Related papers: Checking for optimal solutions in some $NP$-comple…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
Assuming that P is not equal to NP, the worst-case run time of any algorithm solving an NP-complete problem must be super-polynomial. But what is the fastest run time we can get? Before one can even hope to approach this question, a more…
We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…
In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem…
The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with…
We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…
Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm…
The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…
We introduce the Polychromatic Traveling Salesman Problem (PCTSP), where the input is an edge weighted graph whose vertices are partitioned into $k$ equal-sized color classes, and the goal is to find a minimum-length Hamiltonian cycle that…
In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence…
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…
Efficient utilization of cooperating robots in the assembly of aircraft structures relies on balancing the workload of the robots and ensuring collision-free scheduling. We cast this problem as that of allocating a large number of…
Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…
While traditional optimization problems were often studied in isolation, many real-world problems today require interdependence among multiple optimization components. The traveling thief problem (TTP) is a multi-component problem that has…
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…