A heuristic procedure for one dimensional bin packing problem with additional constraints

We proposed a heuristic algorithm to solve the one-dimensional bin-packing problem with additional constraints. The proposed algorithm has been applied to solve a practical vehicle-allocation problem. The experimental results show that our proposed heuristic provides optimal or near-optimal results, and performs better than the first fit decreasing algorithm modified to incorporate additional constraints.

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

An NP-Hard combinatorial optimization problem that has significant industrial applications is the Multiple Knapsack Problem. If approximate solution approaches are used to solve the Multiple Knapsack Problem there are no guarantees on solution quality and exact solution approaches can be intricate and challenging to implement.  This article demonstrates the iterative use of general-purpose integer programming software (Gurobi) to generate solutions for test problems that are available in the literature. Using the software package Gurobi on a standard PC, we generate in a relatively straightforward manner solutions to these problems in an average of less than a minute that are guaranteed to be within 0.16% of the optimum.  This algorithm, called the Simple Sequential Increasing Tolerance (SSIT) algorithm, iteratively increases tolerances in Gurobi to generate a solution that is guaranteed to be close to the optimum in a short time. This solution strategy generates bounded solutions in a timely manner without requiring the coding of a problem-specific algorithm. This approach is attractive to management for solving industrial problems because it is both cost and time effective and guarantees the quality of the generated solutions.  Finally, comparing SSIT results for 480 large multiple knapsack problem instances to results using published multiple knapsack problem algorithms demonstrates that SSIT outperforms these specialized algorithms

Properties of some ILP formulations of a class of partitioning problems

AbstractWe discuss possible integer linear programming formulations of a class of partitioning problems, which includes vertex (and edge) coloring and bin packing, and present some basic properties of the associated linear programming relaxations, possibly improved by means of valid inequalities. In particular, we show that these relaxations are sometimes easily solved without resorting to an LP solver, and derive the worst-case performance of the associated bound on the optimal solution value. We also show which is the contribution of each inequality to this bound. Our analysis provides a general framework to unify and generalize some results previously presented in the literature, and should be taken into account whenever one considers the possibility of using the formulations addressed

Upper bounds and algorithms for the maximum cardinality bin packing problem

info:eu-repo/semantics/publishe

Upper bounds and algorithms for the maximum cardinality bin packing problem

Language of publication: enInternational audienceno abstrac

A Branch-and-Price Algorithm for Bin Packing Problem

Bin Packing Problem examines the minimum number of identical bins needed to pack a set of items of various sizes. Employing branch-and-bound and column generation usually requires designation of the problem-specific branching rules compatible with the nature of the pricing sub-problem of column generation, or alternatively it requires determination of the k-best solutions of knapsack problem at level kth of the tree. Instead, we present a new approach to deal with the pricing sub-problem of column generation which handles two-dimensional knapsack problems. Furthermore, a set of new upper bounds for Bin Packing Problem is introduced in this work which employs solutions of the continuous relaxation of the set-covering formulation of Bin Packing Problem. These high quality upper bounds are computed inexpensively and dominate the ones generated by state-of-the-art methods