Improvement Research On The Grey Wolf Optimizer

Optimization problems are widespread in real life.Many complex management and engineering problems in daily practice activities,such as NP-hard problems,operation scheduling,management decision optimization,workshop management,production planning,etc.,are often solved by transforming them into special optimization problems and selecting appropriate techniques.Therefore,optimization plays a key role in management science and is widely employed in engineering,life sciences,medicine and other scientific research fields.However,optimization problems in practice are usually marked as non-concave,highly nonlinear,non-differentiable,etc.These characteristics of the complex problems denote that it is difficult to solve them by adopting traditional mathematical-based theories and methods.Therefore,it is necessary and urgent for managers,engineers and scientists to pursue more effective algorithms to replace the traditional mathematical analysis techniques.In the past few decades,more and more heuristic optimization techniques have occured in people’s field of vision,and have been successfully applied in solving complex optimization problems.Heuristic algorithms based on single-solution and group-solutions are the two typical optimization methods.However,when compared the single-solution based methods,the group-based intelligent optimization algorithms have received more extensive interesting.The grey wolf optimizer(GWO)is known as a type of heuristic swarm intelligence optimization algorithm.Since it is proposed,it has received extensive attention and research around the world.The GWO is developed inspired by the special hunting behavior of grey wolves.In the grey wolf pack,the group is divided into four levels.The first three levels are the leader of the group and with fewer individuals.The latter level is the executive group,which are exist many ordinary individuals.The individual in the first leadership is called alpha,represented by the symbol "α";the individual in the second leadership is called beta,represented by the symbol "β";the individual in the third leadership is called delta,which is represented by the symbol "δ";and the individuals in the executive group are called omega,which are represented by the symbol "ω".In the grey wolf pack,α is responsible for commanding and leading β,δ and ω to hunting;β is responsible for leading δ and ω to hunting;δ is responsible for leading ω to hunting.GWO is precisely by simulating this unique hunting mechanism of grey wolve pack to guide individuals to search the solution space globally.Similar to other swarm intelligence algorithms,the GWO uses individuals to iteratively search the solution space continuously to obtain the global optimal solution.Due to its simple principle,structure and easy to computer programming,the GWO has been successfully applied to different optimization fields.Although the GWO has the above advantages,its shortcomings are also obvious,mainly manifested in two aspects: weak global exploration ability and poor solution quality for the complex multi-modal problems.Therefore,to improve the GWO is very necessary and extremely challenging.Firstly,this thesis classifies and introduces the types of heuristic algorithms briefly.Secondly,the inspiring ideas,basic framework and theoretical model of the GWO are sorted out.Thirdly,an objective and comprehensive analysis of the defects of the GWO is carried out.Finally,the targeted improvements and application research are carried out based on the shortcomings of the GWO algorithm.The main research contents and innovations of this thesis are summarized as follows:(1)A chaotic grey wolf optimization algorithm(CGWO)is proposed based on the Cubic chaos theory.In the CGWO,the Cubic chaotic map operator is used to improve the position update equation of the GWO.In addition,a new nonlinear parameter control strategy is designed based on the improved position update equation,and this control strategy is used to improve the exploration performance of the algorithm.In order to search the solution space in depth,a chaotic random parameter based on the Cubic operator is proposed to replace the random control parameters in GWO,and this chaotic random parameter has also with the characteristics of the Cubic operator,that are strong ergodicity,good sensitivity and high non-repeatability.Since the diversity of the population particles is relatively high in the early search,a smaller control parameter is needed to speed up the convergence.On the contrary,in the later stage of the search,larger control parameters are required to reduce the convergence speed,so that the algorithm can search the solution space in depth.Based on the above analysis,a reasonable nonlinear control parameter is redesigned for the GWO algorithm.The proposed CGWO algorithm is applied to function optimization and training multi-layer perceptrons.Experimental results confirm that the performance of the CGWO algorithm in function optimization and training multi-layer perceptrons is superior to the standard GWO algorithm and its comparison algorithms.(2)A non-inferior solution grey wolf optimization(NGWO)algorithm is proposed.In the NGWO,the local neighborhood search and non-inferior solution search mechanisms are introduced.In the local neighborhood search strategy,the first three local optimal solutions of each iteration are used to replace the first three global optimal to guide the GWO algorithm to exploit its local neighborhood.In the non-inferior solution search strategy,those individuals(particles)that are near to the global optimal solution and meet some certain constraints are defined as non-inferior solutions,and the search mechanism of this strategy is to utilize those of the standard GWO algorithm to find out these non-inferior solutions,and then to filter out the individuals that are better than the global individual and replace it.The solutions of the search are better than the current global optimal individual has increased the diversity of individuals,which further increases the possibility of the GWO to jumping out of the local optimal.Finally,the local neighborhood search and non-inferior solution search are combined to form the NGWO algorithm in this thesis.The NGWO algorithm not only has a strong local search ability,but also with a strong ability to avoidance local optimal.By applying the NGWO algorithm to the power economic load dispatch(ELD)problem,the experimental results show that the NGWO algorithm has better solution performance in solving ELD problems than the standard GWO algorithm and other comparison algorithms.(3)A dynamic dimensional search grey wolf optimization(DGWO)algorithm based on the location interactive information is proposed.In the DGWO algorithm,we proposed a spiral predation strategy and introduced a dynamic dimensional search(DDS)mechanism to switch the spiral predation strategy to the direct encircling predation strategy of the GWO to enhance its search ability.Based on drawback that the standard GWO algorithm does not consider the lack of information communication mechanism between grey wolves in the process of predation,this thesis proposes a location update strategy by introducing the position information interaction,and the goal is to promote information exchange between grey wolves.In addition,a non-linear control parameter strategy is redesigned to improve the global search capability of the DGWO.The experimental results on several typical test functions and several classical engineering problems show that the performance of the DGWO is better than its comparison algorithms.(4)A new weight-distance grey wolf optimization(GWO-WD)algorithm is proposed.The proposed algorithm is based on analyzing the different shortcomings of the two different weight-distance,which can be consulted from the literature,and then proposes a new weight distance to overcome the drawbacks of these two weight distances.The position-update equation of the standard GWO is improved by using the proposed new weight distance,so as to guide the individual to search the solution space fully.In addition,in order to improve the exploration and local optimal avoidance abilities of the GWO-WD,an elimination and reinitialization strategy is proposed.This strategy enables the GWO-WD algorithm to perform search for a certain number of iterations on some poor individuals in the population.This method is to reinitialize these poor individuals near to the global optimal solution,thereby increasing their optimization performance and improving the search ability of the entire group.Finally,the proposed GWO-WD is tested on several well-known benchmark test functions.The test results confirm that the optimization performance of the GWO-WD is better than the GWO and other algorithms.In addition,the GWO-WD is employed to the parameter identification problem of the photovoltaic(PV)system,the experimental results further show that the effectiveness of the GWO-WD in practical engineering problems.(5)Based on the comprehensive analysis and comparison for the four improved GWO versions of this thesis,the advantages and disadvantages of each algorithm are summarized.Combining the advantages and disadvantages of the four algorithms,four typical hybrid algorithms are also proposed.By applying these four typical hybrid optimization techniques to simulation on three kinds of complex optimization problems,the interesting results are drawn out.The results shown that the four improved GWO algorithms are complementary to each other through the use of mutual advantages,and therefore,their optimization performance is enhanced to some degree.Finally,based on the pros and cons of each improved GWO algorithm,a brief description of its application fields is given,which provides a certain reference for related researchers who use the algorithm.