RIGA: A Regret-Based Interactive Genetic Algorithm

In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms

How to Handle Missing Values in Multi-Criteria Decision Aiding?

International audienceIt is often the case in the applications of Multi-Criteria Decision Making that the values of alternatives are unknown on some attributes. An interesting situation arises when the attributes having missing values are actually not relevant and shall thus be removed from the model. Given a model that has been elicited on the complete set of attributes, we are looking thus for a way-called restriction operator-to automatically remove the missing attributes from this model. Axiomatic characterizations are proposed for three classes of models. For general quantitative models, the restriction operator is characterized by linearity, recursivity and decomposition on variables. The second class is the set of monotone quantitative models satisfying normal-ization conditions. The linearity axiom is changed to fit with these conditions. Adding recursivity and symmetry, the restriction operator takes the form of a normalized average. For the last class of models-namely the Choquet integral, we obtain a simpler expression. Finally, a very intuitive interpretation is provided for this last model

Efficient exact computation of setwise minimax regret for interactive preference elicitation

A key issue in artificial intelligence methods for interactive preference elicitation is choosing at each stage an appropriate query to the user, in order to find a near-optimal solution as quickly as possible. A theoretically attractive method is to choose a query that minimises max setwise regret (which corresponds to the worst case loss response in terms of value of information). We focus here on the situation in which the choices are represented explicitly in a database, and with a model of user utility as a weighted sum of the criteria; in this case when the user makes a choice, an agent learns a linear constraint on the unknown vector of weights. We develop an algorithmic method for computing minimax setwise regret for this form of preference model, by making use of a SAT solver with cardinality constraints to prune the search space, and computing max setwise regret using an extreme points method. Our experimental results demonstrate the feasibility of the approach and the very substantial speed up over the state of the art

Minimality and comparison of sets of multi-attribute vectors

In a decision-making problem, there can be uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set A of alternatives available to the decision maker, we can consider the associated utility function, expressing, for each scenario, the maximum utility among the alternatives. We consider two main problems: firstly, finding a minimal subset of A that is equivalent to it, i.e., that has the same utility function. Secondly, we consider how to compare A to another set of alternatives B, where A and B correspond to different initial decision choices. We derive mathematical results that allow different computational techniques for these two problems, using linear programming, and especially, using the extreme points of the epigraph of the utility function