seagull and the optimal seagull.

4. The multi-strategy improved Seagull optimization algorithm according to claim 1, characterized in that: In step 3, the introduction of Brownian motion to update the position of the seagulls during the seagull attack phase includes: The attack phase of the seagull belongs to the local search phase. In this phase, the seagull will appropriately change its attack angle and speed according to the location of the prey, thus approaching the prey in a spiral motion in the air. The spiral motion of the seagull in the x, y, z plane is described as follows: x=r×cosθ y=r×sinθ z＝r×0 r=u×e θv In the formula, r is the radius of the spiral flight of the seagull in the air; θ is a random number in the range [0,2π] that follows a uniform distribution, indicating the attack angle of the seagull; u and v are spiral coefficients. ; The Seagull's attack positions are as follows: HS(t+1)=D s (t)×x×y×z+HS best (t) Introducing Brownian motion in the seagull's attack position: X s+t -X s ~N(0,c 2 t) HS(t+1)=D s (t)×x×y×z+HS best (t)+BM Where BM represents the random process {X t ∶t≥0} satisfies: X t It is an independent incremental process, the increment is stable and obeys the expectation of 0, and the variance is c 2 t is the normal distribution. HS(t+1) is the attack position of the seagull, HS best (t) represents the optimal seagull position.

5. The multi-strategy improved Seagull optimization algorithm according to claim 1, characterized in that: In step 4, the Metropolis criterion is used to eliminate the position of the final seagull update: The Metropolis criterion is defined as follows: The probability that a solid object changes from state i to state j at temperature T Among them, E(i) and E(j) represent the internal energy of the object in state i and state j, and K is the Boltzmann constant. According to the Metropolis criterion, if the newly generated solution HS(t+1) is better than HS(t), the updated solution replaces the original solution. If HS(t+1) is worse than HS(t), a number γ in [0,1] is randomly generated. If γ<exp(d f / tem) accepts the new solution; where d f is the difference between the fitness values ​​of HS(t+1) and HS(t), and tem is the current temperature.

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