New concave penalty functions for improving the Feasibility Pump

Mixed-Integer optimization represents a powerful tool for modeling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibility pump approach using concave non-differentiable penalty functions for measuring solution integrality. We present computational results on binary … Read more

A probabilistic comparison of split and type 1 triangle cuts for two row mixed-integer programs

We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables. Under a simple probabilistic model of the problem parameters, we show that a simple split cut, i.e. a Gomory cut, is more likely to be better than a type 1 triangle cut in … Read more

Aircraft landing problems with aircraft classes

This paper focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount … Read more

On mixed integer reformulations of monotonic probabilistic programming problems with discrete distributions

The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probabilistic programming problems. In the literature … Read more

Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs

We report on experiments with turning the branch-cut-and-price framework SCIP into a generic branch-cut-and-price solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, … Read more

The Mcf-Separator – Detecting and Exploiting Multi-Commodity Flow Structures in MIPs

Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of Scip … Read more

Concrete Structure Design Using Mixed-Integer Nonlinear Programming with Complementarity Constraints

We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative … Read more

Two-Stage Robust Unit Commitment Problem

As an energy market transforms from a regulated market to a deregulated one, the demands for a power plant are highly uncertain. In this paper, we study a two-stage robust optimization formulation and provide a tractable solution approach for the problem. The computational experiments show the effectiveness of our approach. ArticleDownload View PDF

Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard … Read more

Lifting Group Inequalities and an Application to Mixing Inequalities

Given a valid inequality for the mixed integer infinite group relaxation, a lifting based approach is presented that can be used to strengthen this inequality. Bounds on the solution of the corresponding lifting problem and some necessary conditions for the lifted inequality to be minimal for the mixed integer infinite group relaxation are presented. Finally, … Read more