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Ant Colony Optimization (ACO) has time complexity O(t*m*N*N), and its typical application is to solve Traveling Salesman Problem (TSP), where t, m, and N denotes the iteration number, number of ants, number of cities respectively. Cutting…
The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…
The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that…
Search engines and recommendation systems are built to efficiently display relevant information from those massive amounts of candidates. Typically a three-stage mechanism is employed in those systems: (i) a small collection of items are…
This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to…
We consider the problem of characterizing graphs with the maximum spectral radius among the connected graphs with given numbers of vertices and edges. It is well-known that the candidates for extremal graphs are threshold graphs, but only a…
We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination…
The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…
Coverage Path Planning (CPP) is vital in precision agriculture to improve efficiency and resource utilization. In irregular and dispersed plantations, traditional grid-based CPP often causes redundant coverage over non-vegetated areas,…
In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…
We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $\mathbb{R}^d$, for $d\geq 3$) or…
We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…
The Job Shop Schedule Problem (JSSP) refers to the ability of an agent to allocate tasks that should be executed in a specified time in a machine from a cluster. The task allocation can be achieved from several methods, however, this report…
The Electric Vehicle Routing Problem (EVRP) extends the classical Vehicle Routing Problem (VRP) to reflect the growing use of electric and hybrid vehicles in logistics. Due to the variety of constraints considered in the literature,…
Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems,…
The Soft Happy Colouring (SHC) problem, a mathematical framework for identifying homophilic network structures, seeks to maximise the number of $\rho$-happy vertices, i.e. vertices with at least a proportion $\rho$ of neighbours that share…