Generalized assignment problem: Truthful mechanism design without money

We propose truthful approximation mechanisms for strategic variants of the generalized assignment problem (GAP) in a payment-free environment. In GAP, a set of items has to be optimally assigned to a set of bins without exceeding the capacity of any singular bin. In our strategic variant, bins are held by strategic agents and each agent may hide its willingness to receive some items in order to obtain items of higher values. The model has applications in auctions with budgeted bidders.     

Node connectivity augmentation via iterative randomized rounding

Mathematical Programming - Many network design problems deal with the design of low-cost networks that are resilient to the failure of their elements (such as nodes or links). One such problem is...     

Constant approximation for fault-tolerant median problems via iterative rounding

In this paper, we study the fault-tolerant matroid median and fault-tolerant knapsack median problems. These two problems generalize many fundamental clustering and facility location problems, such as uniform fault-tolerant k-median, uniform fault-tolerant facility location, matroid median, knapsack median, etc. We present a versatile iterative rounding framework and obtain a unifying constant-factor approximation algorithm.     

Algorithmic construction of low-discrepancy point sets via dependent randomized rounding

We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on recent results on randomized roundings respecting hard constraints and their derandomization. It is structurally much simpler than a previous algorithm presented for this problem in [B. Doerr, M. Gnewuch, A. Srivastav, Bounds and constructions for the star discrepancy via δ$\delta$-covers, J. Complexity, 21 (2005) 691–709]. Besides leading to better theoretical running time bounds, our approach also can be implemented with reasonable effort. We implemented this algorithm and performed numerical comparisons with other known low-discrepancy constructions. The experiments take place in dimensions ranging from 5 to 21 and indicate that our algorithm leads to superior results if the dimension is relatively high and the number of points that have to be constructed is rather small.     

A-optimal chemical balance weighing design with correlated errors

In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound oftr (X′G ^?1 X)^?1 is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.     

Penalty mechanism design

Penalty is a crucial approach to maintain society in order in both the legal and the political philosophies. How to establish a rational and efficient penalty mechanism is exceedingly important in practice in economics and politics and this paper explores the optimal mechanism design of penalty. A penalty under monopoly mechanism design theory is established and developed in this piece of work. By establishing the penalty mechanism design model, this paper finds that stricter punishment can efficiently deter violation of the regulations but can decrease the profits of the monopoly firm at the same time. Furthermore, penalty increases the concavity of the monopoly firm’s profit function, which makes it easier for the firm to make decisions and which means strict penalty results in optimal decisions. We also show that punishment is in general costly, which is highly consistent with the phenomena in practice.     

Optimization and mechanism design

Mechanism design is about optimizing the allocation of resources when the parameters needed to determine an optimal allocation are privately held by the agents who will consume the resources. An agent’s report of her information will influence the resulting allocation which in turn will affect her utility. In such a situation, how can one simultaneously elicit the information that is privately held and choose the optimal allocation? This paper illustrates how standard results in linear programming play a role in the analysis of mechanism design problems. It is not a comprehensive survey. Rather, it focuses on two variations of a particular problem: the allocation of a single object.     

The steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.     

Analysis of heuristics for the design of tree networks

We analyze the tour partitioning heuristics for the Capacitated Minimum Spanning Tree problem. Lower bounds for the worst-case performance ratios of these heuristics are obtained by using worst-case examples. We also generalize the heuristics to the multi-center case with the same worst-case bounds.The work of the first author was supported by a Dean Summer Research Grant from Owen Graduate School of Management, Vanderbilt University.Work done in part in the Department of Industrial Engineering and Operations Research at Columbia University.The work of the last two authors was supported in part by ONR contract N00014-90-J-1649, NSF contract DDM-8922712 and the Center for Telecommunications Research under NSF contract CDR 84-21402.     

Invariant tracking control design via integrator backstepping

A tracking control problem for systems in state representation possessing a Lie symmetry group G is considered. By designing an invariant feedback control law based on invariant tracking errors the symmetry group G can be preserved under feedback. An extension of this approach to the popular integrator backstepping design method is presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating the number of undetected software errors via the correlated capture–recapture model

Sometimes a complex software system fails because of errors undiscovered in the design stage of the development process. Detecting these errors early in the process would eliminate many downstream problems. The so-called “capture–recapture” model, initially used by biologists to estimate the size of wildlife populations, has been widely used to estimate the number of software design errors. However, one simplifying assumption in capture–recapture models is that the inspections performed by various inspectors are statistically independent from each other. In the paper, we propose a novel method that is based on the correlation matrix of multiple inspectors. In a numerical analysis, we show that our method outperforms other traditional models that are based on the independence assumption.     

Key design parameters and optimal design of a five-point double-toggle clamping mechanism

The toggle mechanism is highly efficient and yields excellent results; it is widely in the clamping units of injection-molding machines. This work explores the effect of key design parameters – the speed profile of the moving platen, the stroke of the clamping hydraulic cylinder and mold-opening, the ration of force amplification, and the initial angle of mold-closing on the performance of a five-point double-toggle clamping mechanism, drawing on a newly developed formulation of motion. The genetic algorithm (GA) is adopted to obtain the optimal solution of a clamping mechanism with reference to the key design parameters. Finally, the results of the primary mechanism are compared with those obtained using the optimal GA design and the GA design method is found to outperform the motion characteristics.     

Synchronization of generalized Henon map via backstepping design

This paper proposes a backstepping method to resolve the synchronization of discrete-time chaotic systems. The proposed scheme offers systematic design method for the synchronization of a class of discrete-time hyper-chaotic systems, which implies much complicated high-order chaotic systems can be used to improve the security in chaos communications. A well-known chaotic systems: generalized Henon map is considered as illustrative example to demonstrate the general applicability of backstepping design. Numerical simulations verify the effectiveness of the approach.     

Management of food-chain systems via Liapunov design control

A general food-chain system involving control is considered. A Liapunov design methodology is used to establish a control growth policy of qualitative nature, aimed to restrict the fluctuations of the size of the chain elements (populations, consumers, resources). The policy is based on the concept of avoidance control.Invited talk at 14 Symposium on Operations Research, Ulm, September 1989.     

Modelling and design optimization of textiles via homogenization

This article deals with optimization of large structures of linear elastic material with contact modeled by Robin-type boundary conditions. Homogenization is used to represent the structures as homogenous elastic bodies and is essential for formulation of the optimization problems, where optimization of the effective properties is considered. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion

Mathematical Programming - Clique tree conversion solves large-scale semidefinite programs by splitting an $$ntimes n$$ matrix variable into up to n smaller matrix variables, each representing a...     

Homothetic vector fields of LRS Bianchi type-I spacetimes via the RIF tree approach

Theoretical and Mathematical Physics - We adopt a new approach to the study of homothetic vector fields of locally rotationally symmetric Bianchi type- I spacetimes. The obtained results are...