scholarly journals Improved Whale Optimization Algorithm for Solving Constrained Optimization Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Gui-Ying Ning ◽  
Dun-Qian Cao
Keyword(s):  
Constrained Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Convergence Speed ◽  
Whale Optimization Algorithm ◽  
Initial Population ◽  
Local Optimum ◽  
Penalty Function Method ◽  
Constrained Optimization Problems ◽  
Whale Optimization

In view of the shortcomings of the whale optimization algorithm (WOA), such as slow convergence speed, low accuracy, and easy to fall into local optimum, an improved whale optimization algorithm (IWOA) is proposed. First, the standard WOA is improved from the three aspects of initial population, convergence factor, and mutation operation. At the same time, Gaussian mutation is introduced. Then the nonfixed penalty function method is used to transform the constrained problem into an unconstrained problem. Finally, 13 benchmark problems were used to test the feasibility and effectiveness of the proposed method. Numerical results show that the proposed IWOA has obvious advantages such as stronger global search ability, better stability, faster convergence speed, and higher convergence accuracy; it can be used to effectively solve complex constrained optimization problems.

scholarly journals A Hybrid Whale Optimization Algorithm for Global Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1477
Author(s):  
Chun-Yao Lee ◽  
Guang-Lin Zhuo
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Whale Optimization Algorithm ◽  
Initial Population ◽  
Test Functions ◽  
Benchmark Test ◽  
Thermal Exchange ◽  
Whale Optimization ◽  
Benchmark Test Functions

This paper proposes a hybrid whale optimization algorithm (WOA) that is derived from the genetic and thermal exchange optimization-based whale optimization algorithm (GWOA-TEO) to enhance global optimization capability. First, the high-quality initial population is generated to improve the performance of GWOA-TEO. Then, thermal exchange optimization (TEO) is applied to improve exploitation performance. Next, a memory is considered that can store historical best-so-far solutions, achieving higher performance without adding additional computational costs. Finally, a crossover operator based on the memory and a position update mechanism of the leading solution based on the memory are proposed to improve the exploration performance. The GWOA-TEO algorithm is then compared with five state-of-the-art optimization algorithms on CEC 2017 benchmark test functions and 8 UCI repository datasets. The statistical results of the CEC 2017 benchmark test functions show that the GWOA-TEO algorithm has good accuracy for global optimization. The classification results of 8 UCI repository datasets also show that the GWOA-TEO algorithm has competitive results with regard to comparison algorithms in recognition rate. Thus, the proposed algorithm is proven to execute excellent performance in solving optimization problems.

Improved whale optimization algorithm based on variable spiral position update strategy and adaptive inertia weight

2021 ◽  
pp. 1-17
Author(s):  
Maodong Li ◽  
Guanghui Xu ◽  
Yuanwang Fu ◽  
Tingwei Zhang ◽  
Li Du
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Convergence Speed ◽  
Whale Optimization Algorithm ◽  
Original Algorithm ◽  
Inertia Weight ◽  
Whale Optimization ◽  
Multimodal Function ◽  
Update Strategy ◽  
Improved Algorithm

 In this paper, a whale optimization algorithm based on adaptive inertia weight and variable spiral position updating strategy is proposed. The improved algorithm is used to solve the problem that the whale optimization algorithm is more dependent on the randomness of the parameters, so that the algorithm’s convergence accuracy and convergence speed are insufficient. The adaptive inertia weight, which varies with the fitness of individual whales, is used to balance the algorithm’s global search ability and local exploitation ability. The variable spiral position update strategy based on the collaborative convergence mechanism is used to dynamically adjust the search range and search accuracy of the algorithm. The effective combination of the two can make the improved whale optimization algorithm converge to the optimal solution faster. It had been used 18 international standard test functions, including unimodal function, multimodal function, and fixed-dimensional function to test the improved whale optimization algorithm in this paper. The test results show that the improved algorithm has faster convergence speed and higher algorithm accuracy than the original algorithm and several classic algorithms. The algorithm can quickly converge to near the optimal value in the early stage, and then effectively jump out of the local optimal through adaptive adjustment, and has a certain ability to solve large-scale optimization problems.

scholarly journals Opposition-Based Multi-Objective Whale Optimization Algorithm with Multi-Leader Guiding

2021 ◽  
Author(s):  
Yang Li ◽  
Wei-gang Li ◽  
Yun-tao Zhao ◽  
Ao Liu
Keyword(s):  
Optimization Algorithm ◽  
Pareto Front ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Whale Optimization Algorithm ◽  
Benchmark Problems ◽  
Initial Population ◽  
Multi Objective ◽  
Opposition Based Learning ◽  
Whale Optimization

Abstract Over the years, heuristic algorithms have been widely studied, especially in multi-objective optimization problems (MOPs). The multi-objective whale optimization algorithm based on multi-leader guiding (MOWOAMLG) is proposed in this paper, which is the multi-objective version of whale optimization algorithm (WOA). The proposed algorithm adopts several improvements to enhance optimization performance. First, multiple leadership solutions guide the population to search the sparse space to achieve more homogeneous exploration in per iteration, and the leadership solutions are selected on the Pareto front by grid mechanism and the principle of maximum crowding distance. Second, the differential evolution (DE) is employed to generate the offspring for the leadership solutions, while WOA is employed for the ordinary solutions. In addition, a novel opposition-based learning (OBL) strategy is developed to improve the distribution of the initial population. To show the significance of the proposed algorithm, it is tested on the 20 bi-objective and tri-objective unconstrained benchmark problems of varying nature and complexities. The result of numerical experiments shows that the proposed algorithm has competitive advantages in convergence and distribution while compared with other 10 classic or state-of-the-arts algorithms. The convergence curve of IGD indicates that MOWOAMLG is able to obtain good Pareto front in cost of fewer optimization iterations. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned results have indicated that MOWOAMLG is comparatively effective and efficient to solve MOPs.

scholarly journals A Modified Whale Optimization Algorithm with Single-Dimensional Swimming for Global Optimization Problems

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1892
Author(s):  
Pengzhen Du ◽  
Weiming Cheng ◽  
Ning Liu ◽  
Haofeng Zhang ◽  
Jianfeng Lu
Keyword(s):  
Optimization Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Convergence Speed ◽  
Whale Optimization Algorithm ◽  
Well Performance ◽  
Simulation Experiments ◽  
Tent Map ◽  
Whale Optimization ◽  
Logarithm Function

As a novel meta-heuristic algorithm, the Whale Optimization Algorithm (WOA) has well performance in solving optimization problems. However, WOA usually tends to trap in local optimal and it suffers slow convergence speed for large-scale and high-dimension optimization problems. A modified whale optimization algorithm with single-dimensional swimming (abbreviated as SWWOA) is proposed in order to overcome the shortcoming. First, tent map is applied to generate the initialize population for maximize search ability. Second, quasi-opposition learning is adopted after every iteration for further improving the search ability. Third, a novel nonlinearly control parameter factor that is based on logarithm function is presented in order to balance exploration and exploitation. Additionally, the last, single-dimensional swimming is proposed in order to replace the prey behaviour in standard WOA for tuning. The simulation experiments were conducted on 20 well-known benchmark functions. The results show that the proposed SWWOA has better performance in solution precision and higher convergence speed than the comparison methods.

scholarly journals An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 48
Author(s):  
Jin Zhang ◽  
Li Hong ◽  
Qing Liu
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Relevant Literature ◽  
Population Diversity ◽  
Traveling Salesman ◽  
Whale Optimization Algorithm ◽  
Neighborhood Search ◽  
Whale Optimization ◽  
The Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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