Nonlinear inverse optimization approach for determining the weights of objective function in standing reach tasks

This paper presents a nonlinear inverse optimization approach to determine the weights for the joint displacement function in standing reach tasks. This inverse optimization problem can be formulated as a bi-level highly nonlinear optimization problem. The design variables are the weights of a cost function. The cost function is the weighted summation of the differences between two sets of joint angles (predicted posture and the actual standing reach posture). Constraints include the normalized weights within limits and an inner optimization problem to solve for joint angles (predicted standing reach posture). The weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 52 degree-of-freedom (DOF) human whole body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the actual standing reach posture. A total of 12 subjects (three subjects for each percentile in stature of 5th percentile female, 50th percentile female, 50th percentile male and 95th percentile male) are selected to run the experiment for 30 tasks. Among these subjects one is Turkish, two are Chinese, and the rest subjects are Americans. Three sets of weights for the general standing reach tasks are obtained for the three zones by averaging all weights in each zone for all subjects and all tasks. Based on the obtained sets of weights, the predicted standing reach postures found using the direct optimization-based approach have good correlation with the experimental results. Sensitivity of the formulation has also been investigated in this study. The presented formulation can be used to determine the weights of cost function within any multi-objective optimization (MOO) problems such as any types of posture prediction and motion prediction.     

Two optimization algorithms for solving robotics inverse kinematics with redundancy

The kinematic redundancy in a robot leads to an infinite number of solutions for inverse kinematics, which implies the possibility to select a "best" solution according to an optimization criterion. In this paper, two optimization objective functions are proposed, aiming at either minimizing extra degrees of freedom (DOFs) or minimizing the total potential energy of a multilink redundant robot. Physical constraints of either equality or inequality types are taken into consideration in the objective functions. Since the closed-form solutions do not exist in general for highly nonlinear and constrained optimization problems, we adopt and develop two numerical methods, which are verified to be effective and precise in solving the two optimization problems associated with the redundant inverse kinematics. We first verify that the well established trajectory following method can precisely solve the two optimization problems, but is computation intensive. To reduce the computation time, a sequential approach that combines the sequential quadratic programming and iterative Newton-Raphson algorithm is developed. A 4-DOF Fujitsu Hoap-1 humanoid robot arm is used as a prototype to validate the effectiveness of the proposed optimization solutions.     

多目标函数优化的元胞蚂蚁算法

提出一种求解多目标函数优化的元胞蚂蚁算法．该方法将元胞自动机演化规则引入蚂蚁算法,给出了在连续空间多目标函数优化的算法描述,定义了与蚂蚁信息素释放有关的元胞演化规则及蚂蚁邻域的转移概率,并实现了算法的具体步骤．在Matlab环境下,采用该算法对一些典型的测试函数进行求解和验证．实验结果表明,该方法具有向真实的Pareto前沿逼近的效果,是一种求解多目标优化的有效方法．     

An interactive method for the selection of design criteria and the formulation of optimization problems in computer aided optimal design

This paper presents an interactive method for the selection of design criteria and the formulation of optimization problems within a computer aided optimization process of engineering systems. The key component of the proposed method is the formulation of an inverse optimization problem for the purpose of determining the design preferences of the engineer. These preferences are identified based on an interactive modification of a preliminary optimization result that is the solution of an initial problem statement. A formulation of the inverse optimization problem is presented, which is based on a weighted-sum multi-objective approach and leads to an explicit optimization problem that is computationally inexpensive to solve. Numerical studies on structural shape optimization problems show that the proposed method is able to identify the optimization criteria and the formulation of the optimization problem which drive the interactive user modifications.     

A new heuristic approach for non-convex optimization problems

In this work a new optimization method, called the heuristic Kalman algorithm (HKA), is presented. This new algorithm is proposed as an alternative approach for solving continuous, non-convex optimization problems. The principle of HKA is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum. A specific procedure, based on the Kalman estimator, was developed to improve the quality of the estimate obtained through the measurement process. The main advantage of HKA, compared to other metaheuristics, lies in the small number of parameters that need to be set by the user. Further, it is shown that HKA converges almost surely to a near-optimal solution. The efficiency of HKA was evaluated in detail using several non-convex test problems, both in the unconstrained and constrained cases. The results were then compared to those obtained via other metaheuristics. The numerical experiments show that HKA is a promising approach for solving non-convex optimization problems, particularly in terms of computation time and success ratio.     

Sparse optimization for inverse problems in atmospheric modelling

We consider inverse problems in atmospheric modelling represented by a linear system which is based on a source-receptor sensitivity matrix and measurements. Instead of using the ordinary least squares, we add a weighting matrix based on the topology of measurement points and show the connection with Bayesian modelling. Since the source-receptor sensitivity matrix is usually ill-conditioned, the problem is often regularized, either by perturbing the objective function or by modifying the sensitivity matrix. However, both these approaches may be heavily dependent on specified parameters. To ease this burden, we propose to use techniques looking for a sparse solution with a small number of positive elements. Finally, we compare all these methods on the European Tracer Experiment (ETEX) data where there is no apriori information apart from the release position and some measurements.     

A novel approach to combine features for salient object detection using constrained particle swarm optimization

Despite significant amount of research works, the best available visual attention models still lag far behind human performance in predicting salient object. In this paper, we present a novel approach to detect a salient object which involves two phases. In the first phase, three features such as multi-scale contrast, center-surround histogram and color spatial distribution are obtained as described in Liu et al. model. Constrained Particle Swarm Optimization is used in the second phase to determine an optimal weight vector to combine these features to obtain saliency map to distinguish a salient object from the image background. To achieve this, we defined a simple fitness function which highlights a salient object region with well-defined boundary and effectively suppresses the background regions in an image. The performance is evaluated both qualitatively and quantitatively on a publicly available dataset. Experimental results demonstrate that the proposed model outperforms existing state-of-the-art methods in terms of precision, recall, F -measure and area under curve.     

Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions

This paper presents a new algorithm for derivative-free optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. The proposed algorithm, called ConstrLMSRBF, uses radial basis function (RBF) surrogate models and is an extension of the Local Metric Stochastic RBF (LMSRBF) algorithm by Regis and Shoemaker (2007a) [1] that can handle black-box inequality constraints. Previous algorithms for the optimization of expensive functions using surrogate models have mostly dealt with bound constrained problems where only the objective function is expensive, and so, the surrogate models are used to approximate the objective function only. In contrast, ConstrLMSRBF builds RBF surrogate models for the objective function and also for all the constraint functions in each iteration, and uses these RBF models to guide the selection of the next point where the objective and constraint functions will be evaluated. Computational results indicate that ConstrLMSRBF is better than alternative methods on 9 out of 14 test problems and on the MOPTA08 problem from the automotive industry (Jones, 2008 [2]). The MOPTA08 problem has 124 decision variables and 68 inequality constraints and is considered a large-scale problem in the area of expensive black-box optimization. The alternative methods include a Mesh Adaptive Direct Search (MADS) algorithm (Abramson and Audet, 2006 [3]; Audet and Dennis, 2006 [4]) that uses a kriging-based surrogate model, the Multistart LMSRBF algorithm by Regis and Shoemaker (2007a) [1] modified to handle black-box constraints via a penalty approach, a genetic algorithm, a pattern search algorithm, a sequential quadratic programming algorithm, and COBYLA (Powell, 1994 [5]), which is a derivative-free trust-region algorithm. Based on the results of this study, the results in Jones (2008) [2] and other approaches presented at the ISMP 2009 conference, ConstrLMSRBF appears to be among the best, if not the best, known algorithm for the MOPTA08 problem in the sense of providing the most improvement from an initial feasible solution within a very limited number of objective and constraint function evaluations.     

A genetic algorithm approach for multi-objective optimization of supply chain networks

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management. It is an important and strategic operations management problem in supply chain management, and usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective SCN design problem. To deal with multi-objective and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. An experimental study using actual data from a company, which is a producer of plastic products in Turkey, is carried out into two stages. While the effects of weight approaches on the performance of proposed solution procedure are investigated in the first stage, the proposed solution procedure and simulated annealing are compared according to quality of Pareto-optimal solutions in the second stage.     

Penalty function approach for the mixed discrete nonlinear problems by particle swarm optimization

In this paper, the basic characteristics of particle swarm optimization (PSO) for the global search are discussed at first, and then the PSO for the mixed discrete nonlinear problems (MDNLP) is suggested. The penalty function approach to handle the discrete design variables is employed, in which the discrete design variables are handled as the continuous ones by penalizing at the intervals. As a result, a useful method to determine the penalty parameter of penalty term for the discrete design variables is proposed. Through typical mathematical and structural optimization problems, the validity of the proposed approach for the MDNLP is examined.     

Evaluation of multiple muscle loads through multi-objective optimization with prediction of subjective satisfaction level: Illustration by an application to handrail position for standing

Proposed here is an evaluation of multiple muscle loads and a procedure for determining optimum solutions to ergonomic design problems. The simultaneous muscle load evaluation is formulated as a multi-objective optimization problem, and optimum solutions are obtained for each participant. In addition, one optimum solution for all participants, which is defined as the compromise solution, is also obtained. Moreover, the proposed method provides both objective and subjective information to support the decision making of designers. The proposed method was applied to the problem of designing the handrail position for the sit-to-stand movement. The height and distance of the handrails were the design variables, and surface electromyograms of four muscles were measured. The optimization results suggest that the proposed evaluation represents the impressions of participants more completely than an independent use of muscle loads. In addition, the compromise solution is determined, and the benefits of the proposed method are examined.     

A multiobjective approach for maximizing the reach or GRP of different brands in TV advertising

This paper focuses on a multiobjective optimization problem in TV advertising from an advertising agency's perspective, which involves deciding on which commercial breaks to air the ads of various brands to jointly maximize reach or gross rating point (GRP) for the different brands subject to budget constraints, brand competition constraints, and other scheduling constraints. We present a multiobjective integer programming formulation of this problem and develop and implement algorithms for generating provably Pareto‐optimal solutions. We also develop reduction and visualization procedures to aid a decision maker in choosing suitable subsets of the Pareto‐optimal solutions obtained. Numerical experiments on five TV advertising problems involving 20–40 objective functions and thousands of decision variables and constraints demonstrate the effectiveness of the proposed formulation and solution methods in generating Pareto‐optimal objective vectors that reflect brand priorities and that are well distributed along the Pareto front.     

Multi-objective optimization of volume shrinkage and clamping force for plastic injection molding via sequential approximate optimization

Process parameters in plastic injection molding (PIM), such as the packing pressure, the mold temperature, the melt temperature, and so on, are generally determined by a trial-and error method through the experiments. Computer-aided engineering (CAE) in the PIM is an alternative approach to determine the optimal process parameters. In cap-type plastic product, large volume shrinkage makes the clamping difficult. Furthermore, small clamping force leads to high productivity as well as cost reduction. Both volume shrinkage and clamping force should then be minimized simultaneously, and a multi-objective design optimization is formulated. Inappropriate process parameters easily lead to short shot that the melt plastic is not fully filled into cavity. In this paper, short shot is handled as the design constraint. Numerical simulation of the PIM is so expensive that the response surface approach is valid. In particular, a sequential approximate optimization (SAO) that the response surface is repeatedly constructed and optimized with some new sampling points is recognized as one of the most powerful tools available. In this paper, the radial basis function (RBF) network is adopted for the SAO, and the pareto-frontier is identified with a small number of simulation runs. Numerical result shows that the pareto-frontier is well identified with a small number of simulation runs.     

A linear goal programming approach to determining the relative importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is a planning tool used in new product development and quality management. It aims at achieving maximum customer satisfaction by listening to the voice of customers. To implement QFD, customer requirements (CRs) should be identified and assessed first. The current paper proposes a linear goal programming (LGP) approach to assess the relative importance weights of CRs. The LGP approach enables customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats, which may differ from one customer to another but have no need to be transformed into the same format, thus avoiding information loss or distortion. A numerical example is tested with the LGP approach to demonstrate its validity, effectiveness and potential applications in QFD practice.     

The impact of the objective function in multi-site and multi-variable calibration of the SWAT model

Automatic calibration of complex hydro-ecological models is an increasingly important issue which involves making decisions. One of the most relevant is the choice of the objective function, but its effects have been scarcely studied in complex models. We have used the SWAT model to assess the impact of the objective function for a multi-site (4 stations) and multi-variable (OrgP, OrgN, NO₃⁻, PO₄³⁻) calibration of the Odense catchment (Denmark). Six calibration schemes were tested, varying the objective function and the nutrient fractions targeted. The best performance metrics (R², NSE, PBIAS) were obtained when using NSE as objective function and targeting N-fractions and P-fractions separately. The scheme was validated in another SWAT set-up in northern Denmark. Although NSE is often questioned, we found it as an adequate objective function when addressing a multi-site and multi-variable calibration. Our findings may serve as guideline for hydro-ecological modellers, being useful to achieve watershed management goals.     

基于改进的遗传算法在函数优化中的应用

针对传统遗传算法在函数优化过程中容易陷入局部最优解、收敛慢等缺点,提出了一种新的自适应遗传算法NAGA。该算法考虑了种群适应度的多种集中分散程度,并且非线性地自适应调节遗传算法的交叉概率与变异概率;为了加快寻优效率,在选择算子方面将引进的选择算子与最优保存策略相结合;为了使遗传操作过程中种群数量恒定,又提出了保留亲本的策略。通过仿真实验发现,与经典遗传算法GA和IAGA相比,改进的自适应遗传算法在收敛速度与精准度等方面都有较大的进步。     

Analytical approach for the evaluation of the torques using inverse multibody dynamics

A mathematical model for the analysis of human motion is presented in this paper. This model is based on linkage dynamics in order to understand trajectory and internal moment of force coordination. Mobility at the base of the supporting limb is a critical factor in the freedom to fall forward. The approach used to state a coupled system of differential equations of motion consists in introducing the displacement of the center of mass together with the displacement of each segment of the body and to evaluate the final system as a whole. The resultant methodology is task independent. The main goal of this study is to assist the work of health care professionals in the determination of the torques at the joints generated to maintain the movement. The evaluation of a weighted average of all the forces has served as a basis for other authors to obtain the center of pressure. In this work, the resultant ground reaction force passes through the center of mass of the body system enabling the calculation of the location of this force.     

Revisiting the gap function of a multicriteria optimization problem

This paper improves one of the properties of the gap function for a convex multicriteria optimization problem.     

Effects of sitting and standing, reach distance, and arm orientation on isokinetic pull strengths in the horizontal plane

In recent years, isokinetic strengths (dynamic strength exertions at constant speed) have almost replaced isometric (static) strengths in laboratory studies as measures of a person's strength exertion capabilities. Many industries are also showing a keen interest in replacing static strength usage with dynamic strength usage. The increasing acceptance of isokinetic strengths as a more valid and accurate measure of people's strength exertion capability has necessitated the development of isokinetic strength databases. This paper presents one-arm isokinetic pull strength profiles of males, engaged in infrequent exertion in a horizontal plane, as a function of posture (sitting and standing), reach distance (25, 40, and 55 cm for the sitting posture; 45, 65, and 85 cm for the standing posture), and angle of the preferred (stronger) arm from the frontal plane (0—frontal plane, 30, 60, 90, 120, and 150 deg). Twenty-five males participated in the study. The results indicated that more strength is exerted while standing. The strength also increases with the reach distance. The strength exertion becomes stronger as the angle of the arm increases to 90° from the frontal plane (i.e., the arm moves to the sagittal plane) and then weakens.     

Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system

The main objective of this paper is to solve the bi-objective reliability redundancy allocation problem for series-parallel system where reliability of the system and the corresponding designing cost are considered as two different objectives. In their formulation, reliability of each component is considered as a triangular fuzzy number. In order to solve the problem, developed fuzzy model is converted to a crisp model by using expected values of fuzzy numbers and taking into account the preference of decision maker regarding cost and reliability goals. Finally the obtained crisp optimization problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Examples are shown to illustrate the method. Finally statistical simulation has been performed for supremacy the approach.