Reference Point Method Research Articles

A new classifier based on the reference point method with application in bankruptcy prediction

The finance industry relies heavily on the risk modelling and analysis toolbox to assess the risk profiles of entities such as individual and corporate borrowers and investment vehicles. Such toolbox includes a variety of parametric and nonparametric methods for predicting risk class belonging. In this paper, we expand such toolbox by proposing an integrated framework for implementing a full classification analysis based on a reference point method, namely in-sample classification and out-of-sample classification. The empirical performance of the proposed reference point method-based classifier is tested on a UK data-set of bankrupt and nonbankrupt firms. Our findings conclude that the proposed classifier can deliver a very high predictive performance, which makes it a real contender in industry applications in banking and investment. Three main features of the proposed classifier drive its outstanding performance, namely its nonparametric nature, the design of our RPM score-based cut-off point procedure for in-sample classification, and the choice of a k-nearest neighbour as an out-of-sample classifier which is trained on the in-sample classification provided by the reference point method-based classifier.

Solving multi-objective optimization problems in conservation with the reference point method.

Managing the biodiversity extinction crisis requires wise decision-making processes able to account for the limited resources available. In most decision problems in conservation biology, several conflicting objectives have to be taken into account. Most methods used in conservation either provide suboptimal solutions or use strong assumptions about the decision-maker’s preferences. Our paper reviews some of the existing approaches to solve multi-objective decision problems and presents new multi-objective linear programming formulations of two multi-objective optimization problems in conservation, allowing the use of a reference point approach. Reference point approaches solve multi-objective optimization problems by interactively representing the preferences of the decision-maker with a point in the criteria (objectives) space, called the reference point. We modelled and solved the following two problems in conservation: a dynamic multi-species management problem under uncertainty and a spatial allocation resource management problem. Results show that the reference point method outperforms classic methods while illustrating the use of an interactive methodology for solving combinatorial problems with multiple objectives. The method is general and can be adapted to a wide range of ecological combinatorial problems.

Overall Efficiency and its Decomposition in a Two-Stage Network DEA Model

This paper aims to propose a new approach to decompose an overall data envelopment analysis model into equivalent two-stage models. In this approach, we use a minimax reference point method to set the weights and reliabilities of the two stage models so that the combined efficiency of the two stages is equal to the overall efficiency. The equivalent multi-stage models are useful to support planning for performance improvement. An illustrative example is first explored to compare the results from the new approach with those of four other existing approaches. The main finding from the comparisons is that the new decomposition approach of this paper satisfies the proposed assumptions. A case study is then conducted on a two-stage process of steel manufacturing to illustrate the validity and applicability of the proposed approach.

The Reference Point Method, a “hyperreduction” technique: Application to PGD-based nonlinear model reduction

A new approximation technique, called Reference Point Method (RPM), is proposed in order to reduce the computational complexity of algebraic operations for constructing reduced-order models in the case of time dependent and/or parametrized nonlinear partial differential equations. Even though model reduction techniques enableone to decrease the dimension of the initial problem in the sense that far fewer degrees of freedom are needed to represent the solution, the complexity of evaluating the nonlinear terms and assembling the low dimensional operator associated with the reduced-order model still scales with the size of the original high-dimensional model. This point can be critical, especially when the reduced-order basis changes throughout the solution strategy as it is the case for model reduction techniques based on Proper Generalized Decomposition (PGD). Based on the concept of spatial, parameter/time reference points and influence patches, the RPM defines a compressed version of the data from which an approximate low-rank separated representation by patch of the operators can be constructed by explicit formulas at low-cost without resorting to SVD-based techniques. An application of the RPM to PGD-based model reduction for a nonlinear parametrized elliptic PDE previously studied by other authors with reduced-basis method and EIM is proposed. It is shown that computational complexity to construct the reduced-order model can be divided in practice by one order of magnitude compared with the classical PGD approach.

Lexicographic extension of the reference point method applied in radiation therapy treatment planning

In radiation therapy treatment planning, generating a treatment plan is a multi-objective optimisation problem. The decision-making strategy is uniform for each group of cancer patients, e.g. prostate cancer, and can thus be automated. Predefined priorities and aspiration levels are assigned to each objective, and the strategy is to attain these levels in order of priority. Therefore, a straightforward lexicographic approach is sequential ϵ-constraint programming where objectives are sequentially optimised and constrained according to predefined rules, mimicking human decision-making. The clinically applied 2-phase ϵ-constraint (2pϵc) method captures this approach and generates clinically acceptable treatment plans.However, the number of optimisation problems to be solved for the 2pϵc method, and hence the computation time, scales linearly with the number of objectives. To improve the daily planning workload and to further enhance radiation therapy, it is extremely important to reduce this time. Therefore, we developed the lexicographic reference point method (LRPM), a lexicographic extension of the reference point method, for generating a treatment plan by solving a single optimisation problem. The LRPM processes multiple a priori defined reference points into modified partial achievement functions. In addition, a priori bounds on a subset of the partial trade-offs can be imposed using a weighted sum component.The LRPM was validated for 30 randomly selected prostate cancer patients. While the treatment plans generated using the LRPM were of similar clinical quality to those generated using the 2pϵc method, the LRPM decreased the average computation time from 12.4 to 1.2 minutes, a speed-up factor of 10.

Fast and fuzzy multi-objective radiotherapy treatment plan generation for head and neck cancer patients with the lexicographic reference point method (LRPM)

Previously, we have proposed Erasmus-iCycle, an algorithm for fully automated IMRT plan generation based on prioritised (lexicographic) multi-objective optimisation with the 2-phase ϵ-constraint (2pϵc) method. For each patient, the output of Erasmus-iCycle is a clinically favourable, Pareto optimal plan. The 2pϵc method uses a list of objective functions that are consecutively optimised, following a strict, user-defined prioritisation. The novel lexicographic reference point method (LRPM) is capable of solving multi-objective problems in a single optimisation, using a fuzzy prioritisation of the objectives. Trade-offs are made globally, aiming for large favourable gains for lower prioritised objectives at the cost of only slight degradations for higher prioritised objectives, or vice versa.In this study, the LRPM is validated for 15 head and neck cancer patients receiving bilateral neck irradiation. The generated plans using the LRPM are compared with the plans resulting from the 2pϵc method.Both methods were capable of automatically generating clinically relevant treatment plans for all patients. For some patients, the LRPM allowed large favourable gains in some treatment plan objectives at the cost of only small degradations for the others. Moreover, because of the applied single optimisation instead of multiple optimisations, the LRPM reduced the average computation time from 209.2 to 9.5 min, a speed-up factor of 22 relative to the 2pϵc method.

A Dynamic Reference Point Method for Emergency Response Under Hesitant Probabilistic Fuzzy Environment

According to the characteristics of emergency decision-making in crisis management, this paper proposes a dynamic decision-making method using the hesitant probabilistic fuzzy set to deal with the inadequate information, uncertainty and dynamic trends. This method is suitable for emergency decision-making as it provides supports for the dynamic and evolutionary characteristics of emergency responses and the uncertain probability about external environment is also considered. In order to make a continuous adjustment with the development of situations, we give a definition of the expectation level, based on which the dynamic reference point method is proposed to obtain the optimal emergency response plan under the hesitant probabilistic fuzzy environment. We also analyze the probability of different situations that may occur in the process of emergency decision-making and provide an algorithm for solving this problem. Finally, a practical case of hazardous goods leakage pollution accident is given to illustrate our method, and then, the optimal decision alternative chain is obtained.

POD-based error control for reduced-order bicriterial PDE-constrained optimization

In the present paper, a bicriterial optimal control problem governed by an abstract evolution problem and bilateral control constraints is considered. To compute Pareto optimal points and the Pareto front numerically, the (Euclidean) reference point method is applied, where many scalar constrained optimization problems have to be solved. For this reason a reduced-order approach based on proper orthogonal decomposition (POD) is utilized. An a-posteriori error analysis ensures a desired accuracy for the Pareto optimal points and for the Pareto front computed by the POD method. Numerical experiments for evolution problems with convection-diffusion illustrate the efficiency of the presented approach.

PROJECT Method for Optimization of Target Model in DEA

In this paper, we concentrate on performance assessment of special target model in data envelopment analysis (DEA) with use a comprehensive interactive method with name PROJECT method. Interactive methods in multiple objectives programming (MOP) are methods that can help to decision maker (DM) to generate the most preferred solution (MPS). The PROJECT method is able to obtain any efficient solution, contain nonsupport efficient solution and also identify the MPS, even in nonconvex cases. This comprehensive model belongs to the class of interactive local trade-off methods, which is generated by combination the projection of the gradient of an implicit utility function on to the tangent plane of efficient frontier and the reference-point method to search for the best compromise solution within a local region. In this study, we will use the target model since this model focuses on decreasing total input consumption and increasing total output production which results in solving one mathematical model instead of n models, also the PROJECT method to showing the decision maker (DM) preferences in the process of assessing efficiency in the target model in DEA with any prior judgments. Numerical example is examined how the DEA model efficiency analysis can be conducted using the interactive PROJECT for setting realistic target values.

Application of Graph Theory to Cost-Effective Fire Protection of Chemical Plants During Domino Effects.

In the present study, we have introduced a methodology based on graph theory and multicriteria decision analysis for cost-effective fire protection of chemical plants subject to fire-induced domino effects. By modeling domino effects in chemical plants as a directed graph, the graph centrality measures such as out-closeness and betweenness scores can be used to identify the installations playing a key role in initiating and propagating potential domino effects. It is demonstrated that active fire protection of installations with the highest out-closeness score and passive fire protection of installations with the highest betweenness score are the most effective strategies for reducing the vulnerability of chemical plants to fire-induced domino effects. We have employed a dynamic graph analysis to investigate the impact of both the availability and the degradation of fire protection measures over time on the vulnerability of chemical plants. The results obtained from the graph analysis can further be prioritized using multicriteria decision analysis techniques such as the method of reference point to find the most cost-effective fire protection strategy.

Comparison of Selected Fair-optimization Methods for Flow Maximization between Given Pairs of Nodes in Telecommunications Network

Dimensioning of telecommunications networks requires the allocation of the ows (bandwidth) to given trac demands for the source-destination pairs of nodes. Unit ow allocated to the given demand is associated with revenue that may vary for dierent demands. Problem the decision-making basic algorithms to maximize the total revenue may lead to the solutions that are unacceptable, due to "starvation" or "locking" of some demand paths less attractive with respect to the total revenue. Therefore, the fair optimization approaches must be applied. In this paper, two fair optimization methods are analyzed: the method of ordered weighted average (OWA) and the reference point method (RPM). The study assumes that ows can be bifurcated thus realized in multiple path schemes. To implement optimization model the AMPL was used with general-purpose linear programming solvers. As an example of the data, the Polish backbone network was used.

Reference points and approximation algorithms in multicriteria discrete optimization

Mathematical research on multicriteria optimization problems predominantly revolves around the set of Pareto optimal solutions. In practice, on the other hand, methods that output a single solution are more widespread. Reference point methods are a successful example of this approach and are widely used in real-world multicriteria optimization. A reference point solution is the solution closest to a given reference point in the objective space.We study the connection between reference point methods and approximation algorithms for multicriteria optimization problems over discrete sets. In particular, we establish that, in terms of computational complexity, computing approximate reference point solutions is polynomially equivalent to approximating the Pareto set. Complementing these results, we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization. In particular, we lift the link between dynamic programming and FPTAS, as well as certain LP-rounding techniques. The latter applies, e.g., to Set Cover and several machine scheduling problems.

Robustness evaluation of seismic pile response considering uncertainty mechanism of soil properties

Robustness analysis of the seismic pile response of a structure–pile–soil system with uncertain soil properties and concrete Young’s modulus is presented in this paper. The bounds of the bending moment of a pile are investigated by means of the previously proposed uncertainty analysis method (Updated Reference-Point method) and the newly developed revised method (NURP method). An efficient finite-element model of a structure–pile–soil system with smart displacement functions for connecting elements is adopted and a response spectrum method is applied in the evaluation of the seismic pile responses of the system. Two cases of soil uncertainties resulting from different uncertainty mechanisms are considered. It is shown that the worst combination of uncertain soil parameters can be determined by the NURP method in an accurate manner.

A Method of Reference Point Range for Field Navigation of Agricultural Robot

This paper presents a new method of agriculture robot ground navigation reference point ranging based on binocular system. This method is applicable to the camera installation position at any angle and height, calibrating the agricultural robot binocular with the improve BP neural network and then the left and right image coordinates of the reference point can be obtained with the improved SIFT feature matching and the trained BP neural network saved during calibration is output, and then the world coordinates of the navigation reference point corresponding to the agricultural robot are output, and finally the horizontally straight line distance between the reference point and the robot body can be obtained. Experimental results show that in a certain field of view, the total time of field navigation reference point ranging is 55ms with the accuracy up to 99%, able to meet the operational requirements of the agricultural robot in most cases.

POD-Based Bicriterial Optimal Control by the Reference Point Method

In the present paper a bicriterial optimal control problem governed by a parabolic partial differential equation (PDE) and bilateral control constraints is considered. For the numerical optimization the reference point method is utilized. The PDE is discretized by a Galerkin approximation utilizing the method of proper orthogonal decomposition (POD). POD is a powerful approach to derive reduced-order approximations for evolution problems. Numerical examples illustrate the efficiency of the proposed strategy.

Multistage Multiattribute Group Decision-Making Method Based on Triangular Fuzzy MULTIMOORA

This paper proposed a new multiattribute group decision-making method, in which the period significance coefficients and the attribute significance coefficients are completely unknown, and the attribute values are triangular fuzzy numbers. At first, to obtain the period significance coefficients, the period significance coefficients optimization model is constructed according to the time degree and the differences of the decision information in different periods. Then, attribute significance coefficients are determined by the maximum deviation method. Based on this, alternatives are ranked by the triangular fuzzy ratio system method, the triangular fuzzy reference point method, and the triangular fuzzy full multiplicative form, respectively. The dominance theory is used for aggregating the subordinate rankings into the final ranking. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed method.

Multiobjective optimal control of fluid mixing

AbstractIn this contribution an efficient numerical method to solve multiobjective optimal control problems of fluid flow mixing governed by the advection equation is presented. To obtain well‐mixed behavior for non‐diffusive processes, the multi‐scale mixing of measure introduced in [1] is used in the formulation of the multiobjective optimal control problem. For the approximation of the Pareto set we combine reference point methods with an adjoint based optimization approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A prospect theory-based interval dynamic reference point method for emergency decision making

Urgent or critical situations, such as terrorist attacks and natural disasters, often require decision makers (DMs) to take crucial decisions. Emergency decision making (EDM) problems have become a very active research field in recent years. The existing studies focus mainly on the information inadequacy or incomplete information in emergencies, and selecting ideal emergency alternatives, neglecting the psychological behavior of DMs under emergencies. Few studies consider a DM's psychological behavior, although there is some focus on the dynamic features of emergency events and limited DM judgments under risk and uncertainty. Motivated by such problems, this study proposes a prospect theory-based interval dynamic reference point method for EDM. The technique for order preference by similarity to ideal solution (TOPSIS) method is a popular decision technique, as decision makers are always bounded rational under risk and uncertainty and their psychological behavior plays an important role in EDM. However, the existing TOPSIS methods are seldom concerned with this issue. Based on such a problem, this study proposes a TOPSIS method with an interval reference point, which considers the DM's psychological behavior. Two examples are presented to illustrate the feasibility and validity of the proposed methods for solving EDM problems in the real world. Based on the final rankings of alternatives in the examples, each of our methods validates the other and matches the actual EDM.

Prediction of worst combination of variable soil properties in seismic pile response

Robustness analysis of seismic pile response of a structure–pile–soil system with uncertain soil properties is presented in this paper. The uncertainties of soil properties are extremely large compared to superstructures and inherent. The upper and lower bounds of the bending moment of a pile are investigated by means of the previously proposed uncertainty analysis method (Updated Reference-Point method). Soil stiffnesses and damping ratios as uncertain parameters are treated as interval parameters. The earthquake ground motion defined in the engineering bedrock in the form of a response spectrum is used as the input. An efficient finite-element model of an overall structure–pile–soil system is adopted and a response spectrum method is applied in the evaluation of the seismic pile responses of the system. It is shown that the worst combination of uncertain soil parameters can be determined and this information certainly upgrades the robustness of the structure–pile–soil system.

BIDDING DECISION IN LAND AUCTION USING PROSPECT THEORY

Land auction is widely practiced in company and government decisions, especially in China. Bidders are always faced with two or more auctions in the period of a decision cycle. The outcome of the auction is under high risk. The bidder's risk attitude and preference will have a great influence on his/her bidding price. Prospect theory is currently the main descriptive theory of decision under risk. In this paper, we will consider the preferences of the decision-makers in land bidding decisions with the multi-attribute additive utility and reference point method in cumulative prospect theory. Three land auction models are proposed based on the appearance time of the land auctions. The simultaneous model uses cumulative prospect theory without considering the relationships between the auctions. The time sequential model involves the exchange auction decisions at different time with the third-generation prospect theory. The event sequential model further considers the reference point prediction in sequential land auction decisions. The three models can help the decision-makers make better bidding price decision when they are faced with several land auctions in the period of a decision cycle. A case study illustrates the processes and results of our approaches.