Related papers: Branch and bound algorithm for the traveling sales…
This paper outlines the ideas behind developing a graph-based heuristic-driven routing algorithm designed for a particular instance of a goods transportation problem with a single good type. The proposed algorithm solves the optimization…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
Given a directed graph $G=(V,A)$, the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree (i.e., an out-branching) with as many leaves as possible. By designing a Branch-and-Reduced algorithm combined with…
We study a new version of the Traveling Salesperson Problem, called \VectorTSP, where the traveler is subject to discrete acceleration constraints, as defined in the paper-and-pencil game Racetrack (also known as Vector Racer). In this…
In this paper, we apply the random walk model in designing a raindrop algorithm to find the global optimal solution of a non-linear programming problem. The raindrop algorithm does not require the information of the first or second order…
In this work we compare several new computational approaches to an inventory routing problem, in which a single product is shipped from a warehouse to retailers via an uncapacitated vehicle. We survey exact algorithms for the Traveling…
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of $n$ regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present…
The genetic algorithm includes some parameters that should be adjusted, so as to get reliable results. Choosing a representation of the problem addressed, an initial population, a method of selection, a crossover operator, mutation…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a…
In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.
In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box…
A well-studied continuous model of graphs, introduced by Dearing and Francis [Transportation Science, 1974], considers each edge as a continuous unit-length interval of points. For $\delta \geq 0$, we introduce the problem $\delta$-Tour,…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
This paper describes TSP exact solution of polynomial complexity. It is considered properties of proposed method. Effectiveness of proposed solution is illustrated by outcomes of computer modeling.
We show that a direct shooting method is mathematically equivalent to an indirect method in the sense of certain first-order conditions. Specific mathematical formulas pertaining to the equivalence of a direct shooting method with an…
Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…