4 research outputs found
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
A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences
International audienceCore-selection is a crucial property of rules in the literature of resource allocation. It is also desirable, from the perspective of mechanism design, to address the incentive of agents to cheat by misreporting their preferences. This paper investigates the exchange problem where (i) each agent is initially endowed with (possibly multiple) indivisible goods, (ii) agents' preferences are assumed to be conditionally lexicographic, and (iii) side payments are prohibited. We propose an exchange rule called augmented top-trading-cycles (ATTC), based on the original TTC procedure. We first show that ATTC is core-selecting and runs in polynomial time with respect to the number of goods. We then show that finding a beneficial misreport under ATTC is NP-hard. We finally clarify relationship of misreporting with splitting and hiding, two different types of manipulations, under ATTC
LP Solvable Models for Multiagent Fair Allocation problems
International audienceThis paper proposes several operational approaches for solving fair allocation problems in the context of multiagent optimization. These problems arise in various contexts such as assigning conference papers to referees or sharing of indivisible goods among agents. We present and discuss various social welfare functions that might be used to maximize the satisfaction of agents while maintaining a notion of fairness in the distribution. All these welfare functions are in fact non-linear, which precludes the use of classical min-cost max-flow algorithms for finding an optimal allocation. For each welfare function considered, we present a Mixed Integer Linear Programming formulation of the allocation problem that can be efficiently solved using standard solvers. The results of numerical tests we conducted on realistic cases are given at the end of the paper to confirm the practical feasibility of the proposed approaches