In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose MILP formulations for the RCPSP base...

This paper presents results from recent hardware experiments using two forms of on-line Mixed-integer Linear Programming (MILP). The demonstrations were performed on wheeled ground vehicles, with a view to future use on autonomous teams of UAVs. The first experiment uses MILP at a high-level to account for a limited detection horizon while maneuvering in the presence of obstacles. The second pe...

This paper addresses the solution of a nonlinear boolean quadratic programming problem using three different approaches. The first uses a classic linearization technique to transform the original problem into a Mixed Integer Linear Programming (MILP) problem for which multiple formulations are studied. The second uses the capabilities of current MILP solvers to deal with Mixed Integer Quadratic...

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero ob...

xvii 1 CLP–MILP: Introduction 1 1.1 Preliminary Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis’ Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 CLP–MILP: Overview of Main Characteristics 7 2.

We first introduce a novel modeling framework, called linear coupled component automata (LCCA), to facilitate the modeling of discrete-continuous dynamical systems with piecewise constant derivatives. Second, we provide a procedure for transforming models in this framework to mixed-integer linear programming (MILP) constraints. Traditionally, such systems have been modeled directly with MILP co...

The optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems is considered. Two approaches are proposed to solve this optimal control problem for multiple trains: the greedy approach and the simultaneous approach. In each solution approach, the trajectory planning problem is transformed into a mixed integer linear programming...

A wide range of problems can be modeled as Mixed Integer Linear Programming (MILP) problems using standard formulation techniques. However, in some cases the resulting MILP can be either too weak or to large to be effectively solved by state of the art solvers. In this survey we review advanced MILP formulation techniques that result in stronger and/or smaller formulations for a wide class of p...

We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to timedependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints, in particular on restrictions on the number of switches on a fixed time grid. We propose a novel approach that is based ...

This paper presents a novel mixed integer linear programing (MILP) formulation for finding the optimal layout of a fixed number of identical turbines that maximizes wind farm power generation. Previous MILP formulations with power maximizing objectives discretize the feasible space by using a grid of possible turbine locations. The proposed MILP formulation takes a different approach by allowin...