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We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means…
This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses…
The convex hull cheapest insertion heuristic produces good solutions to the Euclidean Traveling Salesperson Problem, but it has never been extended to the non-Euclidean problem. This paper uses multidimensional scaling to first project the…
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…
We have studied numerically the frequency distribution $\rho (n)$ of the n-th neighbour along the optimal tour in the Euclidean travelling salesman problem for N cities, in dimensions d=2 and d=3. We find there is no significant dependence…
The paper introduces a special case of the Euclidean distance matrix completion problem (edmcp) of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…
Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical…
We compute the two-point correlation function for spin configurations which are obtained by solving the Euclidean matching problem, for one family of points on a grid, and the second family chosen uniformly at random, when the cost depends…
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace…
This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Such cost to serve analysis has application both strategically and operationally in…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…