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.     

Evolutionary trajectory planning for an industrial robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator (AdeptOne XL robot) in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE), have been used for the optimization. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.     

Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles

Optimal trajectory planning for robot manipulators is always a hot spot in research fields of robotics. This paper presents two new novel general methods for computing optimal motions of an industrial robot manipulator (STANFORD robot) in presence of obstacles. The problem has a multi-criterion character in which three objective functions, a maximum of 72 variables and 103 constraints are considered. The objective functions for optimal trajectory planning are minimum traveling time, minimum mechanical energy of the actuators and minimum penalty for obstacle avoidance. By far, there has been no planning algorithm designed to treat the objective functions simultaneously. When existing optimization algorithms of trajectory planning tackle the complex instances (obstacles environment), they have some notable drawbacks viz.: (1) they may fail to find the optimal path (or spend much time and memory storage to find one) and (2) they have limited capabilities when handling constraints. In order to overcome the above drawbacks, two evolutionary algorithms (Elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm) are used for the optimization. Two methods (normalized weighting objective functions method and average fitness factor method) are combinedly used to select best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure and ratio of non-dominated individuals) are used to evaluate strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.     

Robust RST control design based on Multi-Objective Particle Swarm Optimization approach

In this paper, a novel method for the digital two-Degrees-Of-Freedom (2DOF) controller design, called canonical RST structure, is proposed and successfully implemented based on a Multi-Objective Particle Swarm Optimization (MOPSO) approach. This is a polynomial control structure allowing independently the regulation and the tracking of discrete-time systems. An application to the variable speed control of an electrical DC Drive is investigated. The RST design and tuning problem is formulated as a multi-objective optimization problem. The proposed MOPSO algorithm which is based on the Pareto dominance is used to identify the non-dominated solutions. This approach used the leader selection strategy that is called a geographically-based system. In addition, the adaptive grid method is used to produce well-distributed Pareto fronts in the multi-objective formalism. The well known NSGA-II and the proposed MOPSO algorithms are evaluated and compared with each other in terms of several performance metrics in order to show the superiority and the effectiveness of the proposed method. Simulation results demonstrate the advantages of the MOPSO-tuned RST control structure in terms of performance and robustness.

     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

多目标优化在特征选择子集评价中的应用

特征选择是处理高维大数据常用的降维手段,但其中牵涉到的多个彼此冲突的特征子集评价目标难以平衡。为综合考虑特征选择中多种子集评价方式间的折中,优化子集性能,提出一种基于子集评价多目标优化的特征选择框架,并重点对多目标粒子群优化（MOPSO）在特征子集评价中的应用进行了研究。该框架分别根据子集的稀疏度、分类能力和信息损失度设计多目标优化函数,继而基于多目标优化算法进行特征权值向量寻优,并通过权值向量Pareto解集膝点选取确定最优向量,最终实现基于权值向量排序的特征选择。设计实验对比了基于多目标粒子群优化算法的特征选择（FS_MOPSO）与四种经典方法的性能,多个数据集上的结果表明,FS_MOPSO在低维空间表现出更高的分类精度,并保证了更少的信息损失。     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.     

Pareto frontier for simultaneous structural and manufacturing optimization of a composite part

Optimized design of composite structures requires simultaneous optimization of structural performance and manufacturing process. Such a challenge calls for a multi-objective optimization. Here, a generating multi-objective optimization method called normalized normal constraint method, which attains a set of optimal solutions and allows the designer to explore design alternatives before making the final decision, is coupled with a local-global search called constrained globalized bounded Nelder–Mead method. The proposed approach is applied to the design of a Z-shaped composite bracket for optimization of structural and manufacturing objectives. Comparison of the results with non-dominated sorting genetic algorithm (NSGA-II) shows that when only a small number of function evaluations are possible and a few Pareto optima are desired, the proposed method outperforms NSGA-II in terms of convergence to the true Pareto frontier. The results are validated by an enumeration search and by exploring the neighbourhood of the final solutions.     

Multi-objective evolutionary optimization of polynomial neural networks for modelling and prediction of explosive cutting process

In this paper, evolutionary algorithms (EAs) are deployed for multi-objective Pareto optimal design of group method of data handling (GMDH)-type neural networks which have been used for modelling an explosive cutting process using some input–output experimental data. In this way, multi-objective EAs (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity-preserving mechanism are used for Pareto optimization of such GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are, namely, training error (TE), prediction error (PE), and number of neurons (N) of such neural networks. Different pairs of theses objective functions are selected for 2-objective optimization processes. Therefore, optimal Pareto fronts of such models are obtained in each case which exhibit the trade-off between the corresponding pair of conflicting objectives and, thus, provide different non-dominated optimal choices of GMDH-type neural networks models for explosive cutting process. Moreover, all the three objectives are considered in a 3-objective optimization process, which consequently leads to some more non-dominated choices of GMDH-type models representing the trade-offs among the training error, prediction error, and number of neurons (complexity of network), simultaneously. The overlay graphs of these Pareto fronts also reveal that the 3-objective results include those of the 2-objective results and, thus, provide more optimal choices for the multi-objective design of GMDH-type neural networks in terms of minimum training error, minimum prediction error, and minimum complexity.     

Comparisons of some improving strategies on MOPSO for multi-objective (r, Q) inventory system

This paper presents comparisons of some recent improving strategies on multi-objective particle swarm optimization (MOPSO) algorithm which is based on Pareto dominance for handling multiple objective in continuous review stochastic inventory control system. The complexity of considering conflict objectives such as cost minimization and service level maximization in the real-world inventory control problem needs to employ more exact optimizers generating more diverse and better non-dominated solutions of a reorder point and order size system. At first, we apply the original MOPSO employed for the multi-objective inventory control problem. Then we incorporate the mutation operator to maintain diversity in the swarm and explore all the search space into the MOPSO. Next we change the leader selection strategy used that called geographically-based system (Grids) and instead of that, crowding distance factor is also applied to select the global optimal particle as a leader. Also we use ε-dominance concept to bound archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. Finally, the MOPSO algorithms created using these strategies are evaluated and compared with each other in terms of some performance metrics taken from the literature. The results indicate that these strategies have significant influences on computational time, convergence, and diversity of generated Pareto optimal solutions.     

基于分解和差分进化的多目标粒子群优化算法

为了提高多目标优化算法解集的分布性和收敛性,提出一种基于分解和差分进化的多目标粒子群优化算法(dMOPSO-DE).该算法通过提出方向角产生一组均匀的方向向量,确保粒子分布的均匀性;引入隐式精英保持策略和差分进化修正机制选择全局最优粒子,避免种群陷入局部最优Pareto前沿;采用粒子重置策略保证群体的多样性.与非支配排序(NSGA-II)算法、多目标粒子群优化(MOPSO)算法、分解多目标粒子群优化(dMOPSO)算法和分解多目标进化-差分进化(MOEA/D-DE)算法进行比较,实验结果表明,所提出算法在求解多目标优化问题时具有良好的收敛性和多样性.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

Simple heuristics-based selection of guides for multi-objective PSO with an application to electrical distribution system planning

In multi-objective particle swarm optimization (MOPSO), a proper selection of local guides significantly influences detection of non-dominated solutions in the objective/solution space and, hence, the convergence characteristics towards the Pareto-optimal set. This paper presents an algorithm based on simple heuristics for selection of local guides in MOPSO, named as HSG-MOPSO (Heuristics-based-Selection-of-Guides in MOPSO). In the HSG-MOPSO, the set of potential guides (in a PSO iteration) consists of the non-dominated solutions (which are normally stored in an elite archive) and some specifically chosen dominated solutions. Thus, there are two types of local guides in the HSG-MOPSO, i.e., non-dominated and dominated guides; they are named so as to signify whether the chosen guide is a non-dominated or a dominated solution. In any iteration, a guide, from the set of available guides, is suitably selected for each population member. Some specified proportion of the current population members follow their respective nearest non-dominated guides and the rest follow their respective nearest dominated guides. The proposed HSG-MOPSO is firstly evaluated on a number of multi-objective benchmark problems along with investigations on the controlling parameters of the guide selection algorithm. The performance of the proposed method is compared with those of two well-known guide selection methods for evolutionary multi-objective optimization, namely the Sigma method and the Strength Pareto Evolutionary Algorithm-2 (SPEA2) implemented in PSO framework. Finally, the HSG-MOPSO is evaluated on a more involved real world problem, i.e., multi-objective planning of electrical distribution system. Simulation results are reported and analyzed to illustrate the viability of the proposed guide selection method for MOPSO.     

A hybrid multi-objective approach based on the genetic algorithm and neural network to design an incremental cellular manufacturing system

One important issue related to the implementation of cellular manufacturing systems (CMSs) is to decide whether to convert an existing job shop into a CMS comprehensively in a single run, or in stages incrementally by forming cells one after the other, taking the advantage of the experiences of implementation. This paper presents a new multi-objective nonlinear programming model in a dynamic environment. Furthermore, a novel hybrid multi-objective approach based on the genetic algorithm and artificial neural network is proposed to solve the presented model. From the computational analyses, the proposed algorithm is found much more efficient than the fast non-dominated sorting genetic algorithm (NSGA-II) in generating Pareto optimal fronts.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

基于Pareto的快速多目标克隆选择算法

基于免疫系统中克隆选择原理,提出了一种多目标克隆选择算法MCSA。该方法只对部分当前所得到的Pareto最优解进行进化操作,所求得的Pareto最优解保留在一个不断更新的外部记忆库中,并选用一种简单的多样性保存机制来保证其具有良好的分布特征。实验结果表明,该方法能够很快地收敛到Pareto最优前沿面,同时较好地保持解的多样性和分布的均匀性。对于公认的多目标benchmark问题,MCSA在解集分布的均匀性、多样性与解的精确性及算法收敛速度等方面均优于SPEA、NSGA-II等算法。     

New mechanism for archive maintenance in PSO-based multi-objective feature selection

In classification problems, a large number of features are typically used to describe the problem’s instances. However, not all of these features are useful for classification. Feature selection is usually an important pre-processing step to overcome the problem of “curse of dimensionality”. Feature selection aims to choose a small number of features to achieve similar or better classification performance than using all features. This paper presents a particle swarm Optimization (PSO)-based multi-objective feature selection approach to evolving a set of non-dominated feature subsets which achieve high classification performance. The proposed algorithm uses local search techniques to improve a Pareto front and is compared with a pure multi-objective PSO algorithm, three well-known evolutionary multi-objective algorithms and a current state-of-the-art PSO-based multi-objective feature selection approach. Their performances are examined on 12 benchmark datasets. The experimental results show that in most cases, the proposed multi-objective algorithm generates better Pareto fronts than all other methods.     

An integrated method of multi-objective optimization for complex mechanical structure

An integrated method of multi-objective optimization for complex mechanical structures is presented, which integrates prototype modeling, FEM analysis and optimization. To explore its advantages over traditional methods, optimization of a manipulator in hybrid mode aerial working vehicle (HMAWV) is adopted. The objective is to increase its working domain and decrease the cost under the constraint of enough strength, and the design variables are geometric dimensions. NLPQL and NSGA-II are synthesized to achieve optimal solutions. The results indicated that this integrated method was more efficient than enumerative search algorithm. NSGA-II could approximate the global Pareto front precisely, and the relative error between NLPQL and NSGA-II is trivial. Therefore, this integrated method is effective and shows a potential in engineering applications.     

Multi-objective optimization of hybrid backorder inventory model

This paper addresses inventory problem for the products that are sold in monopolistic and captive markets experiencing hybrid backorder (i.e., fixed backorder and time-weighted backorder). The problem with stochastic demand is studied first by developing single objective (cost) inventory model. Computational results of a numerical problem show the effectiveness of hybrid backorder inventory model over fixed backorder inventory model. The model is later extended to multi-objective inventory model. Three objectives of multi-objective inventory model are the minimization of total cost, minimization of stockout units and minimization of the frequency of stockout. A multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the inventory model and generate Pareto curves. The Pareto curves obtained for hybrid backorder inventory model are compared with the existing Pareto curves that are based on fixed backorder. The results show a substantial reduction in stockout units and frequency of stockout with a marginal rise in cost with proposed hybrid backorder inventory system in comparison to existing fixed backorder inventory system. Sensitivity analysis is done to study the robustness of total cost, order quantity, and safety stock factor with the change in holding cost. In the end, the performance of the MOPSO algorithm is compared with the multi-objective genetic algorithm (MOGA). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread.     

A hybrid project scheduling and material ordering problem: Modeling and solution algorithms

A novel combination of a multimode project scheduling problem with material ordering, in which material procurements are exposed to the total quantity discount policy is investigated in this paper. The study aims at finding an optimal Pareto frontier for a triple objective model derived for the problem. While the first objective minimizes the makespan of the project, the second objective maximizes the robustness of the project schedule and finally the third objective minimizes the total costs pertaining to renewable and nonrenewable resources involved in a project. Four well-known multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm II (SPEAII), multi objective particle swarm optimization (MOPSO), and multi objective evolutionary algorithm based on decomposition (MOEAD) solve the developed triple-objective problem. The parameters of algorithms are tuned by the response surface methodology. The algorithms are carried out on a set of benchmarks and are compared based on five performance metrics evaluating their efficiencies in terms of closeness to the optimal frontier, diversity, and variance of results. Finally, a statistical assessment is conducted to analyze the results obtained by the algorithms. Results show that the NSGAII considerably outperforms others in 4 out of 5 metrics and the MOPSO performs better in terms of the remaining metric.