The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

This paper analyzes the elastic net approach (Durbin and Willshaw 1987) to the traveling salesman problem of finding the shortest path through a set of cities. The elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities. The tradeoff between these two require­ ments is controlled by a scale parameter K. A global...

In this paper, the flow-shop scheduling problem with unrelated parallel machines at each stage as well as sequence-dependent setup times under minimization of the sum of earliness and tardiness are studied. The processing times, setup times and due-dates are known in advance. To solve the problem, we introduce a hybrid memetic algorithm as well as a particle swarm optimization algorithm combine...

This paper mainly investigates the traveling salesman problem under uncertain environment, in which not all the edge weights are deterministically present, but are present with uncertain variables. As a result, five types optimal route models for the uncertain traveling salesman problem, i.e., expected optimal route, α-optimal route, distribution optimal route, expected approximation optimal ro...

In order to solve traveling salesman problems that employed completiontimeshortest as the evaluating rule, an encoding method and improved differential evolution algorithm were proposed. In these methods, real number encoding and roulette wheel selection were adopted for improved differential evolution and neighborhood search operator was devised. It was fit for solving symmetric and asymmetric...

Since the computation of an exact solution is very expensive (under the assumption that P 6= NP ), we are interested in approximate solutions – at least for special cases. Particularly, we look for an Polynomial Time Approximation Scheme (PTAS), i.e., for any fixed error parameter ε > 0, the running time is bounded by a polynomial in n and the costs of the computed tour does not exceed (1+ε) ·O...

Several works indicate the relationship between well-solved combinatorial optimization problems and the core non-emptiness of cooperative games associated with them. In this paper, we consider the core of symmetric traveling salesman games and relate it with well-solved cases of traveling salesman problems. We show that the core of a traveling salesman game in which the distance matrix is a sym...

In this paper, we address the problem of reducing the switching activity (SA) in on-chip buses through the use of a bus binding technique in high-level synthesis. While many binding techniques to reduce the SA exist, we present yet another technique for further reducing the switching activity. Our proposed method combines bus binding and data sequence reordering to explore a wider solution spac...