458 research outputs found
On Global Warming (Softening Global Constraints)
We describe soft versions of the global cardinality constraint and the
regular constraint, with efficient filtering algorithms maintaining domain
consistency. For both constraints, the softening is achieved by augmenting the
underlying graph. The softened constraints can be used to extend the
meta-constraint framework for over-constrained problems proposed by Petit,
Regin and Bessiere.Comment: 15 pages, 7 figures. Accepted at the 6th International Workshop on
Preferences and Soft Constraint
Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning
Finding tight bounds on the optimal solution is a critical element of
practical solution methods for discrete optimization problems. In the last
decade, decision diagrams (DDs) have brought a new perspective on obtaining
upper and lower bounds that can be significantly better than classical bounding
mechanisms, such as linear relaxations. It is well known that the quality of
the bounds achieved through this flexible bounding method is highly reliant on
the ordering of variables chosen for building the diagram, and finding an
ordering that optimizes standard metrics is an NP-hard problem. In this paper,
we propose an innovative and generic approach based on deep reinforcement
learning for obtaining an ordering for tightening the bounds obtained with
relaxed and restricted DDs. We apply the approach to both the Maximum
Independent Set Problem and the Maximum Cut Problem. Experimental results on
synthetic instances show that the deep reinforcement learning approach, by
achieving tighter objective function bounds, generally outperforms ordering
methods commonly used in the literature when the distribution of instances is
known. To the best knowledge of the authors, this is the first paper to apply
machine learning to directly improve relaxation bounds obtained by
general-purpose bounding mechanisms for combinatorial optimization problems.Comment: Accepted and presented at AAAI'1
Gestion de flotte avec fenêtres horaires : approches de résolution mixtes utilisant la programmation par contraintes
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal
Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams
Decision diagrams are an increasingly important tool in cutting-edge solvers
for discrete optimization. However, the field of decision diagrams is
relatively new, and is still incorporating the library of techniques that
conventional solvers have had decades to build. We drew inspiration from the
warm-start technique used in conventional solvers to address one of the major
challenges faced by decision diagram based methods. Decision diagrams become
more useful the wider they are allowed to be, but also become more costly to
generate, especially with large numbers of variables. In the original version
of this paper, we presented a method of peeling off a sub-graph of previously
constructed diagrams and using it as the initial diagram for subsequent
iterations that we call peel-and-bound. We tested the method on the sequence
ordering problem, and our results indicate that our peel-and-bound scheme
generates stronger bounds than a branch-and-bound scheme using the same
propagators, and at significantly less computational cost. In this extended
version of the paper, we also propose new methods for using relaxed decision
diagrams to improve the solutions found using restricted decision diagrams,
discuss the heuristic decisions involved with the parallelization of
peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for
sequencing problems. Furthermore, we test the new methods on the sequence
ordering problem and the traveling salesman problem with time-windows (TSPTW),
and include an updated and generalized implementation of the algorithm capable
of handling any discrete optimization problem. The new results show that
peel-and-bound outperforms ddo (a decision diagram based branch-and-bound
solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.Comment: 50 pages, 31 figures, published by JAIR, supplementary materials at
https://github.com/IsaacRudich/ImprovedPnB. arXiv admin note: substantial
text overlap with arXiv:2205.0521
On the vehicle routing problem with stochastic demands and duration constraints: formulations and a hybrid metaheuristic
International audienceThe vehicle routing problem with stochastic demands (VRPSD) consists in designing transportation routes of minimal expected cost to satisfy a set of customers with random demands of known probability distributions. In this research we present two strategies to deal with route duration constraints in the VRPSD. To solve the resulting problem, we proposed a greedy randomized adaptive search procedure (GRASP) with a post optimization procedure. The GRASP component uses a set of randomized route-first, cluster-second heuristics to generate starting solutions and a variable neighborhood descent (VND) procedure to carry on the local search phase. The post optimizer selects the best possible routes to assemble the final solution from the set of all routes found in the local optima reached by the GRASP. We discuss extensive computational experiments analysing the cost of considering route duration constraints on the VRPSD. In addition, we report state-of-the-art solutions for a established set of benchmarks for the classical VRPSD
An adaptive large neighborhood search for a vehicle routing problem with cross-dock under dock resource constraints
International audienceIn this work, we study the impact of dock resource constraints on the cost of VRPCD solutions
A New Class of Compact Formulations for Vehicle Routing Problems
This paper introduces a novel compact mixed integer linear programming (MILP)
formulation and a discretization discovery-based solution approach for the
Vehicle Routing Problem with Time Windows (VRPTW). We aim to solve the
optimization problem efficiently by constraining the linear programming (LP)
solutions to use only flows corresponding to time and capacity-feasible routes
that are locally elementary (prohibiting cycles of customers localized in
space).
We employ a discretization discovery algorithm to refine the LP relaxation
iteratively. This iterative process alternates between two steps: (1)
increasing time/capacity/elementarity enforcement to increase the LP objective,
albeit at the expense of increased complexity (more variables and constraints),
and (2) decreasing enforcement without decreasing the LP objective to reduce
complexity. This iterative approach ensures we produce an LP relaxation that
closely approximates the optimal MILP objective with minimal complexity,
facilitating an efficient solution via an off-the-shelf MILP solver.
The effectiveness of our method is demonstrated through empirical evaluations
on classical VRPTW instances. We showcase the efficiency of solving the final
MILP and multiple iterations of LP relaxations, highlighting the decreased
integrality gap of the final LP relaxation. We believe that our approach holds
promise for addressing a wide range of routing problems within and beyond the
VRPTW domain
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