11,157 research outputs found
A General Large Neighborhood Search Framework for Solving Integer Programs
This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi
A General Large Neighborhood Search Framework for Solving Integer Programs
This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi
A machine learning framework for neighbor generation in metaheuristic search
ABSTRACT: This paper presents a methodology for integrating machine learning techniques into metaheuristics for solving combinatorial optimization problems. Namely, we propose a general machine learning framework for neighbor generation in metaheuristic search. We first define an efficient neighborhood structure constructed by applying a transformation to a selected subset of variables from the current solution. Then, the key of the proposed methodology is to generate promising neighbors by selecting a proper subset of variables that contains a descent of the objective in the solution space. To learn a good variable selection strategy, we formulate the problem as a classification task that exploits structural information from the characteristics of the problem and from high-quality solutions. We validate our methodology on two metaheuristic applications: a Tabu Search scheme for solving a Wireless Network Optimization problem and a Large Neighborhood Search heuristic for solving Mixed-Integer Programs. The experimental results show that our approach is able to achieve a satisfactory trade-offs between the exploration of a larger solution space and the exploitation of high-quality solution regions on both applications
A Constraint-directed Local Search Approach to Nurse Rostering Problems
In this paper, we investigate the hybridization of constraint programming and
local search techniques within a large neighbourhood search scheme for solving
highly constrained nurse rostering problems. As identified by the research, a
crucial part of the large neighbourhood search is the selection of the fragment
(neighbourhood, i.e. the set of variables), to be relaxed and re-optimized
iteratively. The success of the large neighbourhood search depends on the
adequacy of this identified neighbourhood with regard to the problematic part
of the solution assignment and the choice of the neighbourhood size. We
investigate three strategies to choose the fragment of different sizes within
the large neighbourhood search scheme. The first two strategies are tailored
concerning the problem properties. The third strategy is more general, using
the information of the cost from the soft constraint violations and their
propagation as the indicator to choose the variables added into the fragment.
The three strategies are analyzed and compared upon a benchmark nurse rostering
problem. Promising results demonstrate the possibility of future work in the
hybrid approach
A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption
The past decade has seen a substantial increase in the use of small unmanned
aerial vehicles (UAVs) in both civil and military applications. This article
addresses an important aspect of refueling in the context of routing multiple
small UAVs to complete a surveillance or data collection mission. Specifically,
this article formulates a multiple-UAV routing problem with the refueling
constraint of minimizing the overall fuel consumption for all of the vehicles
as a two-stage stochastic optimization problem with uncertainty associated with
the fuel consumption of each vehicle. The two-stage model allows for the
application of sample average approximation (SAA). Although the SAA solution
asymptotically converges to the optimal solution for the two-stage model, the
SAA run time can be prohibitive for medium- and large-scale test instances.
Hence, we develop a tabu-search-based heuristic that exploits the model
structure while considering the uncertainty in fuel consumption. Extensive
computational experiments corroborate the benefits of the two-stage model
compared to a deterministic model and the effectiveness of the heuristic for
obtaining high-quality solutions.Comment: 18 page
Decomposition, Reformulation, and Diving in University Course Timetabling
In many real-life optimisation problems, there are multiple interacting
components in a solution. For example, different components might specify
assignments to different kinds of resource. Often, each component is associated
with different sets of soft constraints, and so with different measures of soft
constraint violation. The goal is then to minimise a linear combination of such
measures. This paper studies an approach to such problems, which can be thought
of as multiphase exploitation of multiple objective-/value-restricted
submodels. In this approach, only one computationally difficult component of a
problem and the associated subset of objectives is considered at first. This
produces partial solutions, which define interesting neighbourhoods in the
search space of the complete problem. Often, it is possible to pick the initial
component so that variable aggregation can be performed at the first stage, and
the neighbourhoods to be explored next are guaranteed to contain feasible
solutions. Using integer programming, it is then easy to implement heuristics
producing solutions with bounds on their quality.
Our study is performed on a university course timetabling problem used in the
2007 International Timetabling Competition, also known as the Udine Course
Timetabling Problem. In the proposed heuristic, an objective-restricted
neighbourhood generator produces assignments of periods to events, with
decreasing numbers of violations of two period-related soft constraints. Those
are relaxed into assignments of events to days, which define neighbourhoods
that are easier to search with respect to all four soft constraints. Integer
programming formulations for all subproblems are given and evaluated using ILOG
CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table
Network Community Detection On Small Quantum Computers
In recent years a number of quantum computing devices with small numbers of
qubits became available. We present a hybrid quantum local search (QLS)
approach that combines a classical machine and a small quantum device to solve
problems of practical size. The proposed approach is applied to the network
community detection problem. QLS is hardware-agnostic and easily extendable to
new quantum computing devices as they become available. We demonstrate it to
solve the 2-community detection problem on graphs of size up to 410 vertices
using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their
performance with the optimal solutions. Our results demonstrate that QLS
perform similarly in terms of quality of the solution and the number of
iterations to convergence on both types of quantum computers and it is capable
of achieving results comparable to state-of-the-art solvers in terms of quality
of the solution including reaching the optimal solutions
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