2,156 research outputs found
Solving Bin Packing Problems Using VRPSolver Models
International audienceWe propose branch-cut-and-price algorithms for the classic bin packing problem and also for the following related problems: vector packing, variable sized bin packing and variable sized bin packing with optional items. The algorithms are defined as models for VRPSolver, a generic solver for vehicle routing problems. In that way, a simple parameterization enables the use of several branch-cut-and-price advanced elements: automatic stabilization by smoothing, limited-memory rank-1 cuts, enumeration, hierarchical strong branching and limited discrepancy search diving heuristics. As an original theoretical contribution, we prove that the branching over accumulated resource consumption (GĂ©linas et al. 1995), that does not increase the difficulty of the pricing subproblem, is sufficient for those bin packing models. Extensive computational results on instances from the literature show that the VRPSolver models have a performance that is very robust over all those problems, being often superior to the existing exact algorithms on the hardest instances. Several instances could be solved to optimality for the first time
A study on exponential-size neighborhoods for the bin packing problem with conflicts
We propose an iterated local search based on several classes of local and
large neighborhoods for the bin packing problem with conflicts. This problem,
which combines the characteristics of both bin packing and vertex coloring,
arises in various application contexts such as logistics and transportation,
timetabling, and resource allocation for cloud computing. We introduce
evaluation procedures for classical local-search moves, polynomial variants of
ejection chains and assignment neighborhoods, an adaptive set covering-based
neighborhood, and finally a controlled use of 0-cost moves to further diversify
the search. The overall method produces solutions of good quality on the
classical benchmark instances and scales very well with an increase of problem
size. Extensive computational experiments are conducted to measure the
respective contribution of each proposed neighborhood. In particular, the
0-cost moves and the large neighborhood based on set covering contribute very
significantly to the search. Several research perspectives are open in relation
to possible hybridizations with other state-of-the-art mathematical programming
heuristics for this problem.Comment: 26 pages, 8 figure
Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design
Heat exchanger network synthesis exploits excess heat by integrating process
hot and cold streams and improves energy efficiency by reducing utility usage.
Determining provably good solutions to the minimum number of matches is a
bottleneck of designing a heat recovery network using the sequential method.
This subproblem is an NP-hard mixed-integer linear program exhibiting
combinatorial explosion in the possible hot and cold stream configurations. We
explore this challenging optimization problem from a graph theoretic
perspective and correlate it with other special optimization problems such as
cost flow network and packing problems. In the case of a single temperature
interval, we develop a new optimization formulation without problematic big-M
parameters. We develop heuristic methods with performance guarantees using
three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy
packing. Numerical results from a collection of 51 instances substantiate the
strength of the methods
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