基于约束满足的多目标双足机器人动态步态参数优化*

目前的步态优化算法仅仅实现了对单一目标的优化,把双足机器人步态优化看做是多目标优化问题,构建了衡量稳定性、能量消耗、步行速度三个目标评价函数。考虑到直接对多个目标加权求和的方法不能很好地处理多目标问题,提出一种新的基于约束满足的多目标步态参数优化算法,其思想是把基于惩罚函数的SPEA2(strength Pareto evolutionary algorithm2 )应用到多目标双足机器人动态步态参数优化问题上,规划出了同时满足这三个目标的动态优化步态。通过仿真实验表明了算法的有效性。     

Evolutionary optimization using epsilon method for resource-constrained multi-robotic disassembly line balancing

This paper concentrates on a resource-constrained multi-robotic disassembly line balancing (RC-MDLB) problem. In this RC-MDLB problem, different types of end-of-life products are disassembled simultaneously on the same line under the following conditions: allocating multiple robots to a workstation to simultaneously process the disassembly tasks that have no precedence relationship with each other, each robot needs a fixed number of limited resources to process tasks, and the total resources for each workstation is fixed. A mathematical model is presented for the RC-MDLB problem to minimize the cycle time and the number of robots being occupied simultaneously. A constrained multi-objective evolutionary algorithm framework and a constrained NSGA-II (E-NSGA-II) algorithm with epsilon method are proposed to handle the constraints of the RC-MDLB problem. The proposed E-NSGA-II is applied to a set of RC-MDLB problem instances introduced in this paper and compared with five representative multi-objective evolutionary algorithms. The experimental results reveal that the proposed E-NSGA-II presents outstanding performance on most of the cases analyzed.     

基于DTC-MOPSO算法的焊接机器人路径规划

点焊机器人在汽车白车身焊接中的应用大大提高了企业的生产效率,本文从焊接路径长度和能量两方面进行焊接机器人多目标路径规划．为了很好地解决这个问题,本文对一种新型多目标粒子群算法（三态协调搜索多目标粒子群优化算法）进行改进,得到适合于求解离散多目标优化问题的离散化三态协调搜索多目标粒子群算法（DTC-MOPSO）．通过和两个经典的优化算法比较,DTC-MOPSO算法在分散性和收敛性方面都有很好的优化性能．最后运用Matlab机器人工具箱对机器人的运动学、逆运动学以及逆动力学进行分析以求解机器人的路径长度和能耗,并将改进的算法应用于焊接机器人路径规划中,结果显示规划后的路径明显优于另外两种算法.     

基于多目标蝗虫优化算法的移动机器人路径规划

在静态多障碍物环境下的移动机器人路径规划问题中，粒子群算法存在容易产生早熟收敛和局部寻优能力较差等缺点，导致机器人路径规划精度低。为此，提出一种多目标蝗虫优化算法（MOGOA）来解决这一问题。根据移动机器人路径规划要求将路径长度、平滑度和安全性作为路径优化的目标，建立相应的多目标优化问题的数学模型。在种群的搜索过程中，引入曲线自适应策略以提高算法收敛速度，并使用Pareto最优准则来解决三个目标之间的共存问题。实验结果表明：所提出的算法在解决上述问题中寻找到的路径更短，表现出更好的收敛性。该算法与多目标粒子群（MOPSO）算法相比路径长度减少了约2.01%，搜索到最小路径的迭代次数减少了约19.34%。     

Multi-objective adaptive trajectory optimization for industrial robot based on acceleration continuity constraint

In noncontact machining, such as welding and spraying, running efficiency and smoothness have been a bottleneck problem in trajectory optimisation of industrial robots. When the dynamic and mechanical properties of robots are fully utilised, significant impact are often produced. Thus, reducing the process impact of the robot and achieving a balance between the efficiency and smoothness of the operation process are complex problems that need to be solved. The trajectory optimisation problem is modelled based on the excellent properties of the convex-optimization (CO) problem. CO parameters were introduced to solve the inconsistency between the constrained and planned spaces. To obtain the weight factor of the multi-objective optimisation problem, a multi-objective adaptive optimisation method was proposed to select the optimal parameters. Aiming at the large process impact of the optimisation problem, which considers running time as the main optimisation objective, an acceleration continuity constraint method was proposed based on the smoothing path. Finally, the objective optimisation problem was transformed into a standardised second-order cone programming problem to complete the solution. The experimental results show that the proposed method can improve the robot operation efficiency and reduce the process impact by approximately 26% and 22%, respectively, from three aspects: optimum time, balance between efficiency and impact, and acceleration continuity.     

Multi-objective mobile robot path planning problem through learnable evolution model

A new multi-objective non-Darwinian-type evolutionary computation approach based on learnable evolution model (LEM) is proposed for solving the robot path planning problem. The multi-objective property of this approach is governed by a robust strength Pareto evolutionary algorithm (SPEA) incorporated in the LEM algorithm presented here. Learnable evolution model includes a machine learning method, like the decision trees, that can detect the right directions of the evolution and leads to large improvements in the fitness of the individuals. Several new refiner operators are proposed to improve the objectives of the individuals in the evolutionary process. These objectives are: the path length, the path safety and the path smoothness. A modified integer coding path representation scheme is proposed where the edge-fixing and top-row fixing procedures are performed implicitly. This proposed robot path planning problem solving approach is assessed on eight realistic scenarios in order to verify the performance thereof. Computer simulations reveal that this proposed approach exhibits much higher hypervolume and set coverage in comparison with other similar approaches. The experimental results confirm that the proposed approach performs in the workspaces with a dense set of obstacles in a significant manner.     

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.     

Multi-objective biogeography-based optimization for supply chain network design under uncertainty

This paper proposes a new two-stage optimization method for multi-objective supply chain network design (MO-SCND) problem with uncertain transportation costs and uncertain customer demands. On the basis of risk-neutral and risk-averse criteria, we develop two objectives for our SCND problem. We introduce two solution concepts for the proposed MO-SCND problem, and use them to define the multi-objective value of fuzzy solution (MOVFS). The value of the MOVFS measures the importance of uncertainties included in the model, and helps us to understand the necessity of solving the two-stage multi-objective optimization model. When the uncertain transportation costs and customer demands have joined continuous possibility distributions, we employ an approximation approach (AA) to compute the values of two objective functions. Using the AA, the original optimization problem becomes an approximating mixed-integer multi-objective programming model. To solve the hard approximating optimization problem, we design an improved multi-objective biogeography-based optimization (MO-BBO) algorithm integrated with LINGO software. We also compare the improved MO-BBO algorithm with the multi-objective genetic algorithm (MO-GA). Finally, a realistic dairy company example is provided to demonstrate that the improved MO-BBO algorithm achieves the better performance than MO-GA in terms of solution quality.     

基于最优激励位姿序列的机械臂负载估计

重力补偿方法广泛地应用于由连杆与旋转机构组成的机器人系统中,更换机器人末端执行器造成了补偿模型的不确定性．针对该问题,提出了一种利用机器人关节力矩与位置信息的负载参数离线辨识方法．基于机器人静力学方法提出了2种负载参数的计算模型,并通过采集机器人在多个静态位姿条件下的关节力矩与位置信息获得负载参数的最小二乘解．进一步,本文针对机器人的辨识位姿选取问题展开研究,提出了同时保证辨识精度与辨识简便性的多目标优化问题,使用多目标粒子群优化方法获得最优辨识位姿．根据辨识后的负载参数,给出了机械臂各关节负载的重力补偿量计算方法．实验结果表明所提方法具有较高的辨识精度,负载质量的辨识误差最小值达到0.007 06 kg,最大值达到0.151 kg,负载质心位置的辨识误差最小值达到0.025 4 m,最大值达到0.122 m,验证了上述方法的可行性与有效性．     

一种多目标不等面积设施布局问题的启发式算法

多目标不等面积设施布局问题（UA-FLP）是将一些不等面积设施放置在车间内进行布局,要求优化多个目标并满足一定的限制条件。以物料搬运成本最小和非物流关系强度最大来建立生产车间的多目标优化模型,并提出一种启发式算法进行求解。算法采用启发式布局更新策略更新构型,通过结合基于自适应步长梯度法的局部搜索机制和启发式设施变形策略来处理设施之间的干涉性约束。为了得到问题的Pareto最优解集,提出了基于Pareto优化的局部搜索和基于小生境技术的全局优化方法。通过两个典型算例对算法性能进行测试,实验结果表明,所提出的启发式算法是求解多目标UA-FLP的有效方法。     

An integrated mathematical model for solving dynamic cell formation problem considering operator assignment and inter/intra cell layouts

The aim of this paper is to present an integrated mathematical model to solve the dynamic cell formation problem considering operator assignment and inter/intra cell layouts problems with machine duplication, simultaneously. The proposed model includes three objectives which the first objective seeks to minimize inter/intra cell part movements and machine relocation, the second objective minimizes machine and operator related costs and the third objective maximizes consecutive forward flows ratio. In order to validate the proposed model, a numerical example is presented and solved by the sum weighted method. Due to NP-hardness of the model, two meta-heuristics namely multi-objective simulated annealing (MOSA) and multi-objective vibration damping optimization (MOVDO) present to solve the proposed model. Finally, two algorithms have been compared using multi-objective criteria.     

Multi-skilled project scheduling with level-dependent rework risk; three multi-objective mechanisms based on cuckoo search

In many projects, multi-skilled workforces are able to perform different tasks with different quality levels. In this paper, a real-life version of the multi-skilled resource constrained project scheduling problem is investigated, in which the reworking risk of each activity depends on the assigned level of multi-skilled workforces. The problem is formulated mathematically as a bi-objective optimization model to minimize total costs of processing the activities and to minimize reworking risks of the activities, concurrently. In order to solve the resulting problem, three cuckoo-search-based multi-objective mechanisms are developed based on non-dominance sorting genetic algorithm, multi-objective particle swarm and multi-objective invasive weeds optimization algorithm. The parameters of the algorithms are tuned using the Taguchi method to improve the efficiency of the solution procedures. Furthermore, a competitive multi-objective invasive weeds optimization algorithm is used to evaluate the performance of the proposed methodologies. Finally, a priority based method is employed to compare the proposed algorithms in terms of different metrics.     

基于分布式神经动态优化的综合能源系统多目标优化调度EI北大核心CSCD

研究了基于神经动态优化的综合能源系统(Integrated energy systems,IES)分布式多目标优化调度问题.首先,将IES元件单元(包含负荷)作为独立的决策主体,联合考量其运行成本和排放成本,并计及多能源设备间的传输损耗,提出了IES多目标优化调度模型,该模型可描述为一类非凸多目标优化问题.其次,针对此类问题的求解,提出了一种基于神经动力学系统的分布式多目标优化算法,该算法基于动态权重的神经网络模型,可以解决不可分离的不等式约束问题.该算法计算负担小,收敛速度快,并且易于硬件实现.仿真结果表明,所提算法能同时协调综合能源系统的经济性和环境性这两个冲突的目标,且获得了整个帕累托前沿,有效降低了综合能源系统的污染物排放量和综合运行成本.     

Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment

In this study, an integrated multi-objective production-distribution flow-shop scheduling problem will be taken into consideration with respect to two objective functions. The first objective function aims to minimize total weighted tardiness and make-span and the second objective function aims to minimize the summation of total weighted earliness, total weighted number of tardy jobs, inventory costs and total delivery costs. Firstly, a mathematical model is proposed for this problem. After that, two new meta-heuristic algorithms are developed in order to solve the problem. The first algorithm (HCMOPSO), is a multi-objective particle swarm optimization combined with a heuristic mutation operator, Gaussian membership function and a chaotic sequence and the second algorithm (HBNSGA-II), is a non-dominated sorting genetic algorithm II with a heuristic criterion for generation of initial population and a heuristic crossover operator. The proposed HCMOPSO and HBNSGA-II are tested and compared with a Non-dominated Sorting Genetic Algorithm II (NSGA-II), a Multi-Objective Particle Swarm Optimization (MOPSO) and two state-of-the-art algorithms from recent researches, by means of several comparing criteria. The computational experiments demonstrate the outperformance of the proposed HCMOPSO and HBNSGA-II.     

A soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem

In this paper, a novel multi-objective location model within multi-server queuing framework is proposed, in which facilities behave as M/M/m queues. In the developed model of the problem, the constraints of selecting the nearest-facility along with the service level restriction are considered to bring the model closer to reality. Three objective functions are also considered including minimizing (I) sum of the aggregate travel and waiting times, (II) maximum idle time of all facilities, and (III) the budget required to cover the costs of establishing the selected facilities plus server staffing costs. Since the developed model of the problem is of an NP-hard type and inexact solutions are more probable to be obtained, soft computing techniques, specifically evolutionary computations, are generally used to cope with the lack of precision. From different terms of evolutionary computations, this paper proposes a Pareto-based meta-heuristic algorithm called multi-objective harmony search (MOHS) to solve the problem. To validate the results obtained, two popular algorithms including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are utilized as well. In order to demonstrate the proposed methodology and to compare the performances in terms of Pareto-based solution measures, the Taguchi approach is first utilized to tune the parameters of the proposed algorithms, where a new response metric named multi-objective coefficient of variation (MOCV) is introduced. Then, the results of implementing the algorithms on some test problems show that the proposed MOHS outperforms the other two algorithms in terms of computational time.     

Evolutionary multi criteria design optimization of robot grippers

This paper explores the use of intelligent techniques to obtain optimum geometrical dimensions of a robot gripper. The optimization problem considered is a non-linear, complex, multi-constraint and multicriterion one. Three robot gripper configurations are optimized. The aim is to find Pareto optimal front for a problem that has five objective functions, nine constraints and seven variables. The problem is divided into three cases. Case 1 has first two objective functions, the case 2 considers last three objective functions and case 3 deals all the five objective functions. Intelligent optimization algorithms namely Multi-objective Genetic Algorithm (MOGA), Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Differential Evolution (MODE) are proposed to solve the problem. Normalized weighting objective functions method is used to select the best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure (SSM) and ratio of non-dominated individuals (RNIs)) are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead (OO) and algorithm effort are used to find the computational effort of MOGA, NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.     

多地貌环境下的移动机器人路径规划研究

针对多地貌环境下的移动机器人路径规划问题,建立多目标优化模型,并采用微粒群算法解决该问题.首先,采用区域权值表示机器人在各种地形下的通行困难度;然后,结合局部优化准则计算机器人的通行时间,通过计算机器人与危险源之间覆盖的面积来衡量路径的危险程度,并将上述问题转化为两目标优化问题;最后,采用多目标微粒群优化算法优化上述问题.仿真结果表明了所提出方法的有效性.     

A multi-objective scatter search for a dynamic cell formation problem

Cellular manufacturing system—an important application of group technology (GT)—has been recognized as an effective way to enhance the productivity in a factory. Consequently, a multi-objective dynamic cell formation problem is presented in this paper, where the total cell load variation and sum of the miscellaneous costs (machine cost, inter-cell material handling cost, and machine relocation cost) are to be minimized simultaneously. Since this type of problem is NP-hard, a new multi-objective scatter search (MOSS) is designed for finding locally Pareto-optimal frontier. To demonstrate the efficiency of the proposed algorithm, MOSS is compared with two salient multi-objective genetic algorithms, i.e. SPEA-II and NSGA-II based on some comparison metrics and statistical approach. The computational results indicate the superiority of the proposed MOSS compared to these two genetic algorithms.     

Application of fuzzy multi-objective linear programming to aggregate production planning

This study develops a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-product aggregate production planning (APP) decision problem in a fuzzy environment. The proposed model attempts to minimize total production costs, carrying and backordering costs and rates of changes in labor levels considering inventory level, labor levels, capacity, warehouse space and the time value of money. A numerical example demonstrates the feasibility of applying the proposed model to APP problem. Its advantages are also discussed. The proposed model yields a compromise solution and the decision maker's overall levels of satisfaction. In particular, in contrast to other APP models, several significant characteristics of the proposed model are presented.     

Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic

Sustainability has been considered as a growing concern in supply chain network design (SCND) and in the order allocation problem (OAP). Accordingly, there still exists a gap in the quantitative modeling of sustainable SCND that consists of OAP. In this article, we cover this gap through simultaneously considering the sustainable OAP in the sustainable SCND as a strategic decision. The proposed supply chain network is composed of five echelons including suppliers classified in different classes, plants, distribution centers that dispatch products via two different ways, direct shipment, and cross-docks, to satisfy stochastic demand received from a set of retailers. The problem has been mathematically formulated as a multi-objective optimization model that aims at minimizing the total costs and environmental effect of integrating SCND and OAP, simultaneously. To tackle the addressed problem, a novel multi-objective hybrid approach called MOHEV with two strategies for its best particle selection procedure (BPSP), minimum distance, and crowding distance is proposed. MOHEV is constructed through hybridization of two multi-objective algorithms, namely the adapted multi-objective electromagnetism mechanism algorithm (AMOEMA) and adapted multi-objective variable neighborhood search (AMOVNS). According to achieved results, MOHEV achieves better solutions compared with the others, and also crowding distance method for BPSP outperforms minimum distance. Finally, a case study for an automobile industry is used to demonstrate the applicability of the approach.