Guided particle swarm optimization method to solve general nonlinear optimization problems

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder–Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.     

Combining discrete and continuous optimization to solve kinodynamic motion planning problems

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamic constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of intermediate points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the intermediate points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost.     

基于粒子群算法的空间直线度误差评定

提出了一种满足最小区域法的空间直线度误差评价的新方法--粒子群算法。根据最小区域条件,建立了空间直线的数学模型以及优化目标函数。阐述了粒子群优化算法的原理和实现方法,然后根据粒子群算法优化求解。实例表明该方法对于空间直线度误差评定等非线性优化问题能得到最优解,可用于三坐标测量机等测量系统的空间直线度误差测量的数据处理。     

基于多传感器融合信息的移动机器人速度控制方法

为提高移动机器人在复杂环境下的速度控制精度和适应能力,提出了一种基于多传感器融合信息的移动机器人速度控制方法。首先,根据多传感器非线性优化融合理论,通过最小化运动观测残差的方法来构建移动机器人运动状态优化估计模型。然后,对利用单目相机、轮式里程计及惯性测量单元（inertial measurement unit,IMU）观测移动机器人运动的方法进行介绍,并计算了各传感器对移动机器人运动的观测残差及其雅可比矩阵。最后,结合移动机器人运动状态估计信息与增量式PID （proportion integration differentiation,比例积分微分）控制策略,设计了移动机器人速度控制系统,并通过多项试验验证了该控制系统的性能。试验结果表明,所提出的移动机器人速度控制方法有效减小了速度估计误差,较基于轮式里程计信息的速度控制方法在精度与稳健性方面有较大提升。研究结果对提升移动机器人在复杂环境下的工作性能有显著意义。     

On the optimal control of steel annealing processes via various versions of genetic and particle swarm optimization algorithms

7 This paper elucidates the computation of optimal controls for steel annealing processes as hybrid systems which comprise of one or more furnaces integrated with plant-wide planning and scheduling operations. A class of hybrid system is considered to capture the trade-off between metallurgical quality requirement and timely product delivery. Various optimization algorithms including particle swarm optimization algorithm (PSO) with time varying inertia weight methods, PSO with globally and locally tuned parameters (GLBest PSO), parameter free PSO (pf-PSO) and PSO like algorithm via extrapolation (ePSO), real coded genetic algorithm (RCGA) and two-phase hybrid real coded genetic algorithm (HRCGA) are considered to solve the optimal control problems for the steel annealing processes (SAP). The optimal solutions including optimal line speed, optimal cost, and job completion time and convergence rate obtained through all these optimization algorithms are compared with each other and also those obtained via the existing method, forward algorithm (FA). Various statistical analyses and analysis of variance (ANOVA) test and hypothesis t-test are carried out in order to compare the performance of each method in solving the optimal control problems of SAP. The comparative study of the performance of the various algorithms indicates that the PSO like algorithms, pf-PSO and ePSO are equally good and are also better than all the other optimization methods considered in this chapter.     

Heuristics for single-pass welding task sequencing

Welding task sequencing is a prerequisite in the offline programming of robot arc welding. Single-pass welding task sequencing can be modelled as a modified travelling salesman problem. Owing to the difficulty of the resulting arc-routing problems, effective local search heuristics are developed. Computational speed becomes important because robot arc welding is often part of an automated process-planning procedure. Generating a reasonable solution in an acceptable time is necessary for effective automated process planning. Several different heuristics are proposed for solving the welding task-sequencing problem considering both productivity and the potential for welding distortion. Constructive heuristics based on the nearest neighbour concept and tabu search heuristics are developed and enhanced using improvement procedures. The effectiveness of the heuristics developed is tested and verified on actual welded structure problems and random problems.     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

Feasibility-Guided Constraint-Handling Techniques for Engineering Optimization Problems

The particle swarm optimization (PSO) algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and fish. PSO is essentially an unconstrained algorithm and requires constraint handling techniques (CHTs) to solve constrained optimization problems (COPs). For this purpose, we integrate two CHTs, the superiority of feasibility (SF) and the violation constraint-handling (VCH), with a PSO. These CHTs distinguish feasible solutions from infeasible ones. Moreover, in SF, the selection of infeasible solutions is based on their degree of constraint violations, whereas in VCH, the number of constraint violations by an infeasible solution is of more importance. Therefore, a PSO is adapted for constrained optimization, yielding two constrained variants, denoted SF-PSO and VCH-PSO. Both SF-PSO and VCH-PSO are evaluated with respect to five engineering problems: the Himmelblau’s nonlinear optimization, the welded beam design, the spring design, the pressure vessel design, and the three-bar truss design. The simulation results show that both algorithms are consistent in terms of their solutions to these problems, including their different available versions. Comparison of the SF-PSO and the VCH-PSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used. We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.     

粒子群优化算法综述

粒子群优化（PSO）算法是一种新兴的优化技术,其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现,可调参数少,已得到广泛研究和应用。详细介绍了PSO的基本原理、各种改进技术及其应用等,并对其未来的研究提出了一些建议。     

Efficient heuristics for robot acquisition planning for a CIM system

In this paper, a planning model and three efficient heuristics are developed for equipment acquisition planning for a CIM system using multiple-type robots. Our planning model considers selection of a proper mix of multiple-type robots such that operational requirements (i.e., time and space) from a given number of work stations are satisfied at minimal system cost. In specific, each robot is characterized by its fixed charge and subject to two capacity constraints on machine time and work space; and each work station has known demands for both machine time and work space, and is to be served by only one robot. The model is formulated as a pure 0–1 mathematical program and is shown to be harder than two-dimensional bin packing, a well-known NP-hard problem. The three heuristics developed are: a greedy heuristic, tabu thresholding, and simulated annealing. All heuristics are tested by solving 450 randomly generated problems. Computational results indicate that all three heuristics are effective and efficient in solving problems of a practical size (i.e., 50 work stations and a maximum of 20 robots). However, none of the heuristics are overwhelmingly better than the others in terms of both solution time and quality. Future research issues are also discussed.     

A highly accurate differential evolution–particle swarm optimization algorithm for the construction of initial value problem solvers

In this work a new evolutionary computation technique is introduced for the construction of initial value solvers based on Runge–Kutta (RK) pairs. The derivation of RK pairs corresponds to solving a nonlinear optimization problem with a multimodal objective function in a high dimensional search space; additional difficulty stems from the fact that only solutions with accuracy at least equal to machine epsilon are acceptable. The proposed approach involves hybridizing a Differential Evolution (DE) strategy with elements from Particle Swarm Optimization (PSO) in order to produce a method for solving optimization problems with high accuracy. The resulting methodology is applied to two different problems of RK pair derivation of orders 5 and 4 and compared with standard DE techniques. Numerical experiments show that the proposed hybrid DE-PSO satisfies the strict accuracy requirements imposed by the particular problem, while outperforming its rivals.     

A new trust region–sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control

In this article, a superlinearly convergent trust region–sequential quadratic programming approach is first proposed, developed and investigated for nonlinear systems based on nonlinear model predictive control. The method incorporates a combination algorithm that allows both the trust region technique and the sequential quadratic programming method to be used. If the attempted search of the trust region method is not accepted, the line search rule will be adopted for the next iteration. Also, having to resolve the quadratic programming subproblem for nonlinear constrained optimization problems is avoided. This gives the potential for fast convergence in the neighbourhood of an optimal solution. Moreover, additional characteristics of the algorithm are that each quadratic programming subproblem is regularized and the quadratic programming subproblem always has a consistent point. The main result is illustrated on a nonlinear system with a variable parameter and a bipedal walking robot system through simulations and is utilized to achieve rapidly stability. Numerical results show that the trust region–sequential quadratic programming algorithm is feasible and effective for a nonlinear system with a variable parameter and a bipedal walking robot system. Therefore, the simulation results demonstrate the usefulness of the trust region–sequential quadratic programming approach with nonlinear model predictive control for real-time control systems.     

Differential evolution techniques for the structure-control design of a five-bar parallel robot

The present work deals with the use of a constraint-handling differential evolution algorithm to solve a nonlinear dynamic optimization problem (NLDOP) with 51 decision variables. A novel mechatronic design approach is proposed as an NLDOP, where both the structural parameters of a non-redundant parallel robot and the control parameters are simultaneously designed with respect to a performance criterion. Additionally, the dynamic model of the parallel robot is included in the NLDOP as an equality constraint. The obtained solution will be a set of optimal geometric parameters and optimal PID control gains. The optimal geometric parameters adjust the dynamic and the kinematic parameters, optimizing then, the link shapes of the robot. The proposed mechatronic design approach is applied to design simultaneously both the mechanical structure of a five-bar parallel robot and the PID controller.     

Flower Pollination Heuristics for Nonlinear Active Noise Control Systems

Abstract In this paper, a novel design of the flower pollination algorithm is presented for model identification problems in nonlinear active noise control systems. The recently introduced flower pollination based heuristics is implemented to minimize the mean squared error based merit/cost function representing the scenarios of active noise control system with linear/nonlinear and primary/secondary paths based on the sinusoidal signal, random and complex random signals as noise interferences. The flower pollination heuristics based active noise controllers are formulated through exploitation of nonlinear filtering with Volterra series. The comparative study on statistical observations in terms of accuracy, convergence and complexity measures demonstrates that the proposed meta-heuristic of flower pollination algorithm is reliable, accurate, stable as well as robust for active noise control system. The accuracy of the proposed nature inspired computing of flower pollination is in good agreement with the state of the art counterpart solvers based on variants of genetic algorithms, particle swarm optimization, backtracking search optimization algorithm, fireworks optimization algorithm along with their memetic combination with local search methodologies. Moreover, the central tendency and variation based statistical indices further validate the consistency and reliability of the proposed scheme mimic the mathematical model for the process of flower pollination systems.     

Solving initial and boundary value problems using learning automata particle swarm optimization

In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method.     

基于微粒群算法的系统可靠性优化

微粒群算法是近来发展起来的一种新的优化计算方法,在简要说明微粒群算法的基础上,将该算法用于系统可靠性优化计算,分别对串联系统的可靠性分配、桥联系统的冗余可靠性优化设计问题进行分析计算,探讨了微粒群算法在系统的可靠性优化计算中应用的可行性,计算机仿真结果表明了微粒群算法求解该问题的可靠性和有效性。     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.     

Hybridization of ABC and PSO algorithms for improved solutions of RCPSP

A resource-constrained project scheduling problem (RCPSP) is one of the most famous intractable NP-hard problems in the operational research area in terms of its practical value and research significance. To effectively solve the RCPSP, we propose a hybrid approach by integrating artificial bee colony (ABC) and particle swarm optimization (PSO) algorithms. Moreover, a novel structure of ABC-PSO is devised based on embedded ABC-PSO (EABC-PSO) and sequential ABC-PSO (SABC-PSO) strategies. The EABC-PSO strategy mainly applies the PSO algorithm to update the process of the ABC algorithm while the SABC-PSO strategy demonstrates an approach in which computational results obtained from the ABC algorithm are further improved based on the PSO algorithm. In both strategies, bees in the ABC process are entitled to learning capacity from the best local and global solutions in terms of the PSO concept. Subsequently, the updates of solutions are premeditated with crossover and insert operators together with double justification methods. Computational results obtained from the tests on benchmark sets show that the proposed ABC-PSO algorithm is efficient in solving RCPSP problems, demonstrating clear advantages over the pure ABC algorithm, the PSO algorithm, and a number of listed heuristics.     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.