Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

A Neuroevolutionary Approach to Stochastic Inventory Control in Multi-Echelon Systems

Stochastic inventory control in multi-echelon systems poses hard problems in optimisation under uncertainty. Stochastic programming can solve small instances optimally, and approximately solve larger instances via scenario reduction techniques, but it cannot handle arbitrary nonlinear constraints or other non-standard features. Simulation optimisation is an alternative approach that has recently been applied to such problems, using policies that require only a few decision variables to be determined. However, to find optimal or near-optimal solutions we must consider exponentially large scenario trees with a corresponding number of decision variables. We propose instead a neuroevolutionary approach: using an artificial neural network to compactly represent the scenario tree, and training the network by a simulation-based evolutionary algorithm. We show experimentally that this method can quickly find high-quality plans using networks of a very simple form

Computing replenishment cycle policy parameters for a perishable item

In many industrial environments there is a significant class of problems for which the perishable nature of the inventory cannot be ignored in developing replenishment order plans. Food is the most salient example of a perishable inventory item. In this work, we consider the periodic-review, single-location, single-product production/inventory control problem under non-stationary stochastic demand and service level constraints. The product we consider can be held in stock for a limited amount of time after which it expires and it must be disposed of at a cost. In addition to wastage costs, our cost structure comprises fixed and unit variable ordering costs, and inventory holding costs. We propose an easy-to-implement replenishment cycle inventory control policy that yields at most 2N control parameters, where N is the number of periods in our planning horizon. We also show, on a simple numerical example, the improvement brought by this policy over two other simpler inventory control rules of common use

Extensible Automated Constraint Modelling

In constraint solving, a critical bottleneck is the formulationof an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature

Data Obsolescence Detection in the Light of Newly Acquired Valid Observations

The information describing the conditions of a system or a person is constantly evolving and may become obsolete and contradict other information. A database, therefore, must be consistently updated upon the acquisition of new valid observations that contradict obsolete ones contained in the database. In this paper, we propose a novel approach for dealing with the information obsolescence problem. Our approach aims to detect, in real-time, contradictions between observations and then identify the obsolete ones, given a representation model. Since we work within an uncertain environment characterized by the lack of information, we choose to use a Bayesian network as our representation model and propose a new approximate concept, $\epsilon$-Contradiction. The new concept is parameterised by a confidence level of having a contradiction in a set of observations. We propose a polynomial-time algorithm for detecting obsolete information. We show that the resulting obsolete information is better represented by an AND-OR tree than a simple set of observations. Finally, we demonstrate the effectiveness of our approach on a real elderly fall-prevention database and showcase how this tree can be used to give reliable recommendations to doctors. Our experiments give systematically and substantially very good results