CN114611801A - Traveler problem solving method based on improved whale optimization algorithm - Google Patents

Traveler problem solving method based on improved whale optimization algorithm Download PDF

Info

Publication number
CN114611801A
CN114611801A CN202210253919.6A CN202210253919A CN114611801A CN 114611801 A CN114611801 A CN 114611801A CN 202210253919 A CN202210253919 A CN 202210253919A CN 114611801 A CN114611801 A CN 114611801A
Authority
CN
China
Prior art keywords
whale
fitness
optimal
individual
positions
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
CN202210253919.6A
Other languages
Chinese (zh)
Inventor
倪伟
郭丹
张粤
王子祥
孙靖康
相福康
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huaiyin Institute of Technology
Original Assignee
Huaiyin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huaiyin Institute of Technology filed Critical Huaiyin Institute of Technology
Priority to CN202210253919.6A priority Critical patent/CN114611801A/en
Publication of CN114611801A publication Critical patent/CN114611801A/en
Withdrawn legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/08—Computing arrangements based on specific mathematical models using chaos models or non-linear system models

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Business, Economics & Management (AREA)
  • Human Resources & Organizations (AREA)
  • Economics (AREA)
  • Evolutionary Computation (AREA)
  • Data Mining & Analysis (AREA)
  • Artificial Intelligence (AREA)
  • Software Systems (AREA)
  • Strategic Management (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Analysis (AREA)
  • Development Economics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Biomedical Technology (AREA)
  • Biophysics (AREA)
  • Computational Linguistics (AREA)
  • General Health & Medical Sciences (AREA)
  • Molecular Biology (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Algebra (AREA)
  • Game Theory and Decision Science (AREA)
  • Nonlinear Science (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Marketing (AREA)
  • Operations Research (AREA)
  • Quality & Reliability (AREA)
  • Tourism & Hospitality (AREA)
  • General Business, Economics & Management (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention relates to the technical field of computer artificial intelligence, and discloses a traveler problem solving method based on an improved whale optimization algorithm, which comprises the following steps: setting algorithm parameters; initializing a population position by utilizing chaotic mapping; calculating individual fitness and recording the current optimal solution individual; entering an iteration stage to obtain an updated probability p; selecting a mode to update the whale position by judging the probability p and the coefficient vector A; entering a simulated annealing stage, and calculating new population fitness; judging whether the positions are updated according to a greedy rule, outputting the globally optimal whale positions and fitness if the positions are updated, otherwise directly receiving the positions of the new population according to the simulated annealing probability P, then outputting the globally optimal whale positions and fitness, and selecting the whale with the minimum fitness value as the optimal path. Compared with the prior art, the method has the advantages of higher precision, high convergence speed, strong robustness and wide global search range, can jump out local optimum, and has outstanding performance.

Description

Traveler problem solving method based on improved whale optimization algorithm
Technical Field
The invention relates to the technical field of computer artificial intelligence, in particular to a traveler problem solving method based on an improved whale optimization algorithm.
Background
Research on the Traveling Salesman Problem (TSP) has long sought an efficient and fast approximation algorithm to accurately solve a large scale problem in a reasonable computational time frame. Typical intelligent optimization algorithms include an ant colony algorithm, a particle swarm algorithm, a wolf algorithm and the like. Although these intelligent optimization algorithms have advantages in handling the traveler Problem (TSP), they sometimes have limitations of many parameters, weak optimizing capability, and easy falling into local extrema, so many scholars discuss the traveler Problem (TSP) and the related applications with the intelligent algorithms.
Whale Optimization Algorithm (WOA) is a novel heuristic optimization algorithm and is proposed by simulating hunting behavior of whale. In the WOA algorithm, the position of each whale in the standing position represents a feasible solution, and in the marine world, the hunting process of the whale in the standing position comprises three processes of searching for a prey, surrounding the prey and predating the prey. To describe this behavior, mirjalii proposes a mathematical model of these three processes. Although Whale Optimization Algorithm (WOA) is simple in structure, easy to understand and successfully applied to projects such as fault diagnosis and photovoltaic cell parameters, the problems of low convergence speed and incapability of finding a global optimal solution still exist in solving the Traveling Salesman Problem (TSP).
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a traveler problem solving method based on an improved whale optimization algorithm, so that the global search capability is enhanced, the convergence speed of the problem solving method is increased, and the stability of the method is improved.
The technical scheme is as follows: the invention provides a traveler problem solving method based on an improved whale optimization algorithm, which comprises the following steps:
step 1: initializing algorithm parameters, taking urban position data of urban path planning in a traveling salesman problem as position information of whale individuals, and simultaneously initializing parameters including population scale N, random number l and maximum iteration number TmaxConstant coefficient b of the helical equation;
step 2: initializing the whale population position by generating a chaotic sequence through Circle chaotic mapping;
and step 3: setting the initial temperature T0Calculating the individual fitness in the population, finding out the optimal individual and the optimal fitness value of the individual, and carrying out Cauchy variation on the optimal individual;
and 4, step 4: entering an iteration stage, updating the convergence factor a, further updating the coefficient vector A and the inertia weight w, and finally obtaining an updated coefficient vector c, a random number l and a probability p;
and 5: entering a judging stage, entering global search if | A | is greater than 1 when p is less than 0.5, updating the individual position, entering surrounding prey if | A | is less than or equal to 1, updating the individual position, entering prey when p is greater than or equal to 0.5, updating the position of the whale, and obtaining parameters of feasible paths from an initial city point to a target point in the selected classical example problem of the travelling merchant problem by using a two-dimensional grid map model to obtain all feasible initial paths of each whale;
step 6: entering a simulated annealing stage, newly generating a progeny whale population, randomizing individual whales, and calculating new population fitness;
and 7: judging whether the positions are updated according to a greedy rule, if so, outputting the globally optimal whale positions and fitness, otherwise, receiving the positions of the new population according to the probability p, then outputting the globally optimal whale positions and fitness, and selecting an optimal path with the minimum fitness as the selected classical example city path planning problem of the traveling salesman problem;
and 8: recording the optimal individual position and fitness of whale and judging whether T is more than TmaxAnd if the condition is not met, t is t +1, and the step 3 is continuously executed until the condition is met.
Further, the method can be used for preparing a novel materialIn step 3, the formula for performing cauchy mutation on the optimal individual is as follows: x is the number of*(t +1) ═ x (t +1) + a · tan (pi · γ -0.5)), where γ ═ a, γ ∈ [0,1 ∈ 0,1 ·)]And t is the current iteration number.
3. The traveler problem solving method based on the improved whale optimization algorithm as claimed in claim 1, wherein the specific way of updating the convergence factor a, the random vector A and the inertia weight w in the step 4 is as follows:
Figure BDA0003548084980000021
A＝2ar-a；
Figure BDA0003548084980000031
wherein r is [0,1 ]]Subject to uniformly distributed random numbers, TmaxIs the maximum number of iterations.
Further, the global search is performed in the step 5, parameters of feasible paths from the starting city point to the target point in the selected classical example problem of the Traveling Salesman (TSP) are obtained, and then the whale position is updated, wherein the formula is as follows:
x(t+1)＝w(t)·xrand(t)-A·|c·xrand(t)-x(t)|,
p＜0.5,|A|＞1
wherein x (t +1) is the whale optimal position point, xrand(t) is the location point of the current population at random for a search volume.
Further, surrounding prey in the step 5, obtaining parameters of feasible paths from the starting city point to the target point in the selected classical example problem of the Traveling Salesman (TSP), and further updating the whale position, wherein the formula is as follows:
x(t+1)＝w(t)·x*(t)-A·|c·x*(t)-x(t)|,
p＜0.5,|A|≤1
wherein x is*(t +1) is the newest whale position point before mutation, and x (t) is the best position of the current whale.
Furthermore, prey is entered in the step 5, parameters of feasible paths from the starting city point to the target point in the classical example problem of the selected Traveling Salesman Problem (TSP) are obtained, and then the whale position is updated, wherein the formula is as follows:
x(t+1)＝w(t)·x*(t)+D2·eblcos(2πl),
p≥0.5
wherein D is2＝|x*(t) -x (t) is a distance vector between the search city point and the target city point, and x (t) is the current whale position.
Further, the greedy rule in step 7 is:
Figure BDA0003548084980000032
simulated annealing probability
Figure BDA0003548084980000033
Wherein x is*(t +1) is the optimal whale position point before variation, fnew(xj) The fitness of the jth whale individual in the annealing stage to generate a new population; f (x)j) Is the fitness of the jth individual of whale.
Has the advantages that:
according to the method, whale populations are initialized through chaotic mapping, the global search capability is enhanced, the global optimal solution is guided by adopting self-adaptive variation and nonlinear time-varying factors, the algorithm convergence speed is accelerated, and the algorithm stability is improved; and jumping out the local optimal trap through the inverse cumulative distribution of the Cauchy distribution in the global search process, and effectively searching the solution space of the TSP. The shortest path length is obtained by testing the TSPLIB data set, and the effectiveness of the improved algorithm is reflected.
Drawings
FIG. 1 is a flow chart of a method for solving the travelling merchant problem of an improved whale optimization algorithm (MWOA) provided by the invention;
fig. 2, fig. 3 and fig. 4 are all performance test results of the present invention compared with other improved whale optimization algorithms in 12 intelligent optimization benchmark test functions.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention discloses a traveler problem solving method based on an improved whale optimization algorithm, which comprises the following steps:
step 1: the algorithm parameters are initialized, data (positions of 30, 51 and 96 cities) in three classical examples (Oliver30, eil51 and gr96) of the traveler problem are used as the position information of the whale individual, and x is ═ x [ -x ] x1,x2,...,xn]Showing that the simultaneous initialization parameters comprise a population size N, a random number l and a maximum iteration number TmaxThe constant coefficient b of the spiral equation.
Step 2: a chaotic sequence is generated through Circle chaotic mapping to initialize the whale population position, and the random sequence formula is as follows:
Figure BDA0003548084980000041
where x (t +1) represents the initialized whale position.
And step 3: setting the initial temperature T0And calculating the individual fitness in the population, finding out the optimal individual and the optimal fitness value of the individual, and carrying out Cauchy variation on the optimal individual, wherein the formula for carrying out Cauchy variation on the optimal individual is as follows: x is the number of*(t +1) ═ x (t +1) + a · tan (pi · γ -0.5)), where γ ═ a, γ ∈ [0,1 ∈ 0,1 ·]And t is the current iteration number.
And 4, step 4: entering an iteration stage, updating the convergence factor a, further updating the coefficient vector A and the inertia weight w, and finally obtaining an updated coefficient vector c, a random number l and a probability p, wherein the specific mode of updating the convergence factor a, the random vector A and the inertia weight w is as follows:
Figure BDA0003548084980000051
A＝2ar-a；
Figure BDA0003548084980000052
wherein r is [0,1 ]]Subject to uniformly distributed random numbers, TmaxIs the maximum number of iterations
And 5: entering a judging stage, entering global search if | A | is larger than 1 when p is smaller than 0.5, updating the individual position, entering surrounding prey if | A | is smaller than or equal to 1, updating the individual position, entering predatory prey when p is larger than or equal to 0.5, updating the position of the whale, and obtaining parameters of a feasible path from an initial city point to a target point in the selected classical instance problem of the Traveling Salesman Problem (TSP) by utilizing a two-dimensional grid map model to obtain all feasible initial paths of each whale.
And entering global search to obtain parameters of feasible paths from an initial city point to a target point in the selected classical example problem of the Traveling Salesman Problem (TSP), and further updating the whale position, wherein the formula is as follows:
x(t+1)＝w(t)·xrand(t)-A·|c·xrand(t)-x(t)|,
p＜0.5,|A|＞1
wherein x (t +1) is the whale optimal position point, xrandIs the position point of a random search body of the current population.
Entering surrounding prey, obtaining the parameter of feasible path from starting city point to target point in classical example problem of selected Travelling Service Provider (TSP), and updating whale position, where the formula is x (t +1) ═ w (t) · x*(t)-A·|c·x*(t)-x(t)|,
p＜0.5,|A|≤1
Wherein x is*(t +1) is the newest whale position point before mutation, and x (t) is the best position of the current whale.
Entering prey, obtaining the parameters of feasible paths from the starting city point to the target point in the classical example problem of the selected Traveling Salesman Problem (TSP), and further updating the whale position according to the formula
x(t+1)＝w(t)·x*(t)+D2·eblcos(2πl),。
p≥0.5
Wherein D is2＝|x*(t) -x (t) is a distance vector between the searching city point and the target city point, and x (t) is the current whale position
Step 6: and (4) entering a simulated annealing stage, newly generating a progeny whale population, randomizing individual whales, and calculating new population fitness.
And 7: judging whether the positions are updated according to a greedy rule, if so, outputting the globally optimal whale positions and fitness, otherwise, receiving the positions of the new populations according to the simulated annealing probability P, then, outputting the globally optimal whale positions and fitness, and selecting an optimal path with the minimum fitness value as the urban path planning problem of the classical examples (Oliver30, eil51 and gr96) of the selected traveler problem (TSP).
The greedy rule is:
Figure BDA0003548084980000061
simulated annealing probability
Figure BDA0003548084980000062
Wherein x is*(t +1) is the optimal whale location point before variation, fnew(xj) The fitness of the jth whale individual in the annealing stage to generate a new population; f (x)j) Is the fitness of the jth individual of whale.
And 8: recording the optimal individual position and fitness of whale and judging whether T is more than TmaxIf t is not satisfied, t +1, and the step 3 is continued until the condition is satisfied.
Comparing a Particle Swarm Optimization (PSO) algorithm, a firefly (GA) algorithm, a wolf optimization (GWO) algorithm, a moth fire suppression (MFO) algorithm, a Bayes (BOA), a simulated annealing-whale optimization algorithm (SA-WOA), an inertia weight-whale optimization algorithm (W-WOA), a Whale Optimization Algorithm (WOA) and an improved whale optimization algorithm (MWOA), calculating 12 reference functions in a table 1, running for 50 times under different algorithms, and recording an average value (Ave) and a standard deviation (Std) of each function, wherein experimental results are given in a table 2 and an attached figure 2.
TABLE 1 reference function
Figure BDA0003548084980000063
Figure BDA0003548084980000071
TABLE 2 Performance test results in 12 Intelligent optimized benchmark test functions compared to other Intelligent optimization algorithms
Figure BDA0003548084980000072
Figure BDA0003548084980000081
The selected intelligent test functions are a unimodal function and a complex multi-modal function respectively, so that the test functions are more representative, and the result shows that: compared with algorithms such as simulated annealing-whale optimization algorithm (SA-WOA), inertial weight-whale optimization algorithm (W-WOA), Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO) and wolf of lady optimization (GWO) in the attached figure 2, the improved whale optimization (MWOA) algorithm provided by the invention is obviously improved in calculation precision and convergence speed, meanwhile, self-adaptive weight is fused with the whale optimization algorithm or simulation results of the simulated annealing algorithm are combined, and finally, the improved whale optimization (MWOA) algorithm is proved to have enhanced global search capability while the convergence speed is increased, and the improved effectiveness is reflected.
In order to test the effect of the improved whale optimization (MWOA) algorithm in the method for solving the problem of the traveller, taking the problems of classic traveller examples Oliver30, eil51 and gr96 as examples, the optimal path length is recorded by comparing the Gray Wolf Optimization (GWO), the Whale Optimization (WOA) algorithm and the improved whale optimization (MWOA) algorithm, and the experimental result is given in table 3.
Table 3 shows the performance test results of the TSP problem in comparison with other algorithms according to the present invention
Figure BDA0003548084980000082
Figure BDA0003548084980000091
The experimental results show that the improved whale optimization (MWOA) algorithm has higher precision, high convergence speed, strong robustness and wide global search range, can jump out local optimum and has outstanding performance.
The above embodiments are merely illustrative of the technical concepts and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered in the protection scope of the present invention.

Claims (7)

1. A traveler problem solving method based on an improved whale optimization algorithm is characterized by comprising the following steps:
step 1: initializing algorithm parameters, taking urban position data of urban path planning in a traveling salesman problem as position information of whale individuals, and simultaneously initializing parameters including population scale N, random number l and maximum iteration number TmaxConstant coefficient b of the helical equation;
and 2, step: initializing the whale population position by generating a chaotic sequence through Circle chaotic mapping;
and step 3: setting the initial temperature T0Calculating the individual fitness in the population, finding out the optimal individual and the optimal fitness value of the individual, and carrying out Cauchy variation on the optimal individual;
and 4, step 4: entering an iteration stage, updating the convergence factor a, further updating the coefficient vector A and the inertia weight w, and finally obtaining an updated coefficient vector c, a random number l and a probability p;
and 5: entering a judging stage, entering global search if | A | is greater than 1 when p is less than 0.5, updating the individual position, entering surrounding prey if | A | is less than or equal to 1, updating the individual position, entering prey when p is greater than or equal to 0.5, updating the position of the whale, and obtaining parameters of feasible paths from an initial city point to a target point in the selected classical example problem of the travelling merchant problem by using a two-dimensional grid map model to obtain all feasible initial paths of each whale;
step 6: entering a simulated annealing stage, newly generating a progeny whale population, randomizing individual whales, and calculating new population fitness;
and 7: judging whether the positions are updated according to a greedy rule, outputting the globally optimal whale positions and fitness if the positions are updated, otherwise, receiving the positions of the new population according to the simulated annealing probability P, then outputting the globally optimal whale positions and fitness, and selecting an optimal path with the minimum fitness as the selected classical example city path planning problem of the traveling salesman problem;
and 8: recording the optimal individual position and fitness of whale and judging whether T is more than TmaxAnd if the condition is not met, t is t +1, and the step 3 is continuously executed until the condition is met.
2. The traveler problem solving method based on improved whale optimization algorithm according to claim 1, wherein the formula for cauchy variation of optimal individuals in step 3 is as follows: x is the number of*(t +1) ═ x (t +1) + a · tan (pi · γ -0.5)), where γ ═ a, γ ∈ [0,1 ∈ 0,1 ·)]And t is the current iteration number.
3. The traveler problem solving method based on the improved whale optimization algorithm as claimed in claim 1, wherein the specific way of updating the convergence factor a, the random vector A and the inertia weight w in the step 4 is as follows:
Figure FDA0003548084970000021
A＝2ar-a；
Figure FDA0003548084970000022
wherein r is [0,1 ]]Subject to uniformly distributed random numbers, TmaxIs the maximum number of iterations.
4. The method for solving the traveling salesman problem based on the improved whale optimization algorithm as claimed in claim 1, wherein the global search is entered in the step 5, parameters of feasible paths from an initial city point to a target point in the selected classic example problem of the Traveling Salesman Problem (TSP) are obtained, and then the whale position is updated, and the formula is as follows:
x(t+1)＝w(t)·xrand(t)-A·|c·xrand(t)-x(t)|,
p＜0.5,|A|＞1
wherein x (t +1) is the whale optimal position point, xrand(t) is the location point of the current population at random for a search volume.
5. The method for solving the traveling salesman problem based on the improved whale optimization algorithm as claimed in claim 1, wherein the step 5 is to surround the prey, obtain the parameters of feasible paths from the starting city point to the target point in the classic example problem of the selected Traveling Salesman Problem (TSP), and further update the whale position, and the formula is:
x(t+1)＝w(t)·x*(t)-A·|c·x*(t)-x(t)|,
p＜0.5,|A|≤1
wherein x is*(t +1) is the newest whale position point before mutation, and x (t) is the best position of the current whale.
6. The improved whale optimization algorithm-based traveler problem solving method according to claim 1, wherein the prey in step 5 is obtained to obtain parameters of feasible paths from a starting city point to a target point in a selected classic example problem of traveler problem (TSP), and then the whale position is updated, and the formula is as follows:
x(t+1)＝w(t)·x*(t)+D2·eblcos(2πl),
p≥0.5
wherein D is2＝|x*(t) -x (t) is a distance vector between the search city point and the target city point, and x (t) is the current whale position.
7. The improved whale optimization algorithm-based traveler problem solving method according to any one of claims 1 to 6, wherein the greedy rule in the step 7 is:
Figure FDA0003548084970000031
simulated annealing probability
Figure FDA0003548084970000032
Wherein x is*(t +1) is the optimal whale position point before variation, fnew(xj) The fitness of the jth whale individual in the annealing stage to generate a new population; f (x)j) Is the fitness of the jth individual of whale.
CN202210253919.6A 2022-03-15 2022-03-15 Traveler problem solving method based on improved whale optimization algorithm Withdrawn CN114611801A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210253919.6A CN114611801A (en) 2022-03-15 2022-03-15 Traveler problem solving method based on improved whale optimization algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210253919.6A CN114611801A (en) 2022-03-15 2022-03-15 Traveler problem solving method based on improved whale optimization algorithm

Publications (1)

Publication Number Publication Date
CN114611801A true CN114611801A (en) 2022-06-10

Family

ID=81862773

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210253919.6A Withdrawn CN114611801A (en) 2022-03-15 2022-03-15 Traveler problem solving method based on improved whale optimization algorithm

Country Status (1)

Country Link
CN (1) CN114611801A (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115080402A (en) * 2022-06-22 2022-09-20 河南工业大学 Whale optimization algorithm-based software defect positioning method and processing device
CN115499916A (en) * 2022-11-15 2022-12-20 中国人民解放军海军工程大学 Wireless sensor network node positioning method based on improved whale optimization algorithm
CN116468181A (en) * 2023-04-26 2023-07-21 山东工商学院 Improved whale-based optimization method
CN116562331A (en) * 2023-05-19 2023-08-08 石家庄铁道大学 Method for optimizing SVM by improving reptile search algorithm and application thereof
CN116721433A (en) * 2023-06-08 2023-09-08 吉首大学 Improved whale optimization algorithm and application method thereof in character recognition

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115080402A (en) * 2022-06-22 2022-09-20 河南工业大学 Whale optimization algorithm-based software defect positioning method and processing device
CN115499916A (en) * 2022-11-15 2022-12-20 中国人民解放军海军工程大学 Wireless sensor network node positioning method based on improved whale optimization algorithm
CN115499916B (en) * 2022-11-15 2023-01-20 中国人民解放军海军工程大学 Wireless sensor network node positioning method based on improved whale optimization algorithm
CN116468181A (en) * 2023-04-26 2023-07-21 山东工商学院 Improved whale-based optimization method
CN116562331A (en) * 2023-05-19 2023-08-08 石家庄铁道大学 Method for optimizing SVM by improving reptile search algorithm and application thereof
CN116562331B (en) * 2023-05-19 2023-11-21 石家庄铁道大学 Method for optimizing SVM by improving reptile search algorithm and application thereof
CN116721433A (en) * 2023-06-08 2023-09-08 吉首大学 Improved whale optimization algorithm and application method thereof in character recognition
CN116721433B (en) * 2023-06-08 2024-01-30 吉首大学 Improved whale optimization algorithm and application method thereof in character recognition

Similar Documents

Publication Publication Date Title
CN114611801A (en) Traveler problem solving method based on improved whale optimization algorithm
Chaudhuri et al. Feature selection using Binary Crow Search Algorithm with time varying flight length
Fan et al. A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems
Xu et al. Comparative study on single and multiple chaotic maps incorporated grey wolf optimization algorithms
CN111880561B (en) Unmanned aerial vehicle three-dimensional path planning method based on improved whale algorithm in urban environment
CN114047770B (en) Mobile robot path planning method for multi-inner-center search and improvement of wolf algorithm
CN111582428A (en) Multi-modal multi-objective optimization method based on grey prediction evolution algorithm
CN116242383B (en) Unmanned vehicle path planning method based on reinforced Harris eagle algorithm
Ajibade et al. A hybrid chaotic particle swarm optimization with differential evolution for feature selection
Dubey et al. Uniform mutation and SPV rule based optimized PSO algorithm for TSP problem
CN116400737B (en) Safety path planning system based on ant colony algorithm
CN115271273A (en) Traveler problem solving method and system based on improved whale optimization algorithm
Sindhu et al. A hybrid SCA inspired BBO for feature selection problems
CN115169517A (en) Improved grey wolf optimization algorithm method
CN116017476A (en) Wireless sensor network coverage design method and device
Shan et al. Cauchy mutation boosted Harris hawk algorithm: Optimal performance design and engineering applications
CN111080035A (en) Global path planning method based on improved quantum particle swarm optimization algorithm
Eluri et al. Chaotic binary pelican optimization algorithm for feature selection
Yang et al. A particle swarm optimization-based approach with local search for predicting protein folding
Liu et al. Swarm intelligence for classification of remote sensing data
Saitou et al. Grey Wolf Optimization using Improved mutation oppositional based learning for optimization problems
Liu et al. Ranked hunger games search algorithms with Gaussian distribution-based fitness distance balance strategy
CN112308229A (en) Dynamic multi-objective evolution optimization method based on self-organizing mapping
Al-Thanoon et al. A new hybrid pigeon-inspired optimization algorithm for solving multidimensional knapsack problems
CN105160436A (en) N neighboring Lipschitz supporting surface-based generalized augmented group global optimization method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WW01 Invention patent application withdrawn after publication

Application publication date: 20220610

WW01 Invention patent application withdrawn after publication