Riccardo Gusso

Particle Swarm Optimization with non-smooth penalty reformulation, for a complex portfolio selection problem

In the classical model for portfolio selection the risk is measured by the variance of returns. It is well known that, if returns are not elliptically distributed, this may cause inaccurate investment decisions. To address this issue, several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NP-hard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO). Since PSO was originally conceived for unconstrained global optimization problems, we apply it to a novel reformulation of our mixed-integer model, where a standard exact penalty function is introduced.

An evolutionary approach to preference disaggregation in a MURAME-based creditworthiness problem

HighlightsFirst application of the particle swarm optimization (PSO) to preference disaggregation problems in a MUlticriteria Ranking MEthod (MURAME) framework.Reformulation of the involved constrained optimization problem in terms of penalized unconstrained optimization problem for the PSO implementation.Application to large real credit scoring and credit ranking problems. In this paper, we propose to use an evolutionary methodology in order to determine the values of the parameters for implementing the MUlticriteria RAnking MEthod (MURAME). The proposed approach has been designed for dealing with a creditworthiness evaluation problem faced by an important north-eastern Italian bank needing to score and/or to rank firms (which act as alternatives) applying for a loan. The point of the matter, known as preference disaggregation, consists in finding the MURAME parameters which minimize the inconsistency between the MURAME evaluations of given alternatives and those properly revealed by the decision maker (DM). To find a numerical solution of the involved mathematical programming problem, we adopt an evolutionary algorithm based on the particle swarm optimization (PSO), which is an iterative metaheuristics grounded on swarm intelligence. The obtained results show a high consistency between the MURAME outputs produced by the PSO-based solution algorithm and the actual scoring/ranking of the applicants provided by the bank (which acts as the DM).

Portfolio selection with an alternative measure of risk: Computational performances of particle swarm optimization and genetic algorithms

In the classical model for portfolio selection the risk is measured by the variance of returns. Recently several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NPhard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO) and we compare the performances of this methodology with respect to another well-known heuristic technique for optimization problems, that is Genetic Algorithms (GA).

Dense orthogonal initialization for deterministic PSO: ORTHOinit+

This paper describes a novel initialization for Deterministic Particle Swarm Optimization (DPSO), based on choosing specific dense initial positions and velocities for particles. This choice tends to induce orthogonality of particles’ trajectories, in the early iterations, in order to better explore the search space. Our proposal represents an improvement, by the same authors, of the theoretical analysis on a previously proposed PSO reformulation, namely the initialization ORTHOinit. A preliminary experience on constrained Portfolio Selection problems confirms our expectations.

Particle Swarm Optimization for Preference Disaggregation in Multicriteria Credit Scoring Problems

In this paper we deal with the problem of preference disaggregation in credit scoring problems developed by using multicriteria analysis. In order to determine the values of the parameters that characterize the preference model of the decision maker, we adopt Particle Swarm Optimization, which is a biologically-inspired heuristics based on swarm intelligence. We test the ability of PSO to find the optimal values of the parameters on a real data set provided by an Italian bank.

A Methodological Proposal for an Evolutionary Approach to Parameter Inference in MURAME-Based Problems

In this paper we propose an evolutionary approach in order to infer the values of the parameters for applying the MURAME, a multicriteria method which allows to score/rank a set of alternatives according to a set of evaluation criteria. This problem, known as preference disaggregation, consists in finding the MURAME parameter values that minimize the inconsistency between the model obtained with those parameters and the true preference model on the basis of a reference set of decisions of the Decision Maker. In order to represent a measure of inconsistency of the MURAME model compared to the true preference one, we consider a fitness function which puts emphasis on the distance between the scoring of the alternatives given by the Decision Maker and the one determined by the MURAME. The problem of finding a numerical solution of the involved mathematical programming problem is tackled by using an evolutionary solution algorithm based on the Particle Swarm Optimization. An application is finally provided in order to give an initial assessment of the proposed approach.