Research And Application Of Meta-Heuristic Optimization Algorithms

The optimization problem refers to the problem that finds the best solution among many alternatives to improve the performance of the system under some constraints.It has been widely used in many fields such as engineering technology,economic management,public management,biomedicine,scientific research and so on.Traditional methods for solving optimization problems,such as simplex method and gradient descent method,can obtain theoretical optimal solutions in some special cases.But it is difficult to solve large-scale nonlinear problems with high-dimension in some practical applications,and it is easy to fall into local optimum.Therefore,inspired by bionics,meta-heuristic optimization algorithms were proposed.Meta-heuristic algorithms get inspiration from the random phenomena in nature,which combine the random algorithm with the local algorithm.It is more likely to jump out of the local optimum and get the global optimal solution.Moreover,meta-heuristic algorithms can solve the problems that cannot be solved by polynomial-time algorithm or the problems that can be solved by polynomial-time algorithm but not found so far.In addition,there are not any special requirements for the objective function(such as differentiable or convex).Meta-heuristic algorithms can be applied not only in some special problems,but also in a wide range of fields.So they have become one of the research focuses in the optimization field.However,meta-heuristic algorithms cannot make sure that the global optimal solution can be obtained,and often fall into local optimum in some applications.Therefore,proposing a new better and more robust meta-heuristic algorithm for more complex optimization problems,which can balance the relationship between exploration and exploitation,becomes the goal of the current researches.Inspired by Bernoulli's principle and kernel trick,this paper proposes two new meta-heuristic optimization algorithms,which have better performance on benchmark functions and in real-world engineering applications.The details are as follows:1.Inspired by Bernoulli's principle in fluid mechanics,a new meta-heuristic algorithm,Fluid Search Optimization(FSO)algorithm,is proposed.In the optimization process,FSO algorithm simulates the reverse process of fluid flowing from high pressure to low pressure,that is,the speed is high at low pressure,and gradually slowdown in the process of flowing to high pressure.With the flow of the fluid particles,they converge at the highest pressure and reach the optimum of the objective function at the end.FSO algorithm redefines the density and pressure of the fluid according to the optimization process,and designs the diffusion mechanism and exponent reduction mechanism to balance the relationship between exploration and exploitation.The experiments on benchmark function test which were widely used showed that the diffusion mechanism and exponent reduction mechanism could improve the performance of FSO.Moreover,FSO obtained better results and was more robust compared with some popular algorithms such as genetic algorithms,particle swarm optimization,gravity search algorithm and firefly algorithm.2.Inspired by the design of FSO and the kernel trick in SVM,another new meta-heuristic algorithm,kernel search optimization algorithm(KSO),is proposed.All the meta-heuristics algorithms search the optimal solution of the objective function through a nonlinear iterative process,which is essentially a linear incremental(finding maximum)or decremental(finding minimum)process in a higher dimensional space.And kernel trick can map the nonlinear objective functions to the linear ones with higher dimensions.Therefore,the optimization process for nonlinear functions can be transformed into that for linear ones by kernel trick.In the transformation process,the objective function is approximated by a kernel function,and the optimal value of the kernel function is approximated to that of the objective function.Through multiple iterations,the optimal value of the kernel function is getting closer to that of the objective function.KSO approximates the search process of increasing or decreasing along the “straight line” in the higher-dimensional space,and obtains the optimal value for the nonlinear function.We try to design KSO as a universal search process covering other meta-heuristic algorithms.The test of massive benchmark functions show that KSO only demanded the necessary parameters,and got better results and shorter CPU time compared with some popular algorithms such as genetic algorithms,particle swarm optimization,gravity search algorithm,differential evolution algorithm,firefly algorithm and artificial bee colony algorithm.The test verified the feasibility and effectiveness of kernel trick for searching the optimal value iteratively.3.The two new algorithms FSO and KSO are applied to the combined economic emission dispatch(CEED)problem respectively.CEED needs to minimize both fuel cost and pollution emission simultaneously,along with a large number of power constraints such as power balance and generation limits.This is essentially a Multi-objective Optimization Problem(MOP)with two conflict objectives.FSO and KSO transform CEED into an unconstrained single-objective optimization problem by weighted sum method and penalty function method.In the real-world cases test,the Pareto-front obtained by FSO and KSO is much better than the best comprise solution of most algorithms.Moreover,no matter the best fuel cost or the best pollution emissions,FSO and KSO performed better than all the compared algorithms in the literature,especially better than those were just on the Pareto-front.So in general,FSO and KSO achieved a better performance on CEED problem,and saved fuel cost or reduced total emission.It is worth noting that,the results obtained by KSO in the larger CEED problem with valve point are better than that of FSO,which indicates KSO has more powerful search ability on continuous problems.4.The new algorithm FSO was applied to gene selection for microarray dataset,and a FSO/SVM framework was designed which can select genes and optimize support vector machine(SVM)parameters simultaneously.The framework binarizes FSO by introducing angle modulation formula,which can select relevant genes and remove irrelevant genes from microarray dataset.And it implements gene selection and SVM parameter optimization simultaneously,which simplifies the process of gene selection effectively.The experimental results showed that FSO/SVM greatly reduced the number of selected genes and improves the classification accuracy.It also showed that FSO had strong ability to jump out of local optimum to obtain better performance FSO is a very effective pre-processing tool to improve feature selection efficiency and classification accuracy.