A robust disaster preparedness model for effective and fair disaster response

Humanitarian network design decisions belonging to the preparedness stage of disaster management life-cycle are of critical importance since they set the frame for all further post-disaster operations. Having an adequate number of strategically located storage and distribution centers for critical supplies is the key that enables effectiveness, efficiency and fairness when responding to a disaster situation. The preparedness model proposed in this study selects locations and inventory levels of these facilities such that the right mix of relief items can be supplied at the right time. Our mixed integer linear model aims to find a robust relief network design that satisfies the demand for all given disaster scenarios, and to help achieve a better response during the response stage when the relief items are distributed. The assumptions and the parameters used in the model are justified by authorities of humanitarian organizations. We propose a logic-based Benders decomposition approach to solve this problem to optimality. Although the problem is NP-hard, our numerical studies demonstrate that it is possible to obtain optimal or very good solutions to problem instances with realistic sizes.     

Fuzzy robust courses scheduling problem

We consider examination courses scheduling at university. Two basic courses sharing at least one student cannot be scheduled at the same time. This scheduling problem will be stated as a graph coloring problem. The stability of the scheduled solution would be desirable in the sense that it remains valid also if some additional students want to do the exams, for example those who failed in earlier examination sessions. This stability is defined as the robustness of scheduling courses. We consider a mean value of the fuzzy number of courses incompatibilities as the robustness measure.     

Fuzzy adaptive decision-making for boundedly rational traders in speculative stock markets

The development of new models that would enhance predictability for time series with dynamic time-varying, nonlinear features is a major challenge for speculators. Boundedly rational investors called “chartists” use advanced heuristics and rules-of-thumb to make profit by trading, or even hedge against potential market risks. This paper introduces a hybrid neurofuzzy system for decision-making and trading under uncertainty. The efficiency of a technical trading strategy based on the neurofuzzy model is investigated, in order to predict the direction of the market for 10 of the most prominent stock indices of U.S.A, Europe and Southeast Asia. It is demonstrated via an extensive empirical analysis that the neurofuzzy model allows technical analysts to earn significantly higher returns by providing valid information for a potential turning point on the next trading day. The total profit of the proposed neurofuzzy model, including transaction costs, is consistently superior to a recurrent neural network and a Buy & Hold strategy for all indices, particularly for the highly speculative, emerging Southeast Asian markets. Optimal prediction is based on the dynamic update and adaptive calibration of the heuristic fuzzy learning rules, which reflect the psychological and behavioral patterns of the traders.     

A transdisciplinary approach for formalized integrated planning and decision-making in complex systems

Multi-sectoral systems, such as cities or regional economies, face strategic challenges of optimal development due to the complexity of interacting perspectives, interests, and preferences of decision-makers and stakeholders. In coping with these challenges, integrated approaches in strategic planning and decision support promise to generate more efficient and effective results than sectoral approaches. In this article, we follow the concept of operational research (OR) by applying a formalized approach to cross-sectoral integrated planning and decision-making in complex, i.e., multi-sectoral systems. The presented Transdisciplinary Integrated Planning and Synthesis (TIPS) approach relies on (soft) OR methods combined in a multi-methodological framework that is adapted to the cognitive skills and habits of the stakeholders and experts involved in mutual and joint learning processes (transdisciplinarity). This methodological contribution structures, formalizes, and empirically illustrates cross-sectoral integrated strategic planning step by step, and evaluates the TIPS methodology against requirements for integrated approaches derived from literature.     

A robust approach for scheduling in hospitals using multiple objectives

Scheduling in hospitals is a challenging task and stochastic influences have a major impact on the final schedule. Therefore, uncertainties of treatment durations and of emergency arrivals have to be taken into account explicitly. In order to avoid re-scheduling we integrate information on stochastic parameters into a scenario-based mixed-integer optimization model. Besides, we focus on different stakeholders’ objectives that are simultaneously considered within a multi-criteria optimization model. Individually optimal solutions are likely to differ and the overall aim is to identify a good and acceptable compromise solution. The presented approach is based on fuzzy sets and merges the interests of several stakeholders. Different schedules are calculated and later on evaluated with randomly generated scenarios for surgery times and emergencies. The resulting objective function values are close to the individually optimal solutions. Finally, the schedules lead to a high rate of utilization and a low amount of overtime.     

A robust approach for modeling limited observability in bilevel optimization

Many applications of bilevel optimization contain a leader facing a follower whose reaction deviates from the one expected by the leader due to some kind of bounded rationality. We consider bilinear bilevel problems with follower's response uncertainty due to limited observability regarding the leader's decision and exploit robust optimization to model the decision making of the follower. We show that the robust counterpart of the lower level allows to tackle the problem via the lower level's KKT conditions.     

A robust multigrid approach for variational image registration models

Variational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly ‘avoided’ in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images.     

A robust multigrid approach for variational image registration models

Variational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly ‘avoided’ in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images.     

A surrogate based multi-fidelity approach for robust design optimization

Robust design optimization (RDO) is a field of optimization in which certain measure of robustness is sought against uncertainty. Unlike conventional optimization, the number of function evaluations in RDO is significantly more which often renders it time consuming and computationally cumbersome. This paper presents two new methods for solving the RDO problems. The proposed methods couple differential evolution algorithm (DEA) with polynomial correlated function expansion (PCFE). While DEA is utilized for solving the optimization problem, PCFE is utilized for calculating the statistical moments. Three examples have been presented to illustrate the performance of the proposed approaches. Results obtained indicate that the proposed approaches provide accurate and computationally efficient estimates of the RDO problems. Moreover, the proposed approaches outperforms popular RDO techniques such as tensor product quadrature, Taylor’s series and Kriging. Finally, the proposed approaches have been utilized for robust hydroelectric flow optimization, demonstrating its capability in solving large scale problems.     

Fuzzy multi-criteria decision-making based on positive and negative extreme solutions

To encompass decision data vagueness, many researchers generalized multi-criteria decision-making (MCDM) methods in certain environment into fuzzy multi-criteria decision-making (FMCDM) methods under fuzzy environment. In these FMCDM methods, ranking fuzzy numbers based on fuzzy pair-wise comparison is normally essential, but the comparison is a complexity work. To avoid fuzzy pair-wise comparison, we propose a FMCDM method based on positive and negative extreme solutions of alternatives. In the proposed method, two extreme solutions of alternatives are obtained by MAX and MIN operations of fuzzy TOPSIS. Then weakness and strength matrices between alternatives and extreme solutions are derived by a difference function revised from fuzzy preference relation of Lee, and multiplied with weight matrix to be weighted weakness and strength indices. The two weighted indices are respectively transferred into positive and negative indices, and then the two indices integrated into a total performance index. Finally, alternatives can be sorted according to their related performance indices, and FMCDM problems are easily solved, not by fuzzy pair-wise comparison.     

A multiple criteria decision-making approach for the selection of stocks

A fundamental principle of modern portfolio theory is that portfolio selectiondecisions are generally made using two criteria, corresponding to the first twomoments of return distributions, namely the expected returnportfolio variance.One criticism over this theory, which has often been addressed both bypractitioners and academics, is that it fails to embody all thedecision-maker's objectives, through the various stages of the decisionprocess. The aim of this paper is to present an alternative methodologicalapproach for modeling one of the most crucial phases of the portfolio managementprocess, the security selection phase. The main characteristic of the proposedapproach is that it fully takes into account the inherent multi-dimensionalnature of the problem, although allowing the decision-maker to incorporate hispreferences in the decision process. The validity of the proposed approach istested through an illustrative application in Athens Stock Exchange. Besides, adetailed categorized bibliography is provided, relative to the application ofthe techniques of multiple criteria decision making to the problems and issuesof portfolio management.     

An interactive approach for hierarchical analysis of helicopter logistics in disaster relief operations

This study develops a mathematical model for helicopter mission planning during a disaster relief operation. The decisions inherent in the problem decompose hierarchically into two sub-problems where tactical decisions are made at the top level, and the operational routing and loading decisions are made at the base level. Consistency between the decomposed problems is achieved with an iterative coordination procedure which transfers anticipated information from the base level to improve the top level decisions. The existence of conflicting multiple objectives in this hierarchical structure requires the development of a multi-criteria analysis, and an interactive procedure is designed with the top level decision-maker to assess the preference of alternative non-dominated solutions.     

Projection-pursuit approach to robust linear discriminant analysis

Discriminant analysis plays an important role in multivariate statistics as a prediction and classification method. It has been successfully applied in many fields of work and research. As it happens with other multivariate methods, discriminant analysis is highly vulnerable to the presence of outliers that commonly occur in many real world data sets. The lack of robustness of the classical estimators on which the linear discriminant function is based is a severe disadvantage and several authors have worked to find efficient ways to prevent the damage that outliers can cause. This paper focuses on the projection-pursuit approach to discriminant analysis. The projection-pursuit estimators are described and theoretical properties are deduced and their relevance is highlighted. These include Fisher consistency, affine equivariance, partial influence functions and asymptotic distributions. Application to real data and a simulation study reveal the robustness of the projection-pursuit approach. In both analyses the data relates to a large number of variables, a situation that is becoming common when new technology is applied to data gathering.     

A new infinitesimal approach to robust estimation

Summary The infinitesimal robustness of the asymptotic variance of location M-estimators is investigated by means of the change-of-variance curve (CVC), which bears some resemblance to the influence curve (IC). It is proved that this CVC leads to a more stringent robustness property than the IC and that the Huber estimators are still optimal in this new sense.     

Benefits analysis—a robust assessment approach

Benefits Analysis has been evolving over the past decade from roots in multi-criteria analysis, causal mapping and multi-methodology. It has now reached a level of maturity such that it deserves to be treated as a method in its own right, and this paper seeks to document the method and provide guidance on its use. Benefits Analysis is a systematic method for formulating complex, multi-factor investment appraisal problems where decision-makers seek to realize non-financial benefits. Such decision problems abound in military OR, particularly the management of equipment capability and research. Benefits Analysis connects qualitative and quantitative OR methods and facilitates robust assessment, including multi-methodology. This paper describes the principles of Benefits Analysis and discusses its application to a variety of real problems, including research management, capability management, balance of investment, business case development and benefit quantification strategies.     

A decision-theoretic approach to robust optimization in multivalued graphs

This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenarios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach.     

A multiple template approach for robust tracking of fast motion target

Target tracking is very important in computer vision and related areas. It is usually difficult to accurately track fast motion target with appearance variations. Sometimes the tracking algorithms fail for heavy appearance variations. A multiple template method to track fast motion target with appearance changes is presented under the framework of appearance model with Kalman filter. Firstly, we construct a multiple template appearance model, which includes both the original template and templates affinely transformed from original one. Generally speaking, appearance variations of fast motion target can be covered by affine transformation. Therefore, the affine transform-enhanced templates match the target of appearance variations better than conventional models. Secondly, we present an improved Kalman filter for approximate estimating the motion trail of the target and a modified similarity evaluation function for exact matching. The estimation approach can reduce time complexity of the algorithm and keep accuracy in the meantime. Thirdly, we propose an adaptive scheme for updating template set to alleviate the drift problem. The scheme considers the following differences: the weight differences in two successive frames; different types of affine transformation applied to templates. Finally, experiments demonstrate that the proposed algorithm is robust to appearance variation of fast motion target and achieves real-time performance on middle/low-range computing platform.