Multi-criteria Objective Function Research Articles

Decision support tool for selecting fabrication parameters in stereolithography

The selection of fabrication (build) parameters is the most important task performed by the operator of a layer manufacturing (LM) system. In order to select the best parameter configuration for a part, the operator should be able to compare different alternatives and evaluate them under specific constraints, in terms of fabrication cost and quality. In the present paper, a software decision support tool for build parameters selection in stereolithography is presented. Build orientation and layer thickness are proposed as the primary parameters for the definition of candidate solutions, which are evaluated according to a weighted multi-criteria objective function. As the objective function criteria, the build time, surface roughness and process error are employed. The criteria estimation is based on experimentally derived analytical equations or computed from the STL representation of the part. To further enhance the evaluation process, the software tool exports VRML models that incorporate surface roughness or stairstepping data through colour codification.

Design of a Comfortable Rotor Airfoil Using Distributed Piezoelectric Actuators

In the present study, several design methodologies are developed for determining the optimal distribution of a limited amount of piezoelectric material aft of the spar in a conformable rotor airfoil section. The design objectives are to maximize the trailing-edge deflection under actuation loads and simultaneously minimize the airfoil deflection under aerodynamic loads. Energy-like functions, mutual potential energy (MPE) and strain energy (SE), are used as measures of the deflections created by the actuation and aerodynamic loads, respectively. The design objectives are achieved by maximizing a multicriteria objective function that represents a ratio of the MPE to SE. Several design optimization techniques are evaluated including topology, geometry, sequential topology-geometry, and concurrent topology-geometry optimizations. The results of the study indicate that the optimized conformable airfoil section obtained using the concurrent topology-geometry optimization can produce a downward trailing-edge deflection equivalent to 4.24 deg of effective flap angle from the actuation loads, with the peak-to-peak deflection being nearly twice the downward deflection. The airfoil deformation caused by the aerodynamic loads alone is extremely small (less than 0.24 deg). Key features of the optimized airfoil are arrangement of actuators near the spar that act to stretch and shrink the skin and a bimorph like mechanism from midchord to the trailing edge. Additional results include a strain analysis, aerodynamic lift-and-drag increment study, and an examination of the effects of skin thickness and volume constraint of the active material.

NETWORK DESIGN OF INTEGRATED E-SUPPLY CHAIN FOR AGILE MANUFACTURING

Supply chains are distributed manufacturing systems composed of various resources belonging to different companies. The configuration of the supply chain network, integrated with Internet and web-based electronic market places, is essential for business to pursue a competitive advantage. This paper develops a model describing the integrated e-supply chain network and formulates a multi-criteria integer linear optimization problem to select the candidates and the links connecting the stages of the e-supply chain. Hence, some multi-criteria objective functions are defined and suited constraints are introduced on the basis of the digraph modelling the supply chain network. The proposed methodology is illustrated by way of a case study describing a network for desktop computer production.

Topological Synthesis of Compliant Mechanisms Using Nonlinear Beam Elements

The article presents a methodology for generating topology of complaint mechanisms using nonlinear deformation theory. In an earlier work, (Joo, J., Kota, S., Kikuchi, N., (2000) Topological synthesis of compliant mechanisms using linear beam elements. Mechanics of Structures and Machines 28(4):245–280), we presented a topology synthesis methodology using linear beam elements. Using large deformation analysis, the article presents a methodology for topology synthesis based on a multicriteria objective function as a ratio of geometrical advantage to strain energy is employed to capture the conflicting functional requirements that are inherent in compliant mechanisms design. The benefits of using nonlinear methods for large deformation problems are illustrated by using three design examples and comparing results from a nonlinear implementation of the optimization procedure with a linear scheme.

Solving the aerial fleet refueling problem using group theoretic tabu search

The aerial fleet refueling problem (AFRP) is concerned with the efficient and effective use of a heterogeneous set of tanker (refueling) aircraft, located at diverse geographical locations, in the required operations associated with the deployment of a diverse fleet of military aircraft to a foreign theater of activity. Typically, the “receiving” aircraft must traverse great distances over large bodies of water and/or over other inhospitable environs where no ground based refueling resources exist. Lacking the ability to complete their flights without refueling, each receiving aircraft must be serviced one or more times during their deployment flights by means of in-flight refueling provided by one of the available tanker aircraft. The receiving aircraft, aggregated into receiver groups (RGs) that fly together, have stipulated departure and destination bases and each RG's arrival time is bounded by a stated desired earliest and latest time. The excellence of a suggested solution to this very challenging decision making problem is measured relative to a rigorously defined hierarchical multicriteria objective function. This paper describes how the AFRP for the Air Mobility Command (AMC), Scott Air Force Base, IL, is efficiently solved using group theoretic tabu search (GTTS). GTTS uses the symmetric group on n letters ( S n ) and applies it to this problem using the Java™ language.

Shape Optimization of a Cementless Hip Stem for a Minimum of Interface Stress and Displacement

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.

A new heuristic for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness

This paper addresses the m-machine flowshop problem with the objective of minimizing a weighted sum of makespan and maximum tardiness. Two types of the problem are addressed. The first type is to minimize the objective function subject to the constraint that the maximum tardiness should be less than a given value. The second type is to minimize the objective without the constraint. A new heuristic is proposed and compared to two existing heuristics. Computational experiments indicate that the proposed heuristic is much better than the existing ones. Moreover, a dominance relation and a lower bound are developed for a three-machine problem. The dominance relation is shown to be quite efficient. Scope and purpose The majority of research on scheduling problems addresses only a single criterion while the majority of real-life problems require the decision maker to consider more than a single criterion before arriving at a decision. The scheduling literature reveals that the research on multi-criteria is mainly focused on the single-machine problem as a result of the difficulty of the multiple machines problem. This paper addresses an m-machine flowshop scheduling problem with a multi-criteria objective function.

Manufacturability analysis of early product designs

The calculation and optimization of product manufacturability during the preliminary stages of design are critical to achieving reduced time to market, high quality and low cost. An aggregate planning method, which translates early product characteristics into manufacturing requirements, forms the basis of a new intelligent support system for which the manufacturing evaluation, optimization and reporting functions are described in this paper. The system 'intelligently explores' the many alternative processing technologies and equipment choices available, seeking solutions that best satisfy a multi-criteria objective function encapsulating quality, cost, delivery and knowledge criteria. The addition of knowledge factors means that both quantitative and qualitative factors can be used to rank alternatives. Importantly, the system prioritizes each element according to its potential for improvement. The designer is thus presented with the opportunity to redefine the design elements or process specifications, which would yield the greatest improvements in production.

Anchor deployment for deep water floating offshore equipments

In this work a planning methodology for deep water anchor deployment in offshore platforms and floating production systems aiming at operational resources optimization is explored, by minimizing a multi criteria objective function. As an additional advantage provided by the proposed methodology, planning automation is achieved. Planning automation overcomes the traditional way, using a trial error basis. With it, an engineer, using an anchoring software, decides how much work wire and anchoring line must be paid out from both the floating system and the tug boat. Additionally, he decides which horizontal force must be applied to the line, trying to settle the anchor on a previously defined target on the ocean floor.

Otimização de recursos para a operação de instalação de âncoras de equipamentos offshore

Neste trabalho é apresentada uma metodologia para o planejamento da operação de instalação de âncoras de equipamentos offshore, navios e plataformas, visando a otimização dos recursos necessários, embarcações de apoio e cabos de trabalho, por meio da minimização de uma função objetivo com base em múltiplos critérios. Como ganho adicional, inerente à metodologia proposta, consegue-se a automação do processo de planejamento de instalação, que nos moldes tradicionais é feito na base da tentativa e erro, onde o planejador, utilizando algum aplicativo para o cálculo de ancoragem, decide quanto de recursos deve ser aplicado ao problema tentando fazer com que a âncora atinja o alvo pré-definido no projeto do sistema de ancoragem.

Through-process modelling of microstructure evolution in hot forming of steels

The objective of the paper is presentation of the complex thermal-mechanical-microstructural model, which simulates the whole process of hot forming, starting from heating of the stock material through the forming operations up to the controlled cooling after forming. The thermal-mechanical finite element solution is the basis of the approach and it is coupled with the closed form equations describing microstructural phenomena. The microstructural equations are solved in each node of the finite element mesh and at each time step, what makes the feedback between the models possible. Three stages of modelling are presented. The first concerns heating of the stock before forming. The model predicts temperature field, stresses and grain size during heating. The second stage uses thermal-mechanical-microstructural model of forming operations. Beyond the conventional closed for equation describing microstructure development, the models based on the internal variable approach are presented. Particular emphasis is put on identification of parameters of the models. The inverse analysis with the multi criterion objective function is applied. Simulation of the controlled cooling of products after hot forming is the third objective of the modeling. The models couple finite-element solution of the thermal problem with equations describing kinetics of phase transformations and properties of materials in the room temperature. Identification of the phase transformation models is based on the inverse analysis combined with the experimental TTT diagrams. Several examples of simulations and experimental validation, which are presented in the paper, confirm good predictive capabilities of the model.

Topological Synthesis of Compliant Mechanisms Using Linear Beam Elements1*

The design of compliant mechanisms poses certain unique challenges because such mechanisms should have adequate flexibility to undergo desired deformations under the action of applied forces and adequate stiffness to withstand external loading. The focus here is to generate the topology of a compliant mechanism starting from input/output force/displacement functional requirements and design constraints. Previous studies [[1][2][3]] and [[4]] employed a multi-criteria objective function comprised of mutual potential energy (MPE) and strain energy (SE) to full ground truss structures. Here an improved and robust objective function and its implementation for a network of linear beam elements is presented. Also discussed is the influence of various geometric and material variables on the objective function. Additionally, the objective function is interpreted in terms of physical design parameters such as mechanical advantage and geometric advantage.

Hybrid genetic algorithmsfor a multiple-objective scheduling problem

This paper describes the characteristics of two hybrid genetic algorithms (GAs) for generating allocation and sequencing of production lots in a flow-shop environment based on a non-linear, multi-criteria objective function. Both GAs are used as search techniques: in the first model the task of the GA is to allocate and sequence the jobs; in the second model, the GA is combined with a dispatching rule (Earliest Due Date, EDD) thus limiting its task only on the allocation of the jobs. Both GAs are characterized by a dynamic population size with dynamic birth rate, as well as by multiple-operator reproduction criteria and by adaptive crossover and mutation rates. A discrete-event simulation model has been used in order to evaluate the performances of the tentative schedules. The proposed algorithms have been subsequently compared with a classical branch and bound method.

Detailed design of reinforced concrete buildings using logic programming

A procedure is proposed leading to an optimal detailed design of reinforced concrete members. The general scheme followed is that of a multi-criterion design optimization. The method synthesizes the information from the cross-sectional level, to the member level and finally, to a group of members where the detailed design of the whole group is decided. At the cross-sectional level, the required reinforcement in cm 2 is converted into reinforcing bars of all possible diameters. At the member and/or group of members level, a number of lists that contain different design scenarios are generated. The method of objective weighting is applied to a multi-criterion objective function, which represents a compromise of the ‘minimum weight’, ‘maximum uniformity’ and ‘minimum number of reinforcing bars’ criteria. By varying the weighting factors, it is possible to generate the Pareto optimal set of the problem. The performance of the system is illustrated with a number of examples. The same building is designed using different weighting factors in the multi-criterion objective. The variation of the detailed designs is discussed and certain values for the weighting factors are recommended.

Genetic algorithms for optimal logical database design

The focus of this paper is database design using automated database design tools or more general CASE tools. We present a genetic algorithm for the optimization of (internal) database structures, using a multi-criterion objective function. This function expresses conflicting objectives, reflecting the well-known time/space trade-off. This paper shows how the solution space of the algorithm can be set up in the form of tree structures (forests), and how these are encoded by a simple integer assignation. Genetic operators (database transformations) defined in terms of this encoding behave as if they manipulate tree structures. Some basic experimental results produced by a research prototype are presented.

An integrated approach to solving the master aggregate scheduling problem

Master scheduling is concerned with synchronizing production activities with product demand, while also coordinating the use of different resources. It will thus be a key schedule in any control system intended for application in an integrated manufacturing environment. This paper combines earlier methodologies, in master scheduling and aggregate planning, to develop a master aggregate schedule (MA-schedule) model, which is better equipped to meet the needs of modern manufacturing facilities. The MA-schedule aggregates capacity, time, and products; models routing and capacity flexibility; considers the availability of material transporters; and has a multi-criteria objective function. The schedule is formulated as a large-scale mixed integer program. Experimental results with some test problems are reported, and the impact of the new features is studied.

Genetic neuro-scheduler for job shop scheduling

This paper describes a hybrid approach between two new techniques, Genetic Algorithms and Artificial Neural Networks, for generating Job Shop Schedules (JSS) in a discrete manufacturing environment based on non-linear multi-criteria objective function. Genetic Algorithm (GA) is used as a search technique for an optimal schedule via a uniform randomly generated population of gene strings which represent alternative feasible schedules. GA propagates this specific gene population through a number of cycles or generations by implementing natural genetic mechanism (i.e. reproduction operator and crossover operator). It is important to design an appropriate format of genes for JSS problems. Specifically, gene strings should have a structure that imposes the most common restrictive constraint; a precedence constraint. The other is an Artificial Neural Network, which uses its highly connected-neuron network to perform as a multi-criteria evaluator. The basic idea is a neural network evaluator which maps a complex set of scheduling criteria (i.e. flowtime, lateness) to evaluate values provided by experienced experts. Once, the network is fully trained, it will be used as an evaluator to access the fitness or performance of those stimulated gene strings. The proposed approach was prototyped and implemented on JSS problems based on different model sizes; namely small, medium, and large. The results are compared to the Shortest Proceesing Time heuristic used extensively in industry.

A multiattribute decision-theoretic approach for the layout design problem

This paper presents an application of decision theory to the layout design problem. Both the quantitative and qualitative aspects of the problem are considered. The approach is to utilize measurement results in defining a multicriteria objective function for layout evaluation. This objective function is used in the context of a heuristic algorithm for generating a layout. The algorithm is embedded in a software package. The effectiveness of using a multicriteria objective function is demonstrated using the proposed algorithm on a ten-department problem.

A novel approach to the design of 2-d recursive digital filters

An efficient method is presented for the design of 2-D circular symmetric recursive digital filters satisfying prescribed magnitude and constant group-delay responses. The transfer function of this class of 2-D filters has a zero-phase non-separable numerator and separable denominator 2-variable polynomials in z 1 and z 2 . In the proposed technique the coefficients of the 2-D filters are calculated in two steps. In the first step the parameters of two 1-D all pole filters 1/D 1(z 1) and 1/D 2(z 2) are calculated by minimizing a multicriterion objective function using a suitable optimization technique so that the magnitude and group- delay responses of the desired 2-D filter along the ω 1 , ω 2 axes are obtained. Essentially, the first step of the proposed design method yields a 2-D all pole separable product filter with rectangular cutoff boundaries with or without constant group-delay responses in the passband of the above filter. In the second step, the parameters of the zero-phase 2-variable non- separable polynomial in z 1 and z 2 in the numerator can be determined through minimization of a cost function using a linear programming approach. Note that the second step acts as a magnitude equalizer to convert a rectangular cutoff boundary to a circular one. An example illustrates the usefulness of the proposed algorithm.

A multicriteria objective function optimization scheme for laminated composites for use in multilevel structural optimization schemes

A multilevel optimization scheme for large laminated composite structures is proposed, and a suitable element/lower-level optimization scheme using a multicriteria objective function is developed. The objective function combines a weight function and a strain energy change function into a utility function which is minimized and in which the relative importance of each part is reflected by weighting coefficients. Minimizing the change in strain energy ensures load path continuity in the overall structure when switching between upper and lower levels of optimization, and so decouples the problems at the two levels. Continuous lamina thickness and ply-angle variation is used to minimize the objective function while satisfying strain, buckling, and gauge constraints. Numerical applications are given to illustrate the effect of the weighting coefficients in the objective function on the final result, and to demonstrate the algorithm's effectiveness as a pure weight minimization routine.