There are various applications where homotopy constraints are useful in trajectory generation for mobile robots. In this paper, we present a method to generate an optimal trajectory restricted to a particular homotopy class, which is specified by a given representative trajectory. The optimality is achieved by formulating the trajectory generation problem as a Mixed-Integer Quadratic Program (M...

The problem of scheduling under resource constraints is widely applicable. One prominent example is power management, in which we have a limited continuous supply of power but must schedule a number of power-consuming tasks. Such problems feature tightly coupled continuous resource constraints and continuous temporal constraints. We address such problems by introducing the Time Resource Network...

Let (QP ) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear constraints. In this paper, we present a general method to solve (QP ) by reformulation of the problem into an equivalent 0-1 program with a convex quadratic objective function, followed by the use of a standard mixed integer quadratic programming solver. Our convexification method, which is...

In this work, we propose a two-stage approach to strengthen piecewise McCormick relaxations for mixed-integer nonlinear programs (MINLP) with multi-linear terms. In the first stage, we exploit Constraint Programing (CP) techniques to contract the variable bounds. In the second stage we partition the variables domains using a dynamic multivariate partitioning scheme. Instead of equally partition...

This paper introduces the concept of transshipment networks, a collection of strategically located transshipment platforms, for efficient and flexible last-mile delivery in congested urban areas. By implementing transshipment platforms, logistics operators can select the locations, light-freight vehicle types and operating schedules that best fit specific distribution strategies, and, simultane...

The objective of this paper is to present a new formulation for the optimal scheduling of multipurpose batch plants where equipment redesign is considered simultaneously with the scheduling decisions. The equipment redesign is characterized by the implementation of modifications in the existent processing units so as to change their suitability to perform certain tasks, while regarding tasks’ c...

Abstract In this article, we prove that every quadratic rational map whose multipliers all lie in the ring of integers a given imaginary field is power map, Chebyshev or Lattès map. particular, provides some evidence support conjecture by Milnor concerning maps have an integer multiplier at each cycle.

Mixed Logical Dynamical (MLD) systems are introduced as a new system type. The MLD form is capable to model a broad class of systems arising in many applications: linear hybrid systems; sequential logical systems (finite state machines, automata); nonlinear dynamic systems, where the nonlinearity can be expressed through combinational logic; some classes of discrete event systems; constrained l...