A new multi-objective discrete robust optimization algorithm for engineering design

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.     

Robust parameter design in resource-constrained environments: An investigation of trade-offs between costs and precision within variable processes

Engineers and scientists often identify robust parameter design as one of the most important process and quality improvement methods. Focused on statistical modeling and numerical optimization strategies, most researchers typically assume a process with reasonably small variability. Realistically, however, industrial processes often exhibit larger variability, particularly in mass production lines. In such cases, many of the modeling assumptions behind the robust parameter design models available in the literature do not hold. Accordingly, the results and recommendations provided to decision makers could generate suboptimal modifications to processes and products. As manufacturers seek improved methods for ensuring quality in resource-constrained environments, experimenters should examine trade-offs to achieve the levels of precision that best support their decision making. In contrast to previous research, this paper proposes a trade-off analysis between the cost of replication and the desired precision of generated solutions. We consider several techniques in the early stages of experimental design, using Monte Carlo simulation as a tool, for revealing potential options to the decision maker. This is perhaps the first study to show the avenue which may lead to more effective robust parameter design models with the optimal combination of cost constraints and desired precision of solutions.     

Constrained optimization using multiple objective programming

In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems.     

Multicriteria equilibrium programming: Extraproximal methods

Multicriteria equilibrium optimization is an efficient tool for mathematical modeling of various situations in operations research, design automation, control, etc. In this paper, a formal formulation of the problem of multicriteria equilibrium optimization is given, and an approach to solving this problem is examined.     

A Graphical Tool to Visualize Predicted Minimum Delay Flights

In this article, we present a graphical decision support tool to aid in analyzing the U.S. air transport network. In addition to displaying simple statistics, our tool can calculate the predictions of both the minimum-delay and quickest routes for a given origin and destination airport using regression, simulation, and network optimization techniques. Using various visualizations allows for less obvious patterns in the data to be displayed. This article has supplementary material online.     

Simulation optimization for an emergency department healthcare unit in Kuwait

This paper integrates simulation with optimization to design a decision support tool for the operation of an emergency department unit at a governmental hospital in Kuwait. The hospital provides a set of services for different categories of patients. We present a methodology that uses system simulation combined with optimization to determine the optimal number of doctors, lab technicians and nurses required to maximize patient throughput and to reduce patient time in the system subject to budget restrictions. The major objective of this decision supporting tool is to evaluate the impact of various staffing levels on service efficiency. Experimental results show that by using current hospital resources, the optimization simulation model generates optimal staffing allocation that would allow 28% increase in patient throughput and an average of 40% reduction in patients’ waiting time.     

Fuzzy multicriteria decision support for budget allocation in the transport sector

Summary This paper compares two ways of providing decision support for the allocation of a fixed financial budget among a set of competing highway investment proposals. The first, which is described only in outline, uses a broadly conventional, hierarchically structured linear additive multicriteria model. The technical focus of the paper, however, is on the second, and approach based in fuzzy multicriteria modelling. The thinking which led us to explore this approach is set out, together with the formal structure of the model. The results of a small case study are given and an assessment is made of how decision makers' understanding of the investment options available can be enhanced by using the two models in tandem.     

A preference disaggregation decision support system for financial classification problems

Classification is one of the most extensively studied problems in the fields of multivariate statistical analysis, operations research and artificial intelligence. Decisions involving a classification of the alternative solutions are of major interest in finance, since several financial decision problems are best studied by classifying a set of alternative solutions (firms, loan applications, investment projects, etc.) in predefined classes. This paper proposes an alternative approach to the classical statistical methodologies that have been extensively used for the study of financial classification problems. The proposed methodology combines the preference disaggregation approach (a multicriteria decision aid method) with decision support systems. More specifically, the FINancial CLASsification (FINCLAS) multicriteria decision support system is presented. The system incorporates a plethora of financial modeling tools, along with powerful preference disaggregation methods that lead to the development of additive utility models for the classification of the considered alternatives into predefined classes. An application in credit granting is used to illustrate the capabilities of the system.     

Multivariate Gaussian criteria in SMAA

We consider stochastic multicriteria decision-making problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions. In many real-life problems the uncertainties of criteria measurements may be dependent. However, it is often difficult to quantify these dependencies. Also, most of the existing methods are unable to handle such dependency information.In this paper, we develop a method for handling dependent uncertainties in stochastic multicriteria group decision-making problems. We measure the criteria, their uncertainties and dependencies using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. Based on the simulation results, we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies. We then use the SMAA-2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions. We demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated European electricity market.     

A general approach to solving a wide class of fuzzy optimization problems

Results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented. A general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described. It involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms. Prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone. The results of the paper are of a universal character and are already being used to solve problems of power engineering.     

Combining expert judgment: On the performance of trimmed mean vote aggregation procedures in the presence of strategic voting

Analytic group decision techniques for selecting a subset of alternatives range between multicriteria decision analysis techniques such as multiattribute utility theory and the analytic hierarchy process to voting techniques where each member of the decision group submits a ranking of the alternatives, and these individual rankings are then aggregated into an overall ranking. The obvious advantage of voting is that it bypasses the rather intensive data generation requirements of multicriteria techniques. In this paper we compare the performance of trimmed mean rank-order aggregation procedures in the case where a subset of the individuals in the group charged with the decision vote strategically. We employ a Monte Carlo simulation experiment on a specific decision instance and find that trimmed mean aggregation compares favorably with other procedures.     

Multicriteria Engineering Optimization Problems: Statement, Solution and Applications

The majority of engineering optimization problems (design, identification, design of controlled systems, optimization of large-scale systems, operational development of prototypes, and so on) are essentially multicriteria. The correct determination of the feasible solution set is a major challenge in engineering optimization problems. In order to construct the feasible solution set, a method called PSI (Parameter Space Investigation) has been created and successfully integrated into various fields of industry, science, and technology. Owing to the PSI method, it has become possible to formulate and solve a wide range of multicriteria optimization problems. In addition to giving an overview of the PSI method, this paper also describes the methods for approximation of the feasible and Pareto optimal solution sets, identification, decomposition, and aggregation of the large-scale systems.     

Nonlinear goal programming using multi-objective genetic algorithms

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.     

Optimal Design of 2 DOF Parallel Kinematics Machines

The aim of this paper is to show the usefulness of the multicriteria approach to optimize the Parallel Kinematic Machines (PKM). Variations of the kinematic performances index remain not constant throughout workspace. Aiming to deal at the same time with multiple criteria in optimal design of PKM, we have developed a Multi-Objective Genetic Algorithm (MOGA) using concepts of Pareto optimality and niching techniques. The obtained results have shown that the use of MOGA in such kind of optimization problem enhances the quality of the optimization outcome, providing a better and more realistic support for the decision maker. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A robust optimization approach to experimental design for model discrimination of dynamical systems

A high-ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization. Quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions. Typically, before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the models up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification. In this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate (worst case) parameter configurations within a parameter range. The design comprises initial values, system perturbations and the optimal placement of measurement time points, the number of measurements as well as the time points are subject to design. The statistical discrimination criterion is worked out rigorously for these settings, a derivation from the Kullback-Leibler divergence as optimization objective is presented for the case of discontinuous Heaviside-functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure. The resulting problem can be classified as a semi-infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated. We present the theoretical framework, algorithmic realization and numerical results.     

Multicriteria decision making on maintenance: Spares and contracts planning

The competitiveness of an industrial system is directly related to decision making in areas of product support logistics, such as the maintenance area. Multicriteria decision making takes into account various aspects associated with competitiveness of the system. This paper presents multicriteria decision models for two maintenance problems: repair contract selection and spares provisioning. In the repair contract problem the model incorporates consequences modelled through a multiattribute utility function. These consequences consist of contract cost and system performance, represented by the system interruption time. Two criteria (risk and cost) are combined through a multiattribute utility function in the spares provisioning decision model. This paper presents the formulation and derivations for both models and the numerical application illustrates the use of models including sensitivity analysis.     

Multicriteria classification models for the identification of targets and acquirers in the Asian banking sector

The purpose of the present study is the development of classification models for the identification of acquirers and targets in the Asian banking sector. We use a sample of 52 targets and 47 acquirers that were involved in acquisitions in 9 Asian banking markets during 1998–2004 and match them by country and time with an equal number of non-involved banks. The models are developed and validated through a tenfold cross-validation approach using two multicriteria decision aid techniques. For comparison purposes we also develop models through discriminant analysis. The results indicate that the multicriteria decision aid models are more efficient that the ones developed through discriminant analysis. Furthermore, in all the cases the models are more efficient in distinguishing between acquirers and non-involved banks than between targets and non-involved banks. Finally, the models with a binary outcome achieve higher accuracies than the ones which simultaneously distinguish between acquirers, targets and non-involved banks.     

Assessing mutual funds’ corporate social responsibility: a multistakeholder-AHP based methodology

Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research. Much less developed, however, is their intersection: the analysis of decision problems involving multiple objectives and stochastically represented uncertainty simultaneously. This is amazing, since in economic and managerial applications, the features of multiple decision criteria and uncertainty are very frequently co-occurring. Part of the existing quantitative approaches to deal with problems of this class apply scalarization techniques in order to reduce a given stochastic multi-objective problem to a stochastic single-objective one. The present article gives an overview over a second strand of the recent literature, namely methods that preserve the multi-objective nature of the problem during the computational analysis. We survey publications assuming a risk-neutral decision maker, but also articles addressing the situation where the decision maker is risk-averse. In the second case, modern risk measures play a prominent role, and generalizations of stochastic orders from the univariate to the multivariate case have recently turned out as a promising methodological tool. Modeling questions as well as issues of computational solution are discussed.