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.

Optimizing agents with genetic programming : an evaluation of hyper-heuristics in dynamic real-time logistics

Dynamic pickup and delivery problems (PDPs) require online algorithms for managing a fleet of vehicles. Generally, vehicles can be managed either centrally or decentrally. A common way to coordinate agents decentrally is to use the contract-net protocol (CNET) that uses auctions to allocate tasks among agents. To participate in an auction, agents require a method that estimates the value of a task. Typically this method is an optimization algorithm. Recently, hyper-heuristics has been proposed for automated design of heuristics. Two properties of automatically designed heuristics are particularly promising: 1) a generated heuristic computes quickly, it is expected therefore that hyper-heuristics heuristics perform especially well for urgent problems, and 2) by using simulationbased evaluation, hyper-heuristics can learn from the past and can therefore create a ‘rule of thumb’ that anticipates situations in the future. In the present paper we empirically evaluate whether hyper-heuristics, more specifically genetic programming (GP), can be used to improve agents decentrally coordinated via CNET. We compare several GP settings and compare the resulting heuristic with existing centralized and decentralized algorithms on a dynamic PDP dataset with varying levels of dynamism, urgency, and scale. The results indicate that the evolved heuristic always outperforms the optimization algorithm in the decentralized MAS and often outperforms the centralized optimization algorithm. Our paper shows that designing MASs using genetic programming is an effective way to obtain competitive performance compared to traditional operational research approaches. These results strengthen the relevance of decentralized agent based approaches in dynamic logistics

Generalizing Backdoors

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 ¯rstly 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 e®ectiveness 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

Quantifying the benefits of vehicle pooling with shareability networks

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad-hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting towards a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.Comment: Main text: 6 pages, 3 figures, SI: 24 page