1,151 research outputs found
Approximability of the Multiple Stack TSP
STSP seeks a pair of pickup and delivery tours in two distinct networks,
where the two tours are related by LIFO contraints. We address here the problem
approximability. We notably establish that asymmetric MaxSTSP and MinSTSP12 are
APX, and propose a heuristic that yields to a 1/2, 3/4 and 3/2 standard
approximation for respectively Max2STSP, Max2STSP12 and Min2STSP12
On the complexity of the multiple stack TSP, kSTSP
The multiple Stack Travelling Salesman Problem, STSP, deals with the collect
and the deliverance of n commodities in two distinct cities. The two cities are
represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the
pick-up tour, the commodities are stored into a container whose rows are
subject to LIFO constraints. As a generalisation of standard TSP, the problem
obviously is NP-hard; nevertheless, one could wonder about what combinatorial
structure of STSP does the most impact its complexity: the arrangement of the
commodities into the container, or the tours themselves? The answer is not
clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is
polynomial to decide whether these tours are or not compatible. Second, for a
given arrangement of the commodities into the k rows of the container, the
optimum pick-up and delivery tours w.r.t. this arrangement can be computed
within a time that is polynomial in n, but exponential in k. Finally, we
provide instances on which a tour that is optimum for one of three distances
d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the
optimum STSP
The double traveling salesman problem with partial last-in-first-out loading constraints
In this paper, we introduce the double traveling salesman problem with partial last-in-first-out loading constraints (DTSPPL). It is a pickup-and-delivery single-vehicle routing problem, where all pickup operations must be performed before any delivery operation because the pickup-and-delivery areas are geographically separated. The vehicle collects items in the pickup area and loads them into its container, a horizontal stack. After performing all pickup operations, the vehicle begins delivering the items in the delivery area. Loading and unloading operations must obey a partial last-in-first-out (LIFO) policy, that is, a version of the LIFO policy that may be violated within a given reloading depth. The objective of the DTSPPL is to minimize the total cost, which involves the total distance traveled by the vehicle and the number of items that are unloaded and then reloaded due to violations of the standard LIFO policy. We formally describe the DTSPPL through two integer linear programming (ILP) formulations and propose a heuristic algorithm based on the biased random-key genetic algorithm (BRKGA) to find high-quality solutions. The performance of the proposed solution approaches is assessed over a broad set of instances. Computational results have shown that both ILP formulations have been able to solve only the smaller instances, whereas the BRKGA obtained good-quality solutions for almost all instances, requiring short computational times
Temperature-driven transition from the Wigner Crystal to the Bond-Charge-Density Wave in the Quasi-One-Dimensional Quarter-Filled band
It is known that within the interacting electron model Hamiltonian for the
one-dimensional 1/4-filled band, the singlet ground state is a Wigner crystal
only if the nearest neighbor electron-electron repulsion is larger than a
critical value. We show that this critical nearest neighbor Coulomb interaction
is different for each spin subspace, with the critical value decreasing with
increasing spin. As a consequence, with the lowering of temperature, there can
occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls
state that is a Bond-Charge-Density Wave with charge occupancies different from
the Wigner crystal. This transition is possible because spin excitations from
the spin-Peierls state in the 1/4-filled band are necessarily accompanied by
changes in site charge densities. We apply our theory to the 1/4-filled band
quasi-one-dimensional organic charge-transfer solids in general and to 2:1
tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene
(TMTSF) cationic salts in particular. We believe that many recent experiments
strongly indicate the Wigner crystal to Bond-Charge-Density Wave transition in
several members of the TMTTF family. We explain the occurrence of two different
antiferromagnetic phases but a single spin-Peierls state in the generic phase
diagram for the 2:1 cationic solids. The antiferromagnetic phases can have
either the Wigner crystal or the Bond-Charge-Spin-Density Wave charge
occupancies. The spin-Peierls state is always a Bond-Charge-Density Wave.Comment: 12 pages, 8 EPS figures. Longer version of previous manuscript.
Contains new numerical data as well as greatly expanded discussio
Heuristic Solution Approaches to the Double TSP with Multiple Stacks
This paper introduces the Double Travelling Salesman Problem with Multiple Stacks and presents three different metaheuristic approaches to its solution. The Double TSP with Multiple Stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed, instead each item can be positioned in one of several rows in the container, such that each row can be considered a LIFO stack, but no mutual constraints exist between the rows. Two different neighbourhood structures are developed for the problem and used with each of the heuristics. Finally some computational results are given along with lower bounds on the objective value.
CAD Adjacency Computation Using Validated Numerics
We present an algorithm for computation of cell adjacencies for well-based
cylindrical algebraic decomposition. Cell adjacency information can be used to
compute topological operations e.g. closure, boundary, connected components,
and topological properties e.g. homology groups. Other applications include
visualization and path planning. Our algorithm determines cell adjacency
information using validated numerical methods similar to those used in CAD
construction, thus computing CAD with adjacency information in time comparable
to that of computing CAD without adjacency information. We report on
implementation of the algorithm and present empirical data.Comment: 20 page
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