34 research outputs found
Lightsolver challenges a leading deep learning solver for Max-2-SAT problems
Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision
problem that is known to be NP-hard. In this paper, we compare LightSolver's
quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT
problem. Experiments on benchmark data sets show that LightSolver achieves
significantly smaller time-to-optimal-solution compared to a state-of-the-art
deep-learning algorithm, where the gain in performance tends to increase with
the problem size
An Active Learning Algorithm for Ranking from Pairwise Preferences with an Almost Optimal Query Complexity
We study the problem of learning to rank from pairwise preferences, and solve
a long-standing open problem that has led to development of many heuristics but
no provable results for our particular problem. Given a set of
elements, we wish to linearly order them given pairwise preference labels. A
pairwise preference label is obtained as a response, typically from a human, to
the question "which if preferred, u or v?u,v\in V{n\choose 2}$ possibilities only. We present an active learning algorithm for
this problem, with query bounds significantly beating general (non active)
bounds for the same error guarantee, while almost achieving the information
theoretical lower bound. Our main construct is a decomposition of the input
s.t. (i) each block incurs high loss at optimum, and (ii) the optimal solution
respecting the decomposition is not much worse than the true opt. The
decomposition is done by adapting a recent result by Kenyon and Schudy for a
related combinatorial optimization problem to the query efficient setting. We
thus settle an open problem posed by learning-to-rank theoreticians and
practitioners: What is a provably correct way to sample preference labels? To
further show the power and practicality of our solution, we show how to use it
in concert with an SVM relaxation.Comment: Fixed a tiny error in theorem 3.1 statemen
Scheduling aircraft landings - the static case
This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia
Travel plan for tourists: minimum access path and route circuit in Jalapão State Park
This article presents the proposal for a model travel plan for tourists in the Jalapão State Park [PEJ - Parque Estadual do Jalapão], located in the State of Tocantins, Brazil. The research shows the use of the Gurobi Optimizer library in Python Software associated with using Miller-Tucker-Zemlin (MTZ) constraints to ensure a viable route circuit. Through the Traveling Salesman Problem (TSP), two viable optimal routes are presented for two research problems: i) minimize the distance of access to the PEJ from the city of Palmas -TO and ii) find an optimal route path for tourists considering some of the most relevant points of the PEJ. The study presents a viable solution to route problems and contributes with an actual model, showing that TSP and the use of restrictions MTZ can be adequate to solve these problems and others to be solved in PEJ.This article presents the proposal for a model travel plan for tourists in the Jalapão State Park [PEJ - Parque Estadual do Jalapão], located in the State of Tocantins, Brazil. The research shows the use of the Gurobi Optimizer library in Python Software associated with using Miller-Tucker-Zemlin (MTZ) constraints to ensure a viable route circuit. Through the Traveling Salesman Problem (TSP), two viable optimal routes are presented for two research problems: i) minimize the distance of access to the PEJ from the city of Palmas -TO and ii) find an optimal route path for tourists considering some of the most relevant points of the PEJ. The study presents a viable solution to route problems and contributes with an actual model, showing that TSP and the use of restrictions MTZ can be adequate to solve these problems and others to be solved in PEJ
A Graph Neural Network-Based QUBO-Formulated Hamiltonian-Inspired Loss Function for Combinatorial Optimization using Reinforcement Learning
Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to
model various NP-hard Combinatorial Optimization problems (CO) in the form of
binary variables. Ising Hamiltonian is used to model the energy function of a
system. QUBO to Ising Hamiltonian is regarded as a technique to solve various
canonical optimization problems through quantum optimization algorithms.
Recently, PI-GNN, a generic framework, has been proposed to address CO problems
over graphs based on Graph Neural Network (GNN) architecture. They introduced a
generic QUBO-formulated Hamiltonian-inspired loss function that was directly
optimized using GNN. PI-GNN is highly scalable but there lies a noticeable
decrease in the number of satisfied constraints when compared to
problem-specific algorithms and becomes more pronounced with increased graph
densities. Here, We identify a behavioral pattern related to it and devise
strategies to improve its performance. Another group of literature uses
Reinforcement learning (RL) to solve the aforementioned NP-hard problems using
problem-specific reward functions. In this work, we also focus on creating a
bridge between the RL-based solutions and the QUBO-formulated Hamiltonian. We
formulate and empirically evaluate the compatibility of the QUBO-formulated
Hamiltonian as the generic reward function in the RL-based paradigm in the form
of rewards. Furthermore, we also introduce a novel Monty Carlo Tree
Search-based strategy with GNN where we apply a guided search through manual
perturbation of node labels during training. We empirically evaluated our
methods and observed up to 44% improvement in the number of constraint
violations compared to the PI-GNN