Beyond Consistency and Substitutability

International audienceElimination of inconsistent values in instances of the constraint satisfaction problem (CSP) conserves all solutions. Elimination of substitutable values conserves at least one solution. We show that certain values which are neither inconsistent nor substitutable can also be deleted while conserving at least one solution. This allows us to state novel rules for the elimination of values in binary CSP. From a practical point of view, we show that one such rule can be applied in the same asymptotic time complexity as neighbourhood substitution but is strictly stronger. An alternative to the elimination of values from domains is the elimination of variables. We give novel satisfiability-preserving variable elimination operations. In each case we show that if the instance is satisfiable, then a solution to the original instance can always be recovered in low-order polynomial time from a solution to the reduced instance

A cultural algorithm for pomdps from stochastic inventory control

Abstract. Reinforcement Learning algorithms such as SARSA with an eligibility trace, and Evolutionary Computation methods such as genetic algorithms, are competing approaches to solving Partially Observable Markov Decision Processes (POMDPs) which occur in many fields of Artificial Intelligence. A powerful form of evolutionary algorithm that has not previously been applied to POMDPs is the cultural algorithm, in which evolving agents share knowledge in a belief space that is used to guide their evolution. We describe a cultural algorithm for POMDPs that hybridises SARSA with a noisy genetic algorithm, and inherits the latter’s convergence properties. Its belief space is a common set of state-action values that are updated during genetic exploration, and conversely used to modify chromosomes. We use it to solve problems from stochastic inventory control by finding memoryless policies for nondeterministic POMDPs. Neither SARSA nor the genetic algorithm dominates the other on these problems, but the cultural algorithm outperforms the genetic algorithm, and on highly non-Markovian instances also outperforms SARSA.

Forecasting Intermittent Demand by Hyperbolic-Exponential Smoothing

Croston's method is generally viewed as superior to exponential smoothing when demand is intermittent, but it has the drawbacks of bias and an inability to deal with obsolescence, in which an item's demand ceases altogether. Several variants have been reported, some of which are unbiased on certain types of demand, but only one recent variant addresses the problem of obsolescence. We describe a new hybrid of Croston's method and Bayesian inference called Hyperbolic-Exponential Smoothing, which is unbiased on non-intermittent and stochastic intermittent demand, decays hyperbolically when obsolescence occurs and performs well in experiments.Comment: Earlier versions of this work were presented at the 25th European Conference on Operations Research, 2012; and at the 54th Annual Conference of the UK Operational Research Society, 2012. A journal version is in preparatio

A State Space Augmentation Algorithm for the Replenishment Cycle Inventory Policy

In this work we propose an efficient dynamic programming approach for computing replenishment cycle policy parameters under non-stationary stochastic demand and service level constraints. The replenishment cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of state space relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using dynamic programming in order to produce a solution for the original problem

Incremental SAT-Based Method with Native Boolean Cardinality Handling for the Hamiltonian Cycle Problem

International audienc

Hybrid Local Search for Constrained Financial Portfolio Selection Problems

Abstract. Portfolio selection is a relevant problem arising in finance and economics. While its basic formulations can be efficiently solved through linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cases to be tackled by approximate algorithms. In this work, we present a hybrid technique that combines a local search, as master solver, with a quadratic programming procedure, as slave solver. Experimental results show that the approach is very promising and achieves results comparable with, or superior to, the state of the art solvers.