185,212 research outputs found
Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems
Packing and vehicle routing problems play an important role in the area of
supply chain management. In this paper, we introduce a non-linear knapsack
problem that occurs when packing items along a fixed route and taking into
account travel time. We investigate constrained and unconstrained versions of
the problem and show that both are NP-hard. In order to solve the problems, we
provide a pre-processing scheme as well as exact and approximate mixed integer
programming (MIP) solutions. Our experimental results show the effectiveness of
the MIP solutions and in particular point out that the approximate MIP approach
often leads to near optimal results within far less computation time than the
exact approach
Combining Generalized Programming and Sampling Techniques for Stochastic Programs with Recourse
This paper deals with an application of generalized linear programming techniques for stochastic programming problems, particularly to stochastic programming problems with recourse. The major points which needed a clarification here were the possibility to use the estimates of the objective function instead of the exact values and to use the approximate solutions of the dual subproblem instead of the exact ones.
In this paper conditions are presented which allow to use estimates and approximate solutions and still maintain convergence. The paper is a part of the effort on the development of stochastic optimization techniques at the Adaptation and Optimization Project of the System and Decision Sciences Program
An introduction to interval-based constraint processing.
Constraint programming is often associated with solving problems over finite domains. Many applications in engineering, CAD and design, however, require solving problems over continuous (real-valued) domains. While simple constraint solvers can solve linear constraints with the inaccuracy of floating-point arithmetic, methods based on interval arithmetic allow exact (interval) solutions over a much wider range of problems. Applications of interval-based programming extend the range of solvable problems from non-linear polynomials up to those involving ordinary differential equations. In this text, we give an introduction to current approaches, methods and implementations of interval-based constraint programming and solving. Special care is taken to provide a uniform and consistent notation, since the literature in this field employs many seemingly different, but yet conceptually related, notations and terminology
A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs
This work deals with a class of problems under interval data uncertainty,
namely interval robust-hard problems, composed of interval data min-max regret
generalizations of classical NP-hard combinatorial problems modeled as 0-1
integer linear programming problems. These problems are more challenging than
other interval data min-max regret problems, as solely computing the cost of
any feasible solution requires solving an instance of an NP-hard problem. The
state-of-the-art exact algorithms in the literature are based on the generation
of a possibly exponential number of cuts. As each cut separation involves the
resolution of an NP-hard classical optimization problem, the size of the
instances that can be solved efficiently is relatively small. To smooth this
issue, we present a modeling technique for interval robust-hard problems in the
context of a heuristic framework. The heuristic obtains feasible solutions by
exploring dual information of a linearly relaxed model associated with the
classical optimization problem counterpart. Computational experiments for
interval data min-max regret versions of the restricted shortest path problem
and the set covering problem show that our heuristic is able to find optimal or
near-optimal solutions and also improves the primal bounds obtained by a
state-of-the-art exact algorithm and a 2-approximation procedure for interval
data min-max regret problems
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