Secondary Objective Function Research Articles

Location based treatment activities for end of life products network design under uncertainty by a robust multi-objective memetic-based heuristic approach

Rapid growth in world population and recourse limitations necessitate remanufacturing of products and their parts/modules. Managing these processes requires special activities such as inspection, disassembly, and sorting activities known as treatment activities. This paper proposes a capacitated multi-echelon, multi-product reverse logistic network design with fuzzy returned products in which both locations of the treatment activities and facilities are decision variables. As the obtained nonlinear mixed integer programming model is a combinatorial problem, a memetic-based heuristic approach is presented to solve the resulted model. To validate the proposed memetic-based heuristic method, the obtained results are compared with the results of the linear approximation of the model, which is obtained by a commercial optimization package. Moreover, due to inherent uncertainty in return products, demands of these products are considered as uncertain parameters and therefore a fuzzy approach is employed to tackle this matter. In order to deal with the uncertainty, a stochastic simulation approach is employed to defuzzify the demands, where extra costs due to opening new centers or extra transportation costs may be imposed to the system. These costs are considered as penalty in the objective function. To minimize the resulting penalties during simulation's iterations, the average of penalties is added to the objective function of the deterministic model considered as the primary objective function and variance of penalties are considered as the secondary objective function to make a robust solution. The resulted bi-objective model is solved through goal programming method to minimizing the objectives, simultaneously.

Negotiated control between the manual and visual systems for visually guided hand reaching movements.

BackgroundControl of reaching movements for manual work, vehicle operation, or interactions with manual interfaces requires concurrent gaze control for visual guidance of the hand. We hypothesize that reaching movements are based on negotiated strategies to resolve possible conflicting demands placed on body segments shared by the visual (gaze) and manual (hand) control systems. Further, we hypothesize that a multiplicity of possible spatial configurations (redundancy) in a movement system enables a resolution of conflicting demands that does not require sacrificing the goals of the two systems.MethodsThe simultaneous control of manual reach and gaze during seated reaching movements was simulated by solving an inverse kinematics model wherein joint trajectories were estimated from a set of recorded hand and head movements. A secondary objective function, termed negotiation function, was introduced to describe a means for the manual reach and gaze directing systems to balance independent goals against (possibly competing) demands for shared resources, namely the torso movement. For both systems, the trade-off may be resolved without sacrificing goal achievement by taking advantage of redundant degrees of freedom. Estimated joint trajectories were then compared to joint movement recordings from ten participants. Joint angles were predicted with and without the negotiation function in place, and model accuracy was determined using the root-mean-square errors (RMSEs) and differences between estimated and recorded joint angles.ResultsThe prediction accuracy was generally improved when negotiation was included: the negotiated control reduced RMSE by 16% and 30% on average when compared to the systems with only manual or visual control, respectively. Furthermore, the RMSE in the negotiated control system tended to improve with torso movement amplitude.ConclusionsThe proposed model describes how multiple systems cooperate to perform goal-directed human movements when those movements draw upon shared resources. Allocation of shared resources can be undertaken by a negotiation process that is aware of redundancies and the existence of multiple solutions within the individual systems.

Multi‐objective fuzzy‐based procedure for enhancing reactive power management

This study proposes a multi-objective fuzzy-based procedure for solving reactive power management in competitive environment. The proposed procedure incorporates both economical and technical aspects of reactive power support. The economical aspect aims to minimise the total costs of reactive power purchase from service providers as primary objective function, whereas the technical aspect is taken care of through the secondary objective function that minimises the total transmission losses. The proposed procedure achieves security constraints such as the bus voltage limits, reactive power capability limits and transmission line reactive transfer limits. The proposed procedure is applied to the west-delta region system as a part of the Egyptian Unified network. The numerical results show that the proposed procedure achieves a minimum real power loss with maximal reactive reserve for power systems for different operating conditions.

Concurrent Aerodynamic Optimization of Rotor Blades Using a Nash Game Method

A multiobjective strategy adapted to the aerodynamic concurrent optimization of helicopter rotor blades is developed. The present strategy is based on Nash games from game theory, where the objective functions are minimized by virtual players involved in a noncooperative concurrent game. A method is presented to split the design vector into two subspaces, defined to be the strategies of the players in charge of the minimization of the primary and the secondary objective functions, respectively. This split of territory allows the optimization of the secondary function while causing the least possible degradation of the first one. This methodology is applied to the model rotor ERATO, seeking to maximize the figure of merit in hover while minimizing the required rotor power in forward flight, assuming frozen structural properties. An initial constrained optimization in hover is conducted using a previously developed adjoint-based technique using the three-dimensional Navier–Stokes solver elsA along with the gradient-based CONMIN algorithm. The chord, twist, and sweep distributions of the baseline blade are parameterized using Bezier and cubic splines for a total of 16 design variables. The obtained optimized rotor is then used as a starting point to launch constrained and unconstrained Nash games. The comprehensive rotor code Eurocopter's Helicopter Overall Simulation Tool (HOST) is used to evaluate forward flight performance, and a surrogate model is built to obtain the hover performance at low computational cost. Twist and sweep distribution laws are optimized independently at first, and then a final joint optimization involving twist, sweep, and chord is performed. The results demonstrate the potential of this technique to obtain helicopter rotor designs realizing interesting trade-offs between strongly antagonistic objectives.

Parametric Representation and Shape Optimization of Flapping Micro Air Vehicle Wings

The effects of wing planform on the aerodynamic performance of a rigid wing in forward flapping flight and hovering configurations were investigated in this paper. The planform design space was parameterized using a new, modified Zimmerman method based on low aspect ratio Zimmerman planform designs. The aerodynamic forces on the wing were calculated using Peters' aerodynamics with an assumed inflow coupled with blade element theory. A multiobjective optimization approach was taken to find the best planform designs for three objectives: wing area, peak power input, and an aerodynamic force based on the kinematic configuration – lift for hovering and thrust for forward flight. A gradient-based optimizer and the ε-constraint method were used to find the Pareto front of optimal designs with the aerodynamic force as the primary objective function. The choice of primary and secondary objective functions is important in determining the optimal planform. The Pareto optimal planforms for the case when only area is considered as a secondary objective function drastically differ from the optimal planforms when only power is taken as a secondary objective function. As the secondary objective ε values change over the design space, so do the optimal planform shapes.

A new ranking method based on cross-efficiency in data envelopment analysis

Data envelopment analysis (DEA) models compute efficiency score for decision making units (DMUs) and discriminate between efficient and inefficient DMUs. Therefore, they rank DMUs except when multiple DMUs have an efficiency score of 1. This paper proposes a new method for complete ranking of DMUs that is based on cross-efficiency evaluation method. One of the drawbacks of the cross-efficiency evaluation method is the existence of multiple cross-efficiency scores due to the presence of alternative optimal solutions of the dual multiplier model. Hence choosing weights between alternative optimal solutions as part of a procedure for ranking DMUs is problematic. Liang et al. (2008) introduced alternative secondary goals in cross-efficiency evaluation. However, this paper finds that their approach is problematic in some situations. As a result, this paper seeks to introduce a new secondary objective function in cross-efficiency evaluation for removing their difficulties. Numerical demonstration reveals the validity of the proposed method by using a real data set of a case study which consists of 20 Iranian bank branches. Key words: Data envelopment analysis (DEA), ranking, cross-efficiency.

Performing co-ordinated turns with articulated wing-tips as multi-axis control effectors

AbstractThis paper investigates a novel method for the control of aircraft. The concept consists of articulated split wing-tips, independently actuated and mounted on a baseline flying wing. The general philosophy behind the concept was that adequate control of a flying wing about its three axes could be obtained through local modifications of the dihedral angle at the wing-tips, thus providing an alternative to conventional control effectors such as elevons and drag rudders. Preliminary computations with a vortex lattice model and subsequent wind tunnel tests and Navier-Stokes computations demonstrate the viability of the concept for co-ordinated turns, with individual and/or combined wing-tip deflections producing multi-axis, coupled control moments. The multi-axis nature of the generated moments tends to over-actuate the flight control system, leading to some redundancy, which could be exploited to optimise secondary objective functions such as drag or bending moment.

The study of a dynamic dial-a-ride problem under time-dependent and stochastic environments

This paper studies a dynamic dial-a-ride problem bearing complex constraints on a time-dependent network. A flexible scheduling scheme is proposed to dynamically cope with different stochastic events, such as the travelling time fluctuation, new requests, absences of customers, vehicle breakdowns, cancellations of requests, traffic jams and so on. A fast heuristic is proposed to re-optimize the schedule when a new event occurs. This heuristic consists of a properly organized local search strategy and uses a secondary objective function to drive the search out of local optima. Intensive computational simulations were carried out to evaluate the performance of this scheduling scheme and the influence of different stochastic factors. The simulation results of different scenarios with different percentage of dynamic requests reveal that this scheduling scheme can generate high quality schedules and is capable of coping with various stochastic events.

Alternative secondary goals in DEA cross-efficiency evaluation

As an extension to data envelopment analysis (DEA), cross-efficiency evaluation not only provides a ranking among the decision-making units (DMUs) but also eliminates unrealistic DEA weighting schemes without requiring a priori information on weight restrictions. A factor that possibly reduces the usefulness of the cross-efficiency evaluation method is that the cross-efficiency scores may not be unique due to the presence of alternate optima. As a result, it is recommended that secondary goals be introduced in cross-efficiency evaluation. This paper seeks to extend the model of Doyle and Green [1994. Efficiency and cross efficiency in DEA: Derivations, meanings and the uses. Journal of the Operational Research Society 45 (5), 567–578], by introducing a number of different secondary objective functions. The models are illustrated with examples.

Congestion pricing for multi-modal transportation systems

In this paper, we extend the toll pricing framework previously developed for vehicular traffic networks to ones with the potential to include many modes of transportation such as walking, driving, and using public conveyance (e.g., buses, subways, and trains). To determine tolls, we construct a user equilibrium and system optimal model. In both models, we assume that users adopt strategies or hyperpaths to travel between each origin-destination pair and the demand between each pair is fixed. However, the choice between driving and using public transportation is determined by a binomial logit function. As in the case of vehicular traffic networks, the set of valid tolls can be obtained from the solution to the system problem and the equilibrium conditions for the user problem. Then, secondary objective functions similar to those for traffic networks can be used to select a toll vector for, e.g., implementation. We provide a numerical example to illustrate our approach.

Design and analysis of kinematically redundant parallel manipulators with configurable platforms

Redundancy can, in general, improve the ability and performance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function. Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator. The additional redundant degrees of freedom are used in reconfiguring the shape of the platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for irregular or large objects or even as a micro-positioning device after grasping the object. Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platform.

Concerning the primary and secondary objectives in robot task definition — the “learn from humans” principle

This paper is concerned with the trajectory definition in robot tasks. Although very often ignored, the specification of robot motion is not the first step in the definition of a robot task. The task definition starts with the description of the final outcome, i.e. with the specification of the job to be performed. When this is done, the proper robot kinematics (motion law) is defined. This step, from the outcome of the task to the robot motion, is sometimes straightforward and dictated by the technology applied. However, even if a multiple choice of motion is possible leading to the same outcome, this possibility is usually avoided by preassuming a certain optimality criterion for the quality of work. Clearly, such an approach does not leave the possibility for some additional optimization in the sense of a secondary objective. So, some potential benefits are lost. This paper starts from the observation that successful operation of a robot does not necessarily imply the maximum quality of its outcome. It is sufficient if the quality is kept at a given (lower) level. Such a suboptimal task execution offers the possibility of some additional secondary optimization. The kinematics of the task is modified according to a secondary objective function. The quality is then treated as a constraint in the minimization of this secondary objective function. This optimization can be based on biomechanical principles. Here the principle: “learn from humans” is adopted, i.e. the kinematics modification is done so as to resemble the behavior of a human worker. The benefits of the approach of the paper are illustrated by two specific examples, namely the handwriting and spray-coating tasks.

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective "as close as possible" to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot. Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.

On the Greedy Solution of Ordering Problems

The greedy method is a well-known approach for problem solving directed mainly at the solution of optimization problems. Leading theoretical frameworks dealing with the optimality of greedy solutions (e.g., the matroid and greedoid theories) tacitly assume that the greedy algorithm is always guided by the cost function to be optimized, namely, it builds a solution by adding, in each step, an element that contributes the most to the value of the cost function. This paper studies a class of problems for which this type of a greedy algorithm does not optimize the given cost function, but for which there exists a secondary objective function, called a greedy rule, such that applying the greedy algorithm to the secondary objective function yields a solution which is optimal with respect to the original cost function. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.