Research On Static And Dynamic Optimization Problems Of Gravitational Search Algorithm

In the scientific study and engineering practice,various complex optmizing problems,static or dynamic,could be seen almost everywhere,including product dispatching,resource allocation,engineering design and fault diagnosis.Any static or dynamic optmizing issues could solved with designed algorithms to acquire the best regulation scheme,parameter setting and controlling strategy,which could bring huge economic benefits for the production.With the optmizing issues getting more complex,the difficulty of designing algorithms to the optimal solution is also increasing.So the study of solution algorithms to static and dynmaic optimizing problems is prevailing in the acamedic and industrial circles.By analayzing the current issues,it can be inffered that the difficulties lie in:(1)the algorithm may fall into local optimum and slow rate of convergence if there occur high space dimensionality,multiple local extremums and complex objective functions;(2)With the increase of targeted space dimensionality,conflicted objective functions disables the only optimal solution to the optimizing problem with only a set of optimal soltuions being obtained after comprise.So it might be hard to acquire a set of optimal solutions with high convergence precision and good distributivity through algorithm.The difficulty of dynamic optmizing problems is the changing objective functions or related parameters along with the time.So the algorithm is required to be able to detect the environment changes and quickly provide the optimal solution or optimal solution set in the changed environment.The evolutionary algorithm is not limited to the forms of problems,mathematical models and initial conditions when dealing with static or dynamic optimizing problems.Besides,it is well capable of dealing with uncertain information,its unique advantage stands out when it comes to massive,highly nonlinear,non-differentiable or discontinuous,or multimodal optimizing problems or those with uncertain mathematical forms.Therefore,the paper adopts Gravity Search Algorithm(GSA),an algorithm with relatively strong capability of optimizing among current evolutionary algorithms,to dive into the theoretical studies of static single-objective,static multi-objective,dynamic single-objective and dynamic multi-objective problems,based on which the solutions are offered to cope with the existing optimizing problems in reality.The key content of the paper is covered in the following five parts:First of all,problems of local optimum and slow rate of convergence easily rise in the static single-objective algorithm targeting the static high-dimensional complex single-objective problems.So the static single-objective GSA is proposed based on the mixed strategy.(1)An individual evolutionary strategy is put forward to conduct the evolutionary operation on the suitable particles after evaluating their evolutionary speed in the two-round iteration.(2)A directional mutation strategy is adopted that is operated on particles at different stages of population evolution to balance the diversity and convergence of the population,avoiding the local optimum.The simulated research result has verified that the improved algorithm could certainly effectively solve the static single-objective problems.Secondly,based on the decomposition technique,the static multi-objective GSA is raised to solve the problems of low convergence and distributivity.(1)weight adaptive generation strategy to predict the concavity of the frontier after solving several sets of preference sub-problems.The weight vector is obtained based on the prediction results,along with the focuses aligning evenly on the ideal frontier to raise the distributivity of the algorithm.(2)Multi-population serial search strategy is implementd by adopting the GSA to search for each decomposed sub-problem and each sub-population in order to get the optimal initial poluation based on the neibourhood,by which the convergence of the algorithm is improved.(3)a solution set deleting strategy is sued by comparaing the weighted values of similar solutions in the objective space to delete the recessive solutions,balancing the convergence and distributivity of the solution set.The simulated research result has indicated that the improved algorithm can effecitvely solve the static multi-objective problems.Thirdly,a dynamic single-objective GSA based on the multi-population is raised toward the problem of low accuracy of the existing dynamic single-objective algorithms.(1)In a way of multi-population serial search,GSA optimizes the local optimal peak and each sub-population is initiated based on the spotted peaks.The distance detection strategy adopted during searching could terminate the repeated searches of the population,decreasing the calculation cost and increasing the accuracy of algorithm for the local optimal peaks.(2)A new environment monitor strategy could help to calculate and compare the changes of each spotted local extremum at different time,making response timely after evaluating the changing situation.(3)A tracking strategy for the spotted peaks is applied where new population will be fostered around the spotted peaks after the environment has changed,tonarrow the search interval of the sub-population as well as to increase the speed and accuracy of obtaining the optimal solution after environment changes.It has been confirmed by the simulated research result that the improved algorithm could effectively solve the dynamic single-objective problem.Fourthly,to deal with the issues of convergence,distributivity and predictability in solving dynamic multi-objective problems with existing algorithms,the dynamic multi-objective GSA is proposed based on the decomposition technique.(1)The static multi-objective GSA raised in the Chapter Three is introduced to enable the population to find the non-dominant solution set with better convergence and distributivity before environment changes.(2)A mixed preditive model is built to predict the changes in the optimal solution set according to the similarity of the optimal solutions between adjacent sub-problems as well as the similiarity of the optimal solutions led by the similar weighted vectors before and after envrionment changes.Thus the search interval for the optimal solution set is narrowed after the changes with the increased searching speed of the algorithm.Likewie,the simulated research result supports that the improved algorithm could effectively solve the dynamic multi-objective problems.Fifthly,the static optimizing algorithm raised before is applied in the optimizing problems in reality.(1)Due to the low fusion clarity existing in the multi-focus image fusion algorithm,a new one based on the regional features is brought about to extract the regions with high definition in the fusion image through comparing the regional space frequency of two images.Then SCM is adopted to fuse the rest images with the parameters in the model optimized with the static single-objective algorithm raised in the Chapter Three.The effective of the algorithm is proved by the research result.(2)To further improve the coverage of the three-dimensional directional sensor network,a coverage enhancement algorithm is proposed based on the improved GSA,where the static single-objective algorithm raised in the Chapter Three is used to optimize the pitch and deflection angles of the network nodes,thus reducing the coverage overlap and increasing the network coverage.The algorithm is proved to be effective according to the result.(3)To counter the problem of distinct difference between the energy consumptions of nodes and the short network lifecycle of the land isomerism wireless sensor network,two algorithms are put forward,a GSA-based routing algorithm and an energy-difference-based clustering algorithm.The algorithm takes the energy difference ofnodes on the cluster head as objective function to build mathematical optimal model and adopts the static single-objective algorithm in the Chapter Three to optimize the topological structure of the nodes.Then the ideal lifecycles of cluster-head nodes and ordinary nodes are both considered to cluster the ordinary nodes.The effectiveness of the algorithm is verified in the result.(4).Considering the short working life of the underwater wireless sensor network as well as the weak network coverage,a coverage clustering-keeping algorithm is raised based on the node sleeping.At first,the redundancy rate of nodes is calculated to rest the nodes with high redundancy rate with the premise of ensuring the network coverage.Then,targeting the network coverage and balanced energy consumption of nodes,the static multi-objective algorithm raised in the Chapter Three is further optimized to reap a set of non-dominant solutions,where the better solution is chosen with the help of TOPSIS.When certain node dies,the arousing strategy stays to maintain the network coverage.Likewise,the effective of the algorithm is again proved in the result.