1,721,128 research outputs found
Correction to: Stochastic optimization: theory and applications. Preface: special issue in memory of Marida Bertocchi
No full textThis erratum is published due to proofing error as author corrections were overlooked
The stochastic capacitated traveling salesmen location problem: a computational comparison for a United States instance
Full text linkWe study a problem in which a facility has to be located in a given area to serve a given number of customers. The position of the customers is not known. The service to the customers is carried out by several traveling salesmen. Each of them has a capacity in terms of the maximum number of customers that can be served in any tour. The aim is to determine the service zone (in a shape of a circle) that minimizes the expected cost of the traveled routes. The center of the circle is the location of the facility. Once the position of the customers is revealed, the customers located outside the service zone are served with a recourse action at a greater unit cost. For this problem, we compare the performance of two different approaches. The first is a solution based on a heuristic proposed for a similar well known problem and the second is a solution based on a stochastic second–order cone model. An illustrative example on a United States instance with 13509 nodes shows the different solutions and expected costs obtained by the two approaches
A Stochastic Multi-stage Fixed Charge Transportation Problem: Worst-Case Analysis of the Rolling Horizon Approach
Full text linkWe introduce a stochastic multi-stage fixed charge transportation problem, in which a producer has to satisfy an uncertain demand within a deadline. At each time period, a fixed transportation cost can be paid to buy a transportation capacity. If the transportation capacity is used, the supplier also pays an uncertain unit transportation cost. A unit inventory cost is charged for the unsatisfied demand. The aim is to determine the transportation capacities to buy and the quantity to send at each time period in order to minimize the expected total cost. We prove that this problem is NP-hard, we propose a multi-stage stochastic optimization model formulation, and we determine optimal policies for particular cases, with deterministic unit transportation costs or demand and zero fixed costs. Furthermore, we provide the worst–case analysis of the rolling horizon approach, a classical heuristic approach for solving multi-stage stochastic programming models, applied to this NP-hard problem and to polynomially solvable particular cases. Worst–case results show that the rolling horizon approach can be very suboptimal. We also provide experimental results
Solution approaches for the stochastic capacitated traveling salesmen location problem with recourse
Full text linkA facility has to be located in a given area to serve a given number of customers. The position of the customers is not known. The service to the customers is carried out by several traveling salesmen. Each of them has a capacity in terms of the maximum number of customers that can be served in any tour. The aim was to determine the service zone (in a shape of a circle) that minimizes the expected cost of the traveled routes. The center of the circle is the location of the facility. Once the position of the customers is revealed, the customers located outside the service zone are served with a recourse action at a greater unit cost. For this problem, we compare the performance of two different solution approaches. The first is based on a heuristic proposed for the Capacitated Traveling Salesman Problem and the second on the optimal solution of a stochastic second-order cone formulation with an approximate objective function
A new stretch-twist-fold model for fast dynamo
No full textPreliminary results on a new Stretch-Twist-Fold (STF) kinematic model for fast dynamo are presented. The evolution is prescribed by equations that govern the simultaneous stretching, writhing and coiling of a magnetic flux-tube by diffeomorphism of the initial circular configuration. Simple estimates based on minimized magnetic energy show that exponential growth of the magnetic field is indeed possible
Writhing and coiling of closed filaments
No full textThe kinematics of writhing and coiling of circular filaments is here analyzed by new equations that govern the evolution of curves generated by epicycloids and hypocycloids. We show how efficiency of coil formation and compaction depend on writhing rates, relative bending, torsion and mean twist energy. We demonstrate that for coiling formation hypocycloid evolution achieves higher writhing rates, but in terms of deformation energy the epicycloid evolution is much more effective. We also show how the occurrence and multiple appearance of inflexional configurations determine coil formation. Compaction and packing rate are also briefly examined. These results are fundamental and provide useful information for physical applications and for modelling natural phenomena, including relaxation of magnetic fields in the Solar corona, magnetic dynamos in astrophysical flows, tertiary folding of macromolecules in chemical-physics, and DNA packing in cell biology
Analyzing the quality of the expected value solution in stochastic programming
Full text linkStochastic programs are usually hard to solve when applied to real-world problems;
a common approach is to consider the simpler deterministic program in which random parameters
are replaced by their expected values, with a loss in terms of quality of the solution. The
Value of the Stochastic Solution – VSS – is normally used to measure the importance of using
a stochastic model. But what if VSS is large, or expected to be large, but we cannot solve the
relevant stochastic program? Shall we just give up? In this paper we investigate very simple
methods for studying structural similarities and differences between the stochastic solution
and its deterministic counterpart. The aim of the methods is to find out, even when VSS is
large, if the deterministic solution carries useful information for the stochastic case. It turns
out that a large VSS does not necessarily imply that the deterministic solution is useless for
the stochastic setting. Measures of the structure and upgradeability of deterministic solution
such as the loss using the skeleton solution and the loss of upgrading the deterministic solution
will be introduced and basic inequalities in relation to the standard VSS are presented and
tested on different case studies
On the groundstate energy of knotted magnetic flux tubes
No full textNew results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field. Standard minimization of the magnetic energy is carried out under the usual assumptions of volume- and flux-preserving flow, with the additional constraints that the tube cross section remains circular and that the knot length (ropelength) is independent from internal field twist (framing). Under these constraints the minimum energy is determined analytically by a new, exact expression, function of ropelength and framing. Groundstate energy levels of tight knots are determined from ropelength data obtained by the SONO tightening algorithm. Results for torus knots are compared with previous work, and the groundstate energy spectrum of the first prime knots — up to 10 crossings — is presented and analysed in detail. These results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration
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