Several New Algorithms For Global Optimization Problems And Their Applications

The main aim of the global optimization algorithm is to find the global optimal solution or the approximate global optimal solution of global optimization problems within certain constrained conditions.Existing optimization algorithms can be classified into probabilistic and deterministic approaches.With the development of society and the advancement of technology,the current optimization problems are difficult to be solved because of multi-modal,high-dimensional and non-convex features,which promote the further development of the global optimization theory and algorithm.The whale optimization algorithm,as a relatively now population based stochastic optimization algorithm,adopts a parallel search mechanism to search a global optimal within the feasible region of problems,has strong global search ability and greater adaptability in practical problems,which has proved to be a research hotspot for researchers.However,it still has somewhat defects of plaguing into local optima and premature convergence when addressing global optimization problems.As a deterministic optimization algorithm,the filled function method with strong local search capability,can utilize the analytic property of the function to escape from the current local optimal solution,which has always attracted the attention of scholars.However,filled function method is prone to numerical instability and nonconference with the complexity of optimization problems.Based on the whale optimization algorithm and filled function approach,the purpose of this dissertation is to construct global optimization algorithms that can efficiently solve complex global optimization problems and apply the proposed algorithms to deal with practical problems appearing in privacy preservation and supply chain management.The main contents completed are as follows:1.An improved whale optimization algorithm based on multi-strategy,namely MSWOA,is devised to address somewhat deficiencies of convergence speed and accuracy of the basic whale optimization algorithm.First introduces the chaotic theory to generate the initial population with better distribution in search space to maximize the search capability.Meanwhile,nonlinear strategies of convergence factor and inertia weight are designed based on the number of iterations to tune the exploration and exploitation progress,which can better improve accuracy and increase convergence speed.Finally,an optimal based feedback strategy is given to strengthen the stability of basic WOA by utilizing the current best solution information to execute the exploration phase without blindness.Extensive numerical experiments are conducted on 24 benchmark functions to analyze the performance of MSWOA.The effect of each improvement strategy on the WOA optimization ability is discussed,and results show that the change of inertia weight has the greatest effect,followed by the convergence factor,and then the current best solution has significant influence on WOA to solve the optimization problem with multiple local optimal solutions.Moreover,compared with other state of the art meta-heuristic algorithms,the compared results indicate that MSWOA can achieve higher quality solutions within fewer iterative steps,and exhibit faster convergence rate as well as stronger stability.2.A hybrid intelligent algorithm integrating a modified whale optimization algorithm and crisscross optimization algorithm(MWOA-CS)is proposed to efficiently and robustly solve large scale optimization problems.In MWOA-CS,each dimension of the optimization problem updates its position by randomly performing improved WOA or crisscross optimization algorithm during the entire iterative process.The improved WOA adopts the new nonlinear convergence factor and nonlinear inertia weight to amend the ability of exploitation and exploration.To analyze the performance of MWOA-CS,a series of numerical experiments were performed on 30 test benchmark functions with dimension ranging from 300 to 1000.The experimental results revealed that the presented MWOA-CS provides better convergence speed and accuracy,and meanwhile,displays a significantly more effective and robust performance than the original WOA and other state of the art meta-heuristic algorithms for solving large scale global optimization problems.3.Two new continuous differentiable filled functions with different merits are given to tackle the puzzle that global optimization method plunges local optima.According to theory analysis,the corresponding filled function methods are designed,and the effectiveness and feasibility of the presented algorithms are verified by numerical experiments.(1)A new one-parameter filled function with the same local minima as the objective function is constructed.It is theoretically proved that the filled function has the same local minimizers of the objective function,and these minimizers are all better than the current minimizer of the objective function.Therefore,the new filled function method not needs to minimize the objective function except for the first iteration,which breaks the iterative framework of the conventional filled function method improving the computational efficiency.(2)A new non-parameter filled function with simple structure and convenient calculation is proposed.The theory proves that the filled function with better mathematical properties is better to solve,overcoming the shortcomings of the conventional filled functions.4.A new data privacy preservation model based on the proposed improved whale optimization is presented by transforming the process of association rule hiding into a multi-objective optimization problem to balance the relationship between data privacy and utility in the privacy preserving association rule mining.The two main processes of the proposed privacy preservation system are data sanitization and restoration,which are accomplished by the optimal key generation approach.The optimal key generation is optimized using the proposed MWOA-CS algorithm with the parameters such as rate of hiding failure、rate of false hiding,rate of false rule generation and regret of modification.The simulation experiments are conducted on chess,retail,T10 and T40 data sets,and the results reveal that the improved whale optimization algorithm has a better performance to balance the relationship between data privacy and data utility in privacy preservation.5.Considering the inventory decision problem of supply chain management within in planning period,an optimization and coordination model of a two-layer supply chain with three-echelon inventory is conducted,in which dealers place orders in several times with equal quantities,manufacturers order raw materials according to EOQ model.For the general demand function,the minimum cost function model of the integrated supply chain is given to draw up the optimal ordering period of dealer and the best production orders scheme of manufacturer,and transformed into a boxconstrained global optimization problem.The proposed filled function method is used to address many demand rate functions with different periods,and the numerical experiments results show that the constructed filled function method is effective for most types of demand rate functions.The establishment and solution of the model is usability,and has some certain theoretical instructive significance for coordinating raw material procurement,production as well as sales activities.