Related papers: Parameterized Runtime Analyses of Evolutionary Alg…
Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
The $k$-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces $k$ edges of the tour by $k$ other edges, as long as this yields a shorter tour. We…
The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost Hamilton cycle in an edge-weighted graph, where costs are defined on all pairs of edges contained in the Hamilton cycle. This is a more general version than the…
The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…
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…
In this work, we consider the problem of finding a set of tours to a traveling salesperson problem (TSP) instance maximizing diversity, while satisfying a given cost constraint. This study aims to investigate the effectiveness of applying…
Randomized search heuristics have been applied successfully to a plethora of problems. This success is complemented by a large body of theoretical results. Unfortunately, the vast majority of these results regard problems with binary or…
Traveling salesman problem (TSP) is a well-known in computing field. There are many researches to improve the genetic algorithm for solving TSP. In this paper, we propose two new crossover operators and new mechanism of combination…
Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this…
We propose a framework of genetic algorithms which use multi-level hierarchies to solve an optimization problem by searching over the space of simpler objective functions. We solve a variant of Travelling Salesman Problem called…
Computing diverse sets of high-quality solutions has gained increasing attention among the evolutionary computation community in recent years. It allows practitioners to choose from a set of high-quality alternatives. In this paper, we…
The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…
The design space of networked embedded systems is very large, posing challenges to the optimisation of such platforms when it comes to support applications with real-time guarantees. Recent research has shown that a number of inter-related…
The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by…
This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics.…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between…
Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…
Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…