Integer programming formulations describe optimization problems over a set of integer points. A fundamental problem is to determine the minimal size of such formulations, in particular, if the size of the coefficients or sparsity of the constraints is bounded. This article considers lower and upper bounds on these sizes both in the original and in … Read more
We present a branch-and-cut algorithm for solving discrete bilevel linear programs where the upper-level variables are binary and the lower-level variables are either pure integer or pure binary. This algorithm performs local search to find improved bilevel feasible solutions. We strengthen the relaxed node subproblems in the branch-and-cut search tree by generating cuts to eliminate … Read more
In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development … Read more
A regular timetable is a collection of events that repeat themselves every specific time span. This even structure, whenever applied at a whole network, leads to several benefits both for users and the company, although some issues are introduced, especially about dimensioning the service. It is therefore fundamental to properly consider the interaction between the … Read more
In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range … Read more
This paper addresses the problem of generating synthetic test cases for experimentation in linear programming. We propose a method which maps instance generation and instance space search to an alternative encoded space. This allows us to develop a generator for feasible bounded linear programming instances with controllable properties. We show that this method is capable … Read more
Electric vehicles are a prime candidate for use within an urban car sharing system, both from an economic and environmental perspective. However, their relatively short range necessitates frequent and rather time-consuming recharging throughout the day. Thus, charging stations must be built throughout the system’s operational area where cars can be charged between uses. In this … Read more
In this article, we introduce and study a two-stage stochastic optimization problem suitable to solve strategic optimization problems of car-sharing systems that utilize electric cars. By combining the individual advantages of car-sharing and electric vehicles, such electric car-sharing systems may help to overcome future challenges related to pollution, congestion, or shortage of fossil fuels. A … Read more
In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more
A large number of the real world planning problems which are today solved using Operations Research methods are actually multi-objective planning problems, but most of them are solved using single-objective methods. The reason for converting, i.e. simplifying, multi- objective problems to single-objective problems is that no standard multi-objective solvers exist and specialized algorithms need to … Read more