Related papers: On modeling hard combinatorial optimization proble…
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…
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…
We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable…
Starting with M(a), an n X n asymmetric cost matrix, Jonker and Volgenannt transformed it into a 2n X 2n symmetric cost matrix, M(s)where M(s) has unusual properties. One such property is that an optimal tour in M(s) yields an optimal tour…
In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…
In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the…
The symmetric circulant TSP is a special case of the traveling salesman problem in which edge costs are symmetric and obey circulant symmetry. Despite the substantial symmetry of the input, remarkably little is known about the symmetric…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…
A well known N P-hard problem called the Generalized Traveling Salesman Problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…