Evolutionary optimal trajectory planning for industrial robot with payload constraints

This paper presents a new general methodology based on the evolutionary algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE)—for optimal trajectory planning of an industrial robot manipulator (PUMA560) by considering payload constraints. The aim is to minimize a multicriterion cost function with actuator constraints, joint limits, and payload constraints by considering dynamic equations of motion. Trajectories are defined by B-spline functions. This is a nonlinear constrained optimisation problem with five objective functions, 32 constraints, and 252 variables. The multicriterion cost function is a weighted balance of transfer time, total energy involved in the motion, singularity avoidance, joint jerks, and joint accelerations. A numerical example is presented for showing the efficiency of the proposed procedure. Also, the results obtained from NSGA-II and DE techniques are compared and analysed. A comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain optimal solutions using the proposed DE algorithm.     

Selection of machining datum and allocation of tolerance through tolerance charting technique

Tolerance charting is an effective tool to determine the optimal allocation of working dimensions and working tolerances such that the blueprint dimensions and tolerances can be achieved to accomplish the cost objectives.The selection of machining datum and allocation of tolerances are critical in any machining process planning as they directly affect any setup methods/machine tools selection and machining time.This paper mainly focuses on the selection of optimum machining datums and machining tolerances simultaneously in process planning.A dynamic tolerance charting constraint scheme is developed and implemented in the optimization procedure.An optimization model is formulated for selecting machining datum and tolerances and implemented with an algorithm namely Elitist Non-Dominated Sorting Genetic Algorithm(NSGA-II).The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances.     

Optimal tolerance design for mechanical assembly considering thermal impact

In this paper, a cost–tolerance model based on neural network methods is proposed in order to provide product designers and process planners with an accurate basis for estimating the manufacturing cost. Tolerance allocation among the assembly components is carried out to ensure that the functionality and design quality are satisfied considering the effect of dimensional and geometric tolerance of various components of the assembly by developing a parametric computer aided design (CAD) model. In addition, deformations of various components of mechanical assembly due to inertia and temperature effects are determined and the same is integrated with tolerance design. The benefits of integrating the results of finite element simulation in the early stages of tolerance design are discussed. The proposed method is explained with an application example of motor assembly, where variations due to both dimensional and geometric tolerances are studied. The results show that the proposed methods are much effective, cost, and time saving than the ones considered in literature.     

Evolutionary collision-free optimal trajectory planning for intelligent robots

This paper presents optimization procedures based on evolutionary algorithms such as the elitist non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE) for solving the trajectory planning problem of intelligent robot manipulators with the prevalence of fixed, moving, and oscillating obstacles. The aim is the minimization of a combined objective function, with the constraints being actuator constraints, joint limits, and the obstacle avoidance constraint by considering dynamic equations of motion. Trajectories are defined by B-spline functions. This is a non-linear constrained optimization problem with six objective functions, 31 constraints, and 42 variables. The combined objective function is a weighted balance of transfer time, the mean average of actuator efforts and power, penalty for collision-free motion, singularity avoidance, joint jerks, and joint accelerations. The obstacles are present in the workspace of the robot. The distance between potentially colliding parts is expressed as obstacle avoidance. Further, the motion is represented using translational and rotational matrices. The proposed optimization techniques are explained by applying them to an industrial robot (PUMA 560 robot). Also, the results obtained from NSGA-II and DE are compared and analyzed. This is the first research work which considers all the decision criteria for the trajectory planning of industrial robots with obstacle avoidance. A comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal solutions using the proposed DE algorithm.     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

Multi-Input Single Output SSSC based damping controller design by a hybrid Improved Differential Evolution-Pattern Search approach

In this paper, a hybrid Improved Differential Evolution and Pattern Search (hIDEPS) approach is proposed for the design of a PI-Type Multi-Input Single Output (MISO) Static Synchronous Series Compensator (SSSC) based damping controller. The improvement in Differential Evolution (DE) algorithm is introduced by a simple but effective scheme of changing two of its most important control parameters i.e. step size and crossover probability with an objective of achieving improved performance. Pattern Search (PS) is subsequently employed to fine tune the best solution provided by modified DE algorithm. The superiority of a proposed hIDEPS technique over DE and improved DE has also been demonstrated. At the outset, this concept is applied to a SSSC connected in a Single Machine Infinite Bus (SMIB) power system and then extended to a multi-machine power system. To show the effectiveness and robustness of the proposed design approach, simulation results are presented and compared with DE and Particle Swarm Optimization (PSO) optimized Single Input Single Output (SISO) SSSC based damping controllers. It is observed that the proposed approach yield superior damping performance compared to some approaches available in the literature.     

Model and algorithm for fuzzy joint replenishment and delivery scheduling without explicit membership function

We study a joint replenishment and delivery scheduling (JRD) problem in which a central warehouse serves n-retailers in the presence of vague operational conditions such as ordering cost and inventory holding cost. In the proposed fuzzy set-based approach, an exact membership function is not assumed and instead can be approximated using piecewise linear functions based on alpha level sets because of their easy handling and efficiency. Subsequently, the fuzzy total cost is defuzzified by the widely used signed distance method to ranking fuzzy numbers. However, due to the JRD's difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. To find an optimal solution, an effective and efficient differential evolution (DE) algorithm is designed. After determining the appropriate parameters of the DE by parameter tuning test, the effectiveness of the DE is verified by numerical examples. We compare the DE with the available best approach and results show that DE can solve this non-deterministic polynomial hard problem in a robust way with a high convergence rate and low average error.     

Concurrent multi-objective tolerance allocation of mechanical assemblies considering alternative manufacturing process selection

Concurrent design of tolerances by considering both the manufacturing cost and quality loss of each component by alternate processes of the assemblies may ensure the manufacturability, reduce the manufacturing costs, decrease the number of fraction nonconforming (or defective rate), and shorten the production lead time. Most of the current tolerance design research does not consider the quality loss. In this paper, a novel multi-objective optimization method is proposed to enhance the operations of the non-traditional algorithms (Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO)) and systematically distribute the tolerances among various the components of mechanical assemblies. The problem has a multi-criterion character in which three objective functions, one constraint, and three variables are considered. The average fitness factor method and normalized weighted objective function method are used to select the best optimal solution from Pareto-optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto-optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto-optimal fronts and results obtained from various techniques are compared and analysed. Both NSGA-II and MOPSO algorithms are best for this problem.     

A hybrid GA–PSO approach for reliability optimization in redundancy allocation problem

This paper presents a novel hybrid genetic algorithm (GA)-particle swarm optimization (PSO) approach for reliability redundancy allocation problem (RRAP) in series, series–parallel, and complex (bridge) systems. The proposed approach maximizes overall system reliability while minimizing system cost, system weight and volume, simultaneously, under nonlinear constraints. To meet these objectives, an adaptive hybrid GA–PSO approach is developed to identify the optimal solutions and improve computation efficiency for these NP-hard problems. An illustrative example is applied to show the capability and effectiveness of the proposed approach. According to the results, in all three cases, reliability values are improved. Moreover, computational time and variance are decreased compared to the similar studies. The proposed approach could be helpful for engineers and managers to better understand their system reliability and performance, and also to reach a better configuration.     

A modified particle swarm optimization for disaster relief logistics under uncertain environment

Relief logistics is one of the most important elements of a relief operation. This paper investigates a relief chain design problem where not only demands but also supplies and the cost of procurement and transportation are considered as the uncertain parameters. Furthermore, the model considers uncertainty for the locations where those demands can arise and the possibility that a number of the facility could be partially destroyed by the disaster. The proposed model for this study is formulated as a mixed-integer nonlinear programming to minimize the sum of the expected total cost (which includes costs of location, procurement, transportation, holding, and shortage) and the variance of the total cost. The model simultaneously determines the location of relief distribution centers and the allocation of affected area to relief distribution centers. Furthermore, an efficient solution approach based on particle swarm optimization is developed in order to solve the proposed mathematical model. At last, computational results for several instances of the problem are presented to demonstrate the feasibility and effectiveness of the proposed model and algorithm.     

Evolutionary optimization of sliding mode controller for level control system

This paper accords the level control of single-input-single-output (SISO) level control system based on the fusion of sliding mode control (SMC) and evolutionary techniques or bio-inspired techniques. The non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are considered as two evolutionary techniques. Here, a comparative analysis of performances of an optimal proportional–integral (PI) controller, proportional–integral–derivative (PID) controller, conventional SMC, NSGA-II based tuned SMC and SMC parameter tuning using MOPSO algorithm has been carried out through MATLAB/SIMULINK. The objective functions, integral absolute error (IAE), integral squared error (ISE) and an integration of weighted objective function aggregated approach of the error performance indices, IAE and ISE are considered. Realistic conditions are used in a plant for testing the robustness of controller. The stability of the controller is successfully obtained which satisfies the Lyapunov stability criteria. Reduction in long settling time with tiny magnitude variations about an equilibrium point is achieved using bio-inspired techniques. The simulation as well as experimental results reveal that SMC parameter tuning based on NSGA-II algorithm gives a better performance as compared to the other design strategies.     

Multi-objective optimization of collaborative manufacturing chain with time-sequence constraints

To realize the sharing and optimization deployment of manufacturing resources, a concept of collaborative manufacturing chain (CMC) is proposed for the manufacturing of complex products in a networked manufacturing environment. To acquire the optimal CMC, a multi-objective optimization model is developed to minimize the comprehensive cost and the whole production load with time-sequence constraints. Non-dominated sorting genetic algorithm (NSGA-II) is applied to solve optimization functions. The optimal solution set of Pareto is obtained. The technique for order preference by similarity to ideal solution (TOPSIS) approach is then used to identify the optimal compromise solution from the optimal solution set of Pareto. Simulation results obtained in this study indicate that the proposed model and algorithm are able to obtain satisfactory solutions.     

A multi-objective genetic algorithm for solving cell formation problem using a fuzzy goal programming approach

A comprehensive multi-objective mathematical programming model is proposed in this paper to design a cellular manufacturing system. The model considers machine redundancy, production volume, processing time, cost of machines, sequence of operations, and alternative processing plans. A fuzzy goal programming approach is used to convert the proposed multi-objective model into a single-objective one. Due to NP-hard nature of the model, a genetic algorithm is developed for solving the proposed model. Performance of the proposed genetic algorithm is evaluated by adopting four problems from literature. The results indicate effectiveness and efficiency of the proposed algorithm in comparison with those obtained by Lingo and NSGA-II algorithm.     

Optimum tolerance synthesis for complex assembly with alternative process selection using Lagrange multiplier method

Any part cannot be manufactured to the required nominal dimensions due to inherent variations in workmanship, material, and machine. The specification of tolerance on part dimensions plays a major role on performance, quality, and cost of the product. Distribution of tolerance among the components of an assembly is known as tolerance allocation. The selection of alternative processes for tolerance allocation also plays a vital role in reducing manufacturing cost. Near-optimal allocated tolerances are obtained using nontraditional optimization techniques in which the solutions are achieved randomly. Also, there is a chance for omitting the better process for allocation. The results of successive run of the program based on these techniques will not yield consistent results. An attempt has been made in this work to solve the above problem using Lagrange multiplier method for complex assemblies with univariate search method. The methodology has been demonstrated on wheel mounting assembly. The example product after implementing the proposed method would yield 1.4% savings in manufacturing cost as compared with the cost obtained by Singh.     

水平型制造协作联盟订单分配多目标优化模型研究

针对水平型制造协作联盟的订单分配问题,引入了生产负荷参数,建立了最小化综合成本与生产负荷均衡的多目标优化模型。应用改进的非支配排序遗传算法对多目标优化模型进行求解,获得了Pareto最优解集。仿真计算结果表明,所提出的模型和算法能够获得满意的解。     

An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling

Process planning and scheduling are two major sub-systems in a modern manufacturing system. In traditional manufacturing system, they were regarded as the separate tasks to perform sequentially. However, considering their complementarity, integrating process planning and scheduling can further improve the performance of a manufacturing system. Meanwhile, the multiple objectives are needed to be considered during the realistic decision-making process in a manufacturing system. Based on the above requirements from the real manufacturing system, developing effective methods to deal with the multi-objective integrated process planning and scheduling (MOIPPS) problem becomes more and more important. Therefore, this research proposes a multi-objective genetic algorithm based on immune principle and external archive (MOGA-IE) to solve the MOIPPS problem. In MOGA-IE, the fast non-dominated sorting approach used in NSGA-II is utilized as the fitness assignment scheme and the immune principle is exploited to maintain the diversity of the population and prevent the premature condition. Moreover, the external archive is employed to store and maintain the Pareto solutions during the evolutionary process. Effective genetic operators are also designed for MOIPPS. To test the performance of the proposed algorithm, three different scale instances have been employed. And the proposed method is also compared with other previous algorithms in literature. The results show that the proposed algorithm has achieved good improvement and outperforms the other algorithms.     

Composite Planar Tolerance Allocation with Dimensional and Geometric Specifications

A new optimal approach for planar tolerance allocation is proposed in which dimensional and orientation geometric specifications are included. To deal with the increased complexity of planar tolerance analysis, a special relevance graph (SRG) is used to represent the relationships between manufactured elements and their size and tolerance information. In addition, the SRG is also applied for the geometric dimensions and tolerances. Using a suitable algorithm, planar tolerance chains that include geometric specifications can be generated automatically during process planning. Through a graph based analysis, stacks of tolerance zones are obtained. The resultant tolerance zone contains all of the composite links of the tolerance zones. The links are assigned according to the process capacities, which can be considered as constraints. A linear optimal model is established to solve the tolerance allocation problem. A practical example is used to demonstrate the feasibility and effectiveness of the proposed method.     

Cat Swarm Optimization algorithm for optimal linear phase FIR filter design

In this paper a new meta-heuristic search method, called Cat Swarm Optimization (CSO) algorithm is applied to determine the best optimal impulse response coefficients of FIR low pass, high pass, band pass and band stop filters, trying to meet the respective ideal frequency response characteristics. CSO is generated by observing the behaviour of cats and composed of two sub-models. In CSO, one can decide how many cats are used in the iteration. Every cat has its′ own position composed of M dimensions, velocities for each dimension, a fitness value which represents the accommodation of the cat to the fitness function, and a flag to identify whether the cat is in seeking mode or tracing mode. The final solution would be the best position of one of the cats. CSO keeps the best solution until it reaches the end of the iteration. The results of the proposed CSO based approach have been compared to those of other well-known optimization methods such as Real Coded Genetic Algorithm (RGA), standard Particle Swarm Optimization (PSO) and Differential Evolution (DE). The CSO based results confirm the superiority of the proposed CSO for solving FIR filter design problems. The performances of the CSO based designed FIR filters have proven to be superior as compared to those obtained by RGA, conventional PSO and DE. The simulation results also demonstrate that the CSO is the best optimizer among other relevant techniques, not only in the convergence speed but also in the optimal performances of the designed filters.     

Optimum assembly using a component dimensioning method

Many tolerance allocation methods based primarily on cost optimisation have been developed in recent years. However, the dimensions of the assembly parts are usually determined by convenience or design constraints other than the requirements of the assembly itself. The dimensions are often determined to give sufficient clearance during assembly without much consideration given to their tolerances. This is usually followed by a tolerance analysis to check for interference. The dimensions are then adjusted to eliminate any interferences. There is no control over the size of the clearance of an assembly.This paper presents a new approach of dimensioning the components of an assembly which would allow real control over the size of clearance or interference in an assembly. A unique algorithm in conjunction with a relationship matrix is developed to formulate the dimensions in a tolerance chain into a linear equation. This linear equation is then used to develop the tolerance analysis module. The dimensioning module is accomplished using a separate algorithm in conjunction with the linear equation established. The tolerance analysis and the dimensioning modules are subsequently tested on a number of examples.     

Tolerance evolutionary model and algorithm in product growth design

To guarantee the successful transformation from product functional requirement to geometry constraints and finally to dimension constraints between components in a product, an evolutionary tolerance design strategy is proposed on the basis of automation technology in product structure design. In the first part of this paper, the theory of the growth design and the process of tolerance evolutionary design are introduced. Following the evolution of product structure, product tolerance grows from its initial state, defined by accuracy requirements, to its final state, defined as dimension tolerance and geometric tolerance. In this growing process, the basic units in the product growth design, known as functional surfaces and their nominal features, are used as evolutionary carriers. With the help of these basic units, the method for the construction of a two-layer correlation network is proposed. In the second part, the tolerance assertions to assist tolerance evolutionary design are given, based on which the basic process for an evolutionary design of dimensions chain and geometric tolerance are presented. In order to optimize the allocation of the dimension tolerance, a mathematical model is developed in which a correlated sensitivity function between the cost and the tolerance is created. In the model, the design cost, the manufacturing cost, the usage cost, and the depreciation cost of the product are used as constraints to the tolerance allocation. Considering these costs, a multifactor cost function to express quality loss of the product is developed and is applied into the model. The minimum cost is used as the objective function, and the depreciation cost in the objective function is expressed by the discount rate—terminology in economics. The aim was to achieve a final and ideal balance around assembly, manufacturing, and usage through the control of product precision. In the last part, the successful usage of the proposed tolerance evolutionary strategy in the incremental growth product design is demonstrated through a design example.