Bilevel programming model and algorithms for flight gate assignment problem

ABSTRACTConsidering the decision-making requirements of airport, airlines and passengers, a bilevel programming model which contains two parts was proposed in this paper. One part is to improve the utilization of gates of the airport (upper level), so the objective function of the upper level to the minimum overall variance of slack time between two consecutive air crafts at the same gate. The other part looks at maximize the airline revenue and passengers more conveniently and comfortably (lower level). The lower level has two objective functions — the minimum passenger transfer failure and the minimum passenger average transfer time, respectively. According to the latest data of an airport in Eastern China, the adaptive genetic algorithm is used to solve the above-mentioned bilevel optimisation problems. The numerical experiment shows that the model not only reduces the variance of the relaxation time, but also optimises the flight gate allocation and achieves the initial goal.

NIHBA: A Network Interdiction Approach with Hybrid Benders Algorithm for Strain Design

Flux balance analysis (FBA) based bilevel optimisation has been a great success in redesigning metabolic networks for biochemical overproduction. To date, many computational approaches have been developed to solve the resulting bilevel optimisation problems. However, most of them are of limited use due to biased optimality principle, poor scalability with the size of metabolic networks, potential numeric issues, or low quantity of design solutions in a single run. In this work, we have employed a network interdiction model free of growth optimality assumptions, a special case of bilevel optimisation, for computational strain design and have developed a hybrid Benders algorithm (HBA) that deals with complicating binary variables in the model, thereby achieving high efficiency without numeric issues in search of best design strategies. More importantly, HBA can list solutions that meet users’ production requirements during the search, making it possible to obtain numerous design strategies at a small runtime overhead (typically ∼1 hour).

Towards a Closer Integration of Dynamic Programming and Constraint Programming

Three connections between Dynamic Programming (DP) and Constraint Programming (CP) have previously been explored in the literature: DP-based global constraints, DP- like memoisation during tree search to avoid recomputing results, and subsumption of both by bucket elimination. In this paper we propose a new connection: many discrete DP algorithms can be directly modelled and solved as a constraint satisfaction problem (CSP) without backtracking. This has applications including the design of monolithic CP models for bilevel optimisation. We show that constraint filtering can occur between leader and follower variables in such models, and demonstrate the method on network interdiction.