139 research outputs found
Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm
Mixed integer linear programs are commonly solved by Branch and Bound
algorithms. A key factor of the efficiency of the most successful commercial
solvers is their fine-tuned heuristics. In this paper, we leverage patterns in
real-world instances to learn from scratch a new branching strategy optimised
for a given problem and compare it with a commercial solver. We propose FMSTS,
a novel Reinforcement Learning approach specifically designed for this task.
The strength of our method lies in the consistency between a local value
function and a global metric of interest. In addition, we provide insights for
adapting known RL techniques to the Branch and Bound setting, and present a new
neural network architecture inspired from the literature. To our knowledge, it
is the first time Reinforcement Learning has been used to fully optimise the
branching strategy. Computational experiments show that our method is
appropriate and able to generalise well to new instances
On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives
We study a class of procurement auctions with a budget constraint, where an
auctioneer is interested in buying resources or services from a set of agents.
Ideally, the auctioneer would like to select a subset of the resources so as to
maximize his valuation function, without exceeding a given budget. As the
resources are owned by strategic agents however, our overall goal is to design
mechanisms that are truthful, budget-feasible, and obtain a good approximation
to the optimal value. Budget-feasibility creates additional challenges, making
several approaches inapplicable in this setting. Previous results on
budget-feasible mechanisms have considered mostly monotone valuation functions.
In this work, we mainly focus on symmetric submodular valuations, a prominent
class of non-monotone submodular functions that includes cut functions. We
begin first with a purely algorithmic result, obtaining a
-approximation for maximizing symmetric submodular functions
under a budget constraint. We view this as a standalone result of independent
interest, as it is the best known factor achieved by a deterministic algorithm.
We then proceed to propose truthful, budget feasible mechanisms (both
deterministic and randomized), paying particular attention on the Budgeted Max
Cut problem. Our results significantly improve the known approximation ratios
for these objectives, while establishing polynomial running time for cases
where only exponential mechanisms were known. At the heart of our approach lies
an appropriate combination of local search algorithms with results for monotone
submodular valuations, applied to the derived local optima.Comment: A conference version appears in WINE 201
Perspective Cuts for the ACOPF with Generators
International audienceThe alternating current optimal power flow problem is a fundamental problem in the management of smart grids. In this paper we consider a variant which includes activation/deactivation of generators at some of the grid sites. We formulate the problem as a mathematical program, prove its NP-hardness w.r.t. ac-tivation/deactivation, and derive two perspective reformulations
Boolean-controlled systems via receding horizon and linear programing.
We consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programing by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively controlled systems
Computing H/D-Exchange rates of single residues from data of proteolytic fragments
<p>Abstract</p> <p>Background</p> <p>Protein conformation and protein/protein interaction can be elucidated by solution-phase Hydrogen/Deuterium exchange (sHDX) coupled to high-resolution mass analysis of the digested protein or protein complex. In sHDX experiments mutant proteins are compared to wild-type proteins or a ligand is added to the protein and compared to the wild-type protein (or mutant). The number of deuteriums incorporated into the polypeptides generated from the protease digest of the protein is related to the solvent accessibility of amide protons within the original protein construct.</p> <p>Results</p> <p>In this work, sHDX data was collected on a 14.5 T FT-ICR MS. An algorithm was developed based on combinatorial optimization that predicts deuterium exchange with high spatial resolution based on the sHDX data of overlapping proteolytic fragments. Often the algorithm assigns deuterium exchange with single residue resolution.</p> <p>Conclusions</p> <p>With our new method it is possible to automatically determine deuterium exchange with higher spatial resolution than the level of digested fragments.</p
Approximating Source Location and Star Survivable Network Problems
Abstract. In Source Location (SL) problems the goal is to select a minimum cost source set S â V such that the connectivity (or flow) Ï(S, v) from S to any node v is at least the demand dv of v. In many SL problems Ï(S, v) = dv if v â S, namely, the demand of nodes se-lected to S is completely satisfied. In a node-connectivity variant sug-gested recently by Fukunaga [6], every node v gets a âbonus â pv †dv if it is selected to S, namely, Ï(S, v) = pv + Îș(S \ {v}, v) if v â S and Ï(S, v) = Îș(S, v) otherwise, where Îș(S, v) is the maximum number of internally disjoint (S, v)-paths. While the approximability of many SL problems was seemingly settled to Î(ln d(V)) in [18], Fukunaga [6] showed that for undirected graphs one can achieve ratio O(k ln k) for his variant, where k = maxvâV dv is the maximum demand. We improve this by achieving ratio min{p â ln k, k} · O(ln(k/qâ)) for a more general version with node capacities, where p â = maxvâV pv is the maximum bonus and q â = minvâV qv is the minimum capacity. In particular, for the most natural case p â = 1 considered in [6] we improve the ratio from O(k ln k) to O(ln2 k). Our result also implies ratio k for the edge-connectivity version. To derive these results, we consider a particular case of the Survivable Network (SN) problem when all edges of positive cost form a star. We give ratio O(min{lnn, ln2 k}) for this variant, improving over the best ratio known for the general case O(k3 lnn) of Chuzhoy and Khanna [3]. In addition, we show that directed SL with unit costs is âŠ(logn)-hard to approximate even for 0, 1 demands, while SL with uniform demands can be solved in polynomial time. Finally, we consider a generalization of SL where we also have edge-costs {ce: e â E} and flow-cost bounds {bv: v â V}, and require that for every node v, the minimum cost of a flow of value dv from S to v is at most bv. We show that this problem admits approximation ratio O(ln d(V) + ln(nc(E) â b(V)).
Solving the Task Variant Allocation Problem in Distributed Robotics
We consider the problem of assigning software processes (or tasks) to hardware processors in distributed robotics environments. We introduce the notion of a task variant, which supports the adaptation of software to specific hardware configurations. Task variants facilitate the trade-off of functional quality versus the requisite capacity and type of target execution processors. We formalise the problem of assigning task variants to processors as a mathematical model that incorporates typical constraints found in robotics applications; the model is a constrained form of a multi-objective, multi-dimensional, multiple-choice knapsack problem. We propose and evaluate three different solution methods to the problem: constraint programming, a constructive greedy heuristic and a local search metaheuristic. Furthermore, we demonstrate the use of task variants in a real instance of a distributed interactive multi-agent navigation system, showing that our best solution method (constraint programming) improves the systemâs quality of service, as compared to the local search metaheuristic, the greedy heuristic and a randomised solution, by an average of 16, 31 and 56% respectively
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