Multi-strategy hybrid whale optimization algorithms for complex constrained optimization problems

A multi-strategy hybrid whale optimization algorithm(MSHWOA)for complex constrained optimization problems is proposed to overcome the drawbacks of easily trapping into local optimum,slow convergence speed and low optimization precision.Firstly,the population is initialized by introducing the theory of good point set,which increases the randomness and diversity of the population and lays the foundation for the global optimization of the algorithm.Then,a novel linearly update equation of convergence factor is designed to coordinate the abilities of exploration and exploitation.At the same time,the global exploration and local exploitation capabilities are improved through the siege mechanism of Harris Hawks optimization algorithm.Finally,the simulation experiments are conducted on the 6 benchmark functions and Wilcoxon rank sum test to evaluate the optimization performance of the improved algorithm.The experimental results show that the proposed algorithm has more significant improvement in optimization accuracy,convergence speed and robustness than the comparison algorithm.

Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm

This paper presents an application of an Ant Colony Optimization （ACO） algorithm to optimize the parameters in the design of a type of nonlinear PID controller. The ACO algorithm is a novel heuristic bionic algorithm, which is based on the behaviour of real ants in nature searching for food. In order to optimize the parameters of the nonlinear PID controller using ACO algorithm, an objective function based on position tracing error was constructed, and elitist strategy was adopted in the improved ACO algorithm. Detailed simulation steps are presented. This nonlinear PID controller using the ACO algorithm has high precision of control and quick response.

Multiobjective evolutionary algorithm for dynamic nonlinear constrained optimization problems

A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.

Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems

The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.

A New Strategy for Solving a Class of Constrained Nonlinear Optimization Problems Related to Weather and Climate Predictability

There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.

A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations

A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared.

A Method for Crude Oil Selection and Blending Optimization Based on Improved Cuckoo Search Algorithm

Refineries often need to find similar crude oil to replace the scarce crude oil for stabilizing the feedstock property. We introduced the method for calculation of crude blended properties firstly, and then created a crude oil selection and blending optimization model based on the data of crude oil property. The model is a mixed-integer nonlinear programming(MINLP) with constraints, and the target is to maximize the similarity between the blended crude oil and the objective crude oil. Furthermore, the model takes into account the selection of crude oils and their blending ratios simultaneously, and transforms the problem of looking for similar crude oil into the crude oil selection and blending optimization problem. We applied the Improved Cuckoo Search(ICS) algorithm to solving the model. Through the simulations, ICS was compared with the genetic algorithm, the particle swarm optimization algorithm and the CPLEX solver. The results show that ICS has very good optimization efficiency. The blending solution can provide a reference for refineries to find the similar crude oil. And the method proposed can also give some references to selection and blending optimization of other materials.

Nonlinear optimal model and solving algorithms for platform planning problem in battlefield

Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qualities. Firstly, we take into account the relation among tasks and build the single task nonlinear optimal model with a set of platform constraints. The Lagrange relaxation method and the pruning strategy are used to solve the model. Secondly, this paper presents optimization-based planning algorithms for efficiently allocating platforms to multiple tasks. To achieve the balance of the resource assignments among tasks, the m-best assignment algorithm and the pair-wise exchange(PWE)method are used to maximize multiple tasks completion qualities.Finally, a series of experiments are designed to verify the superiority and effectiveness of the proposed model and algorithms.

Blending Scheduling under Uncertainty Based on Particle Swarm Optimization Algorithm

Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

Improved genetic algorithm for nonlinear programming problems

An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.

Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method

In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.

A Novel Self Adaptive Modification Approach Based on Bat Algorithm for Optimal Management of Renewable MG

In the new competitive electricity market, the accurate operation management of Micro-Grid (MG) with various types of renewable power sources (RES) can be an effective approach to supply the electrical consumers more reliably and economically. In this regard, this paper proposes a novel solution methodology based on bat algorithm to solve the op- timal energy management of MG including several RESs with the back-up of Fuel Cell (FC), Wind Turbine (WT), Photovoltaics (PV), Micro Turbine (MT) as well as storage devices to meet the energy mismatch. The problem is formulated as a nonlinear constraint optimization problem to minimize the total cost of the grid and RESs, simultaneously. In addition, the problem considers the interactive effects of MG and utility in a 24 hour time interval which would in- crease the complexity of the problem from the optimization point of view more severely. The proposed optimization technique is consisted of a self adaptive modification method compromised of two modification methods based on bat algorithm to explore the total search space globally. The superiority of the proposed method over the other well-known algorithms is demonstrated through a typical renewable MG as the test system.

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production.In practice,multiple ethylene furnaces are usually run in parallel.The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product.In this paper,given the requirements of both profit and energy saving in actual production process,a multi-objective optimization model contains two objectives,maximizing the average benefits and minimizing the average coking amount was proposed.The model can be abstracted as a multi-objective mixed integer nonlinear programming problem.Considering the mixed integer decision variables of this multi-objective problem,an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables(MDNSGA-Ⅱ)is used to solve the Pareto optimal front of this model,the algorithm adopted crossover and mutation strategy with multi-operators,which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables.Finally,using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.

GBO algorithm for seismic source parameters inversion

The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer(GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization(MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.

Symplectic multi-level method for solving nonlinear optimal control problem

By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.

An Evolutionary Algorithm Based on a New Decomposition Scheme for Nonlinear Bilevel Programming Problems

In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.

基于遗传算法的磨削力模型系数优化及验证

在磨削力模型求解问题中,目前大多使用分段计算法或列方程组直接计算各个待求系数,不仅计算量大且其精度也无法保证。另外,传统的回归模型容易陷入局部最优,难以描述非线性关系。为此,将遗传算法引入到非线性优化函数参数优化中,基于外圆横向磨削力模型、平面磨削力模型、外圆纵向磨削力模型等现有的模型数据,开展磨削力理论模型的系数优化方法研究。相关性分析结果表明:通过计算得到的3种模型磨削力的预测精度提高了14.69%~42.54%,且3种模型所预测的法向磨削力的平均误差分别为5.9%、9.13%、3.23%,切向力平均误差分别为6.78%、8.36%、3.69%。经对比知,优化后的模型拟合度较好,模型预测精度显著提高。遗传算法优化后的非线性优化函数GA-LSQ算法更适合磨削力模型的求解,可对磨削力的预测及实际加工生产中的参数优化提供参考。

基于非线性搜索策略的改进灰狼优化算法及其应用

灰狼算法(GWO)在大工业复杂的优化问题求解中存在许多不足之处,如容易陷入局部最优解、收敛速度慢、最优解精度低等缺点,由此提出一种改进的灰狼优化算法.在灰狼算法的基础上,通过引入非线性参数和新的位置迭代更新方程,构建一种基于非线性策略的灰狼优化算法,并通过软件实现算法.通过8个标准测试函数在多维度下的数值对比实验和一个工程设计优化问题求解,分析验证算法的稳定性和优越性,并证明其性能均优于原有的GWO系列算法,是一种具有潜力的元启发式算法.

可重构智能表面辅助通信系统的非线性优化及实验设计

针对可重构智能表面辅助的通信系统,提出了一种智能反射表面开关选择和功率分配的联合设计方法,以改变电磁波传播环境、提高信号传输效率、减少功率消耗。首先,在保证接收端数据传输速率达到一定门限值等多个约束条件下,建立以系统能量效率最大化为目标的多维变量联合非线性优化问题,其中涉及的优化变量包括:智能反射表面开关选择、相位调整和功率分配。在开关选择方面,采用贪婪算法选择开启起主要作用的元器件,并关掉起次要作用的智能反射表面。在功率分配方面,通过求解凸优化问题得到功率分配的闭式解。基于此,设计出一种高传输速率、低功率消耗的迭代优化算法。最后,设计仿真教学实验,通过MATLAB软件,验证了所提出的联合优化算法通过改变电磁波传播环境,有效地提高了信号传输的速率和能量效率;并分析了实验中导致算法性能发生变化的机理,这也有利于帮助学生提高科研创新能力和工程实践能力。