Optimal Noncollapsing Space-Filling Designs for Irregular Experimental Regions

Space-filling and noncollapsing are two important properties in designing computer experiments. We study how the noncollapsing, space-filling designs for irregular experimental regions can be generated efficiently by the proposed metaheuristic methods. We solve this optimal design problem using variants of the discrete particle swarm optimization (DPSO) approaches. Numerical results, including an application in data center thermal management, are used to illustrate the performances of the proposed algorithms. Based on these numerical results, we assert that the most efficient approach is to reformulate the target optimal design problem as a constrained optimization problem and then use a modified DPSO to solve the constrained optimization problem.     

The construction of infinite families of any κ-tight optimal and singular κ-tight optimal directed double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems. Given the number n of nodes, how to construct a DLN which has minimum diameter? This problem has attracted great attention. A related and longtime unsolved problem is: for any given non-negative integer k, is there an infinite family of k-tight optimal DLN? In this paper, two main results are obtained: (1) for any k ≥ 0, the infinite families of k-tight optimal DLN can be constructed, where the number n(k,e,c) of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c. (2) for any k ≥ 0,an infinite family of singular k-tight optimal DLN can be constructed.     

<Emphasis Type="Italic">T</Emphasis>-optimal designs for discrimination between rational and polynomial models

This paper considers the problem of the analytical construction of experimental designs optimal with respect to the popular T-optimality criterion proposed by A.C. Atkinson and V.V. Fedorov in 1975 for discrimination between the simplest rational and polynomial regression models. It is shown how the classical results from approximation theory can be used to derive explicit formulas describing the behavior of support points and weights of T-optimal designs for different fixed parameter values. An applied discrimination problem for rational and polynomial regression models is considered as an example. For this models the numerical construction of experimental designs optimal with respect to robust analogues of T-criterion is also briefly discussed.     

A general framework on the simulation-based optimization under fixed computing budget

In many real world problems, the design space is huge and the estimation of performance measure has to rely on simulation which is time-consuming. Hence, to find the optimal design in the design space based on the simulation output is not trivial. It is important to have a computing time allocation rule to decide how much effort to spend in sampling the design space, how many designs to sample, and how long to run for each design alternative within a given computing budget. In this paper, we propose a framework for making these allocation decisions. We use the problem of assemble-to-order (ATO) systems to demonstrate how this framework can be applied. The sample average approximation (SAA) method is chosen as the sampling method used in this application example. The numerical results show that this framework provides a good basis for allocation decisions.     

An algorithmic approach to finding factorial designs with generalized minimum aberration

Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure.     

Optimal design of LAN-WAN internetworks: An approach using simulated annealing

This paper addresses the problem of designing LAN-WAN (Local Area Network, Wide Area Network) computer networks with transparent bridges. Bridges are high performance devices that are used to interconnect LANs at the MAC (Medium Access Control) level in the protocol hierarchy. LANs in remote areas are connected by leased telecommunications lines such as T1 and DDS. A requirement of transparent bridges is that networks must be configured in a spanning tree topology. We have developed mathematical models of LAN-WAN networks and formulated an optimization problem. This problem is a nonconvex, nonlinear, mixed integer program. A simulated annealing algorithm is proposed. The algorithm generates sequences of neighboring spanning trees and evaluates design constraints based on maximum flow, bridge capacity, and end-to-end delay. As the annealing temperature parameter is lowered the algorithm moves towards the global optimal solution. Experimental results have shown that LAN-WAN designs using simulated annealing are better than 99.99% of all feasible designs.     

Optimal precision in the presence of uncertainty

We consider the problem of achieving coordinated actions in a real-time distributed system. In particular, we consider how closely (in terms of real time) processors can be guaranteed to perform a particular action, in a system where message transmission is guaranteed, but there is some uncertainty in message transmission time. We present an algorithm to achieve optimal precision in arbitrary networks. In networks where clocks run at the rate of real time, the optimal precision achievable in a network is exactly how tightly clocks can be guaranteed to be synchronized.     

Generalized optimal designs and contingency plans in linear systems

To select an optimal linear design means to select the best subset from a set of possible products or opportunities for commitment and to construct the corresponding optimal contingency plans for coping with the changes of decision parameters. Based on Lee, Shi and Yu, this paper discusses a method for generating generalized good designs from known potentially good designs. We describe how to use the multi-criteria and multi-constraint-level (MC²) simplex method to identify the generalized optimal designs and their related optimal contingency plans. A procedure for effectively and systematically solving the problem of selecting linear designs is proposed.     

Optimal paths in bi-attribute networks with fractional cost functions

An important routing problem is to determine an optimal path through a multi-attribute network which minimizes a cost function of path attributes. In this paper, we study an optimal path problem in a bi-attribute network where the cost function for path evaluation is fractional. The problem can be equivalently formulated as the “bi-attribute rational path problem” which is known to be NP-complete. We develop an exact approach to find an optimal simple path through the network when arc attributes are non-negative. The approach uses some path preference structures and elimination techniques to discard, from further consideration, those (partial) paths that cannot be parts of an optimal path. Our extensive computational results demonstrate that the proposed method can find optimal paths for large networks in very attractive times.     

Effective Heuristics for the GPS Survey Network of Malta: Simulated Annealing and Tabu Search Techniques

A GPS network can be defined as a set of stations, co-ordinated by a series of sessions formed by placing receivers on the stations. This paper shows how to search for the best order in which to observe these sessions giving the cheapest schedule. The complexity of observing GPS networks increases with their size and become highly difficult to solve effectively. To obtain good methods to solve this problem a new area of research is implemented. This area is based on developed heuristic techniques that provide an optimal or near optimal solution for large networks. Comparing their outcome in terms of solution quality and computational effort proves the performance of the developed techniques.     

The construction of infinite families of any κ-tight optimal and singular κ-tight optimal directed double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems. Given the number n of nodes, how to construct a DLN which has minimum diameter? This problem has attracted great attention. A related and longtime unsolved problem is for any given non-negative integer k, is there an infinite family of k-tight optimal DLN? In this paper, two main results are obtained (1) for any k ≥ 0, the infinite families of k-tight optimal DLN can be constructed, where the number n(k,e,c) of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c. (2) for any k ≥ 0,an infinite family of singular k-tight optimal DLN can be constructed.     

One-dimensional nested maximin designs

The design of computer experiments is an important step in black-box evaluation and optimization processes. When dealing with multiple black-box functions the need often arises to construct designs for all black boxes jointly, instead of individually. These so-called nested designs are particularly useful as training and test sets for fitting and validating metamodels, respectively. Furthermore, nested designs can be used to deal with linking parameters and sequential evaluations. In this paper, we introduce one-dimensional nested maximin designs. We show how to nest two designs optimally and develop a heuristic to nest three and four designs. These nested maximin designs can be downloaded from the website . Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14.64 and 19.21%, when nesting two and three designs, respectively.     

A generalized activity network model

In recent years activity networks for projects with both random and deterministic alternative outcomes in key nodes have been considered. The developed control algorithm chooses an optimal outcome direction at every deterministic alternative node which is reached in the course of the project's realization. At each routine decision-making node, the algorithm singles out all the subnetworks (the so-called joint variants) which correspond to all possible outcomes from that node. Decision-making results in determining the optimal joint variant and following the optimal direction up to the next decision-making node. However, such models cover a limited class of alternative networks, namely, only fully-divisible networks which can be subdivided into nonintersecting fragments. In this paper, a more generalized activity network is considered. The model can be applied to a broader spectrum of R&D projects and can be used for all types of alternative networks, for example, for non-divisible networks comprising nodes with simultaneously ‘must follow’, random ‘exclusive OR’ and deterministic ‘exclusive or’ emitters. The branching activities of the third type refer to decision-making outcomes; choosing the optimal outcome is the sole prerogative of the project's management. Such a model is a more universal activity network; we will call it GAAN—Generalized Alternative Activity Network. The problem is to determine the joint variant optimizing the mean value of the objective function subject to restricted mean values of several other criteria. We will prove that such a problem is a NP-complete one. Thus, in general, the exact solution of the problem may be obtained only by looking through all the joint variants on the basis of their proper enumeration. To enumerate the joint variants we will use the lexicographical method in combination with some techniques of discrete optimization. A numerical example will be presented. Various application areas are considered.     

Fast simulation of buffer overflows in tandem networks ofGI/GI/1 queues

Simply because of their rarity, the estimation of the statistics of buffer overflows in well-dimensioned queueing networks via direct simulation is extremely costly. One technique that can be used to reduce this cost is importance sampling, and it has been shown previously that large deviations theory can be used in conjunction with importance sampling to minimize the required simulation time. In this paper, we obtain results on the fast simulation of tandem networks of queues, and derive an analytic solution to the problem of finding an optimal simulation system for a class of tandem networks ofGI/GI/1 queues.Work supported by Australian Telecommunications and Electronics Research Board (ATERB). The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program.     

Achieving sharp deliveries in supply chains through variance pool allocation

Variability reduction and business process synchronization are acknowledged as key to achieving sharp and timely deliveries in supply chain networks. In this paper, we develop an approach that facilitates variability reduction and business process synchronization for supply chains in a cost effective way. The approach developed is founded on an analogy between mechanical design tolerancing and supply chain lead time compression. We first present a motivating example to describe this analogy. Next, we define, using process capability indices, a new index of delivery performance called delivery sharpness which, when used with the classical performance index delivery probability, measures the accuracy as well as the precision with which products are delivered to the customers. Following this, we solve the following specific problem: how do we compute the allowable variability in lead time for individual stages of the supply chain so that specified levels of delivery sharpness and delivery probability are achieved in a cost-effective way? We call this the variance pool allocation (VPA) problem. We suggest an efficient heuristic approach for solving the VPA problem and also show that a variety of important supply chain design problems can be posed as instances of the VPA problem. One such problem, which is addressed in this paper, is the supply chain partner selection problem. We formulate and solve the VPA problem for a plastics industry supply chain and demonstrate how the solution can be used to choose the best mix of supply chain partners.     

A parameter-free self-adapting boundary genetic search for pipe network optimization

Commercial application of genetic algorithms (GAs) to engineering design problems, including optimal design of pipe networks, could be facilitated by the development of algorithms that require the least number of parameter tuning. This paper presents an attempt to eliminate the need for defining a priori the proper penalty parameter in GA search for pipe networks optimal designs. The method is based on the assumption that the optimal solution of a pipe network design problem lies somewhere on, or near, the boundary of the feasible region. The proposed method uses the ratio of the best feasible and infeasible designs at each generation to guide the direction of the search towards the boundary of the feasible domain by automatically adjusting the value of the penalty parameter. The value of the ratio greater than unity is interpreted as the search being performed in the feasible region and vice versa. The new adapted value of the penalty parameter at each generation is therefore calculated as the product of its current value and the aforementioned ratio. The genetic search so constructed is shown to converge to the boundary of the feasible region irrespective of the starting value of the constraint violation penalty parameter. The proposed method is described here in the context of pipe network optimisation problems but is equally applicable to any other constrained optimisation problem. The effectiveness of the method is illustrated with a benchmark pipe network optimization example from the literature.     

Cooperative Cross-Entropy method for generating entangled networks

Survivability is rapidly becoming an important criterion in network design and planning. This is due to our increased dependence on ever more complex communication networks. Another important criterion which plays a central role in design and planning decisions is cost. As a result, network planners tend to design sparse networks to minimise cost. There is a class of networks known as entangled networks which seems to satisfy both criteria of survivability and sparseness. In this paper, we demonstrate how the Cross-Entropy method may be utilised to generate entangled networks. We also propose a cooperative optimisation approach to further improve the generation of an optimal entangled network.     

Exact approaches for lifetime maximization in connectivity constrained wireless multi-role sensor networks

In this paper, we consider the duty scheduling of sensor activities in wireless sensor networks to maximize the lifetime. We address full target coverage problems contemplating sensors used for sensing data and transmit it to the base station through multi-hop communication as well as sensors used only for communication purposes. Subsets of sensors (also called covers) are generated. Those covers are able to satisfy the coverage requirements as well as the connection to the base station. Thus, maximum lifetime can be obtained by identifying the optimal covers and allocate them an operation time. The problem is solved through a column generation approach decomposed in a master problem used to allocate the optimal time interval during which covers are used and in a pricing subproblem used to identify the covers leading to maximum lifetime. Additionally, Branch-and-Cut based on Benders’ decomposition and constraint programming approaches are used to solve the pricing subproblem. The approach is tested on randomly generated instances. The computational results demonstrate the efficiency of the proposed approach to solve the maximum network lifetime problem in wireless sensor networks with up to 500 sensors.     

Optimal infrastructure design and expansion of broadband wireless access networks

This paper investigates the important infrastructure design and expansion problem for broadband wireless access networks subject to user demand constraints and system capacity constraints. For the problem, an integer program is derived and a heuristic solution procedure is proposed based on Lagrangean relaxation. In the computational experiments, our Lagrangean relaxation based algorithm can solve this complex design and expansion problem quickly and near optimally. Based on the test results, it is suggested that the proposed algorithm may be practically used for the infrastructure design and expansion problem for broadband wireless access networks.     

Modeling demand management strategies for evacuations

Evacuations are massive operations that create heavy travel demand on road networks some of which are experiencing major congestions even with regular traffic demand. Congestion in traffic networks during evacuations, can be eased either by supply or demand management actions. This study focuses on modeling demand management strategies of optimal departure time, optimal destination choice and optimal zone evacuation scheduling (also known as staggered evacuation) under a given fixed evacuation time assumption. The analytical models are developed for a system optimal dynamic traffic assignment problem, so that their characteristics can be studied to produce insights to be used for large-scale solution algorithms. While the first two strategies were represented in a linear programming (LP) model, evacuation zone scheduling problem inevitable included integers and resulted in a mixed integer LP (MILP) one. The dual of the LP produced an optimal assignment principle, and the nature of the MILP formulations revealed clues about more efficient heuristics. The discussed properties of the models are also supported via numerical results from a hypothetical network example.