A learning problem might have several measures of complexity (e.g., norm and dimensionality) that affect the generalization error. What is the interaction between these complexities? Dimension-free learning theory bounds and parametric asymptotic analyses each provide a partial picture of the full learning curve. In this paper, we use high-dimensional asymptotics on two classical problems—mean ...

> Context • Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. > Problem • First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. ...

We show that searching the k-change neighborhood is W[1]-hard for metric TSP, which means that finding the best tour in the k-change neighborhood essentially requires complete search (modulo some complexitytheoretic assumptions).

We consider the probabilistic relationship between the value of a random asymmetric traveling salesman problem ATSP (M) and the value of its assignment relaxation AP (M). We assume here that the costs are given by an n × n matrix M whose entries are independently and identically distributed. We focus on the relationship between Pr(ATSP (M) = AP (M)) and the probability pn that any particular en...

A long standing conjecture says that the integrality ratio of the subtour LP for metric TSP is 4/3. A well known family of graphic TSP instances achieves this lower bound asymptotically. For Euclidean TSP the best known lower bound on the integrality ratio was 8/7. We improve this value by presenting a family of Euclidean TSP instances for which the integrality ratio of the subtour LP converges...

Edge Recombination and Maximal Preservative Crossover (MPX) are two operators developed to preserve edge information for the Traveling Salesman Problem. Manderick et al. introduced the notion of a tness landscape to measure the tness correlation between parents and o spring under di erent recombination operators. The work on the tness landscape is extended by studying the interrelationship betw...

The p-hub center problem is to locate p hubs and to allocate non-hub nodes to hub nodes such that the maximum travel time (or distance) between any origin–destination pair is minimized. We address the p-hub center allocation problem, a subproblem of the location problem, where hub locations are given. We present complexity results and IP formulations for several versions of the problem. We esta...

Here we present the implementation of an application capable of planning the shortest delivery route in the city of Medellín, Colombia. We discuss the different approaches to this problem which is similar to the famous Traveling Salesman Problem (TSP), but differs in the fact that, in our problem, we can visit each place (or vertex) more than once. Solving this problem is important since it wou...