Related papers: On modeling hard combinatorial optimization proble…
This paper explores a variation of the Traveling Salesperson Problem, where the agent places a circular obstacle next to each node once it visits it. Referred to as the Traveling Salesperson Problem with Circle Placement (TSP-CP), the aim…
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…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…
The quadratic traveling salesperson problem (QTSP) is a generalization of the traveling salesperson problem, in which all triples of consecutive customers in a tour determine the travel cost. We propose compact optimization models for QTSP…
In this paper we propose a generalization of the extension complexity of a polyhedron $Q$. On the one hand it is general enough so that all problems in $P$ can be formulated as linear programs with polynomial size extension complexity. On…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Among the most important variants of the traveling salesman problem (TSP) are those relaxing the constraint that every locus should necessarily get visited, rather taking into account a revenue (prize) for visiting customers. In the…
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 paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with…
Yannakakis showed that the matching problem does not have a small symmetric linear program. Rothvo{\ss} recently proved that any, not necessarily symmetric, linear program also has exponential size. It is natural to ask whether the matching…
A general framework is given to analyze the falsifiability of economic models based on a sample of their observable components. It is shown that, when the restrictions implied by the economic theory are insufficient to identify the unknown…
In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q larger than 1, the objective function sums the costs for…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…