José M. Cabello

A classification of the weighting schemes in reference point procedures for multiobjective programming

The reference point-based methods form one of the most widely used class of interactive procedures for multiobjective programming problems. The achievement scalarizing functions used to determine the solutions at each iteration usually include weights. In this paper, we have analysed nine weighting schemes from the preferential point of view, that is, examining their performance in terms of which reference values are given more importance and why. As a result, we have carried out a systematic classification of the schemes attending to their preferential meaning. This way, we distinguish pure normalizing schemes from others where the weights have a preferential interpretation. This preferential behaviour can be either designed (thus, predetermined) by the method, or decided by the decision maker. Besides, several figures have been used to illustrate the way each scheme works. This paper enables the potential users to choose the most appropriate scheme for each case.

Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method

Socially Responsible Investing (SRI) is broadly defined as an investment process that integrates not only financial but also social, environmental, and ethical (SEE) considerations into investment decision making. SRI has grown rapidly around the world in the last decades. In the last years, given the causes of the 2008 financial crisis, ethical, social, environmental and governance concerns have become even more relevant investment decision criteria. However, while a diverse set of models have been developed to support investment decision-making based on financial criteria, models including also social responsibility criteria are rather scarce.

An application of reference point techniques to the calculation of synthetic sustainability indicators

Sustainability is nowadays a key factor to analyse the development of the societies. Therefore, measuring sustainability is a main concern of the scientific community. The basic necessity to simultaneously consider the economical, social and environmental aspects make sustainability, by nature, a multicriteria concept, and therefore, multicriteria techniques are to be used to measure it. In this paper, we propose a method to develop synthetic sustainability indicators, based on the double (reservation–aspiration) reference point approach. This scheme is applied to each territorial unit considered, in order to determine, on the base of a given set of indicators, a couple of synthetic indicators that measure the weak and the strong sustainability of the unit.

On the sizing of a solar thermal electricity plant for multiple objectives using evolutionary optimization

Design, implementation and operation of solar thermal electricity plants are no more an academic task, rather they have become a necessity. In this paper, we work with power industries to formulate a multi-objective optimization model and attempt to solve the resulting problem using classical as well as evolutionary optimization techniques. On a set of four objectives having complex trade-offs, our proposed procedure first finds a set of trade-off solutions showing the entire range of optimal solutions. Thereafter, the evolutionary optimization procedure is combined with a multiple criterion decision making (MCDM) approach to focus on preferred regions of the trade-off frontier. Obtained solutions are compared with a classical generating method. Eventually, a decision-maker is involved in the process and a single preferred solution is obtained in a systematic manner. Starting with generating a wide spectrum of trade-off solutions to have a global understanding of feasible solutions, then concentrating on specific preferred regions for having a more detailed understanding of preferred solutions, and then zeroing on a single preferred solution with the help of a decision-maker demonstrates the use of multi-objective optimization and decision making methodologies in practice. As a by-product, useful properties among decision variables that are common to the obtained solutions are gathered as vital knowledge for the problem. The procedures used in this paper are ready to be used to other similar real-world problem solving tasks.

Optimization of the sizing of a solar thermal electricity plant: Mathematical programming versus genetic algorithms

Genetic algorithms (GAs) have been argued to constitute a flexible search thereby enabling to solve difficult problems which classical optimization methodologies may find hard to solve. This paper is intended towards this direction and show a systematic application of a GA and its modification to solve a real-world optimization problem of sizing a solar thermal electricity plant. Despite the existence of only three variables, this problem exhibits a number of other common difficulties - black-box nature of solution evaluation, massive multi-modality, wide and non-uniform range of variable values, and terribly rugged function landscape - which prohibits a classical optimization method to find even a single acceptable solution. Both GA implementations perform well and a local analysis is performed to demonstrate the optimality of obtained solutions. This study considers both classical and genetic optimization on a fairly complex yet typical real-world optimization problems and demonstrates the usefulness and future of GAs in applied optimization activities in practice.

A synchronous reference point-based interactive method for stochastic multiobjective programming

Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely used concept of efficiency has to be redefined for these problems. The use of interactive procedures can somehow ease this complexity, allowing the decision maker to learn about the problem itself, and to look for his most preferred solution. Reference point schemes can be adapted to stochastic problem, by asking the decision maker to provide, not only desirable levels for the objectives, but also the desired probability to achieve these values. In this paper, we analyze the different kinds of achievement scalarizing functions that can be used in this environment, and we study the efficiency (in the stochastic sense) of the different solutions obtained. As a result, a synchronous interactive method is proposed for a class of stochastic multiobjective problems, where only the objective functions are random. Several solutions can be generated by this new method, making use of the same preferential information, using the different achievement scalarizing functions. The preferential information (levels and probabilities for the objectives) is incorporated into the achievement scalarizing functions in a novel way to generate the new solutions. The special case of linear normal problems is addressed separately. The performance of the algorithm is illustrated with a numerical example.

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.

Mutual Funds’ Socially Responsible Portfolio Selection with Fuzzy Data

Socially Responsible Investing (SRI) corresponds to an investment practice that takes into account not only the usual return-risk criteria, but also other non-financial dimensions, namely in terms of environmental, social and governance concerns. However, while a diverse set of models has been developed to support investment decision-making based on classical financial criteria, models including also a socially responsible dimension are rather scarce. In this chapter we present a multicriteria portfolio selection model for mutual funds based on the Reference Point Method which takes into account both a financial and a non-financial dimension. The latter is usually characterized by the imprecise, ambiguous and/or uncertain nature of decision making criteria. This is why fuzzy methodology is used to model social responsibility. The proposed model is intended to be an individual investment decision making tool for mutual funds’ portfolio selection, taking into account the subjective and individual preferences of an individual investor under two different scenarios: a low social responsibility degree and a high social responsibility degree scenario. In order to illustrate the suitability and applicability of the investment decision making model proposed, an empirical study on a set of US domiciled equity mutual funds is carried out.

Portfolio Selection with SRI Synthetic Indicators: A Reference Point Method Approach

In this chapter we present an individual investment decision making tool for stocks’ portfolio selection taking into account the subjective and individual preferences about different financial and socially responsible features of a particular investor. In order to do so, the first problem to be solved is the measurement of the degree of social responsibility of a financial asset. In this work we use a double reference point scheme to obtain synthetic indicators of the social responsibility degree of stocks. Then, a mixed reference point classification scheme is used to solve the resulting multiple criteria portfolio selection model including, together with the classical financial criteria, a social responsibility criterion based on the synthetic social indicators previously obtained. In order to illustrate the suitability and applicability of the proposed investment decision making model, an empirical study on a set of Spanish domiciled stocks is presented.

Portfolio Selection Via Goal Programming

This paper describes a program developed in Visual Basic to assist the periodical portfolio selection. Decision Maker will be able to determine the level of the normal objectives, profitability and risk, depending on his/her preferences. The technique used has been Goal Programming, together with a sequential sensitivity analysis in order to obtain efficient solutions.