The traveling salesman problem: An update of research

During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs. Some account of computational behavior for exact algorithms is provided; however, the primary coverage deals with the strategy of particular procedures. In addition, we include some aspects of nonexact algorithms with major interest confined to the establishment of worst-case bounds.     

Light weight HTPB-clay nanocomposites(HCN)with enhanced ablation performance as inhibition materials for composite propellant

In the present study,organically modified Montmorillonite clay with polar moiety,the Cloisite 30B,is used for preparation of Hydroxyl terminated polybutadiene(HTPB)-clay nanocomposites(HCN)by dispersion of nanoclay in polymer matrix under high shear mixing.The nanocomposites thus prepared are evaluated in composite propellants as inhibitor material for their functional utility.Several inhibition formulations containing 5 wt％-15 wt％of nanoclay,with or without the conventional filler Sb2O3,were prepared.All these formulations were evaluated for their physical,mechanical,thermal,and ablative properties.Ablation rate and density of the compositions containing Cloisite 30B is around 23％and 5％lower respectively in comparison of the base composition.Strain capability of these compositions is twofold higher than that of base composition.These compositions have also been evaluated for their smoke generation tendency by measuring infra red(IR)attenuation in the wavelength range 1.3 μm-5.6 μm and 8 μm-13 μm and thereby compared with the base composition.The corresponding results confirmed that the compositions containing Cloisite 30B as filler have much lower IR attenuation than compositions with conventional filler,Sb2O3.Replacement of 5％Sb2O3 by nanoclay showed 8％reduction in IR attenuation rate which further reduced to 16％on replacement of 15％of Sb2O3.Interfacial bonding of HCN based inhibitors is also comparable or even better than conventional inhibitors.Precisely,the nanoclay composites with Cloisite 30B as filler exhibit all desirable properties of an inhibitor.     

Effect of friction stir processing on mechanical properties and heat transfer of TIG welded joint of AA6061 and AA7075

Tungsten inert gas (TIG) welding is the most commonly used joining process for aluminum alloy for AA6061 and AA7075 which are highly demanded in the aerospace engineering and the automobile sector, but there are some defects occur during TIG welding like micro-crack, coarse grain structure, and porosity. To improve these defects, the TIG welded joint is processed using friction stir processing (FSP). This paper presents the effect of friction stir processing on TIG welding with filler ER4043 and ER 5356 for dissimilar aluminum alloy AA6061 and AA7075. The mechanical characterization, finite element formulation and mathematical equations of heat transfer of TIG + FSP welded joints are investigated using ANSYS Fluent software by adjusting process parameters of FSP. The results show that the maximum compressive residual stress 73 MPa was obtained at the fusion zone (FZ) of the TIG weldment with filler ER4043, whereas minimum compressive residual stress 37 MPa was obtained at stir zone (SZ) of the TIG+FSP with filler 5356. The maximum heat flux 5.33 × 106 W/m2 and temperature 515 ℃ have observed at tool rotation 1600 rpm with a feed rate of 63 mm/min. These results give a satisfactory measure of confidence in the fidelity of the simulation     

The conditional p-center problem in the plane

An algorithm is given for the conditional p-center problem, namely, the optimal location of one or more additional facilities in a region with given demand points and one or more preexisting facilities. The solution dealt with here involves the minimax criterion and Euclidean distances in two-dimensional space. The method used is a generalization to the present conditional case of a relaxation method previously developed for the unconditional p-center problems. Interestingly, its worst-case complexity is identical to that of the unconditional version, and in practice, the conditional algorithm is more efficient. Some test problems with up to 200 demand points have been solved. © 1993 John Wiley & Sons, Inc.     

Setting military reenlistment bonuses

The United States military frequently has difficulty retaining enlisted personnel beyond their initial enlistment. A bonus program within each service, called a Selective Reenlistment Bonus (SRB) program, seeks to enhance reenlistments and thus reduce personnel shortages in critical military occupational specialties (MOSs). The amount of bonus is set by assigning “SRB multipliers” to each MOS. We develop a nonlinear integer program to select multipliers which minimize a function of deviations from desired reenlistment targets. A Lagrangian relaxation of a linearized version of the integer program is used to obtain lower bounds and feasible solutions. The best feasible solution, discovered in a coordinate search of the Lagrangian function, is heuristically improved by apportioning unexpended funds. For large problems a heuristic variable reduction is employed to speed model solution. U.S. Army data and requirements for FY87 yield a 0-1 integer program with 12,992 binary variables and 273 constraints, which is solved within 0.00002% of optimality on an IBM 3033AP in less than 1.7 seconds. More general models with up to 463,000 binary variables are solved, on average, to within 0.009% of optimality in less than 1.8 minutes. The U.S. Marine Corps has used a simpler version of this model since 1986. © 1993 John Wiley & Sons, Inc.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

The multivariate Polya distribution in combat modeling

This paper investigates the multivariate Polya distribution (MPD) for application in combat models for which enemy targets must be randomly assigned to fighting units. Six sets of actual combat data motivate the allocation model. Scenarios include air‐to‐air combat, tank, and submarine warfare. Goodness of fit tests are derived which verify the validity of the MPD, and reinforce the notion that multinomial allocation is too simplistic for such combat models. Simulations to determine optimal allocations for minimal combat cost are applied in order to illustrate the role of the MPD in combat modeling. © 2001 John Wiley & Sons,Inc. Naval Research Logistics 48: 1–17, 2001