Models of social contagion

This paper argues that social choice from among more than two feasible alternatives should not be based on social choice from two‐alternative subsets. It considers in some detail the case where one alternative ties or beats every other alternative on the basis of simple majorities, and raises the question of whether such an alternative should be chosen. A condition of ‘stochastic unanimity’, introduced in this context, is shown to be incompatible with the simple majority rule when it can apply. This new condition plus a consideration of ties leads into a brief discussion of the use of individual expected utility in social choice theory.     

Optimal control of impulsive switched systems with minimum subsystem durations

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations.     

Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling

Simulated computer experiments have become a viable cost-effective alternative for controlled real-life experiments. However, the simulation of complex systems with multiple input and output parameters can be a very time-consuming process. Many of these high-fidelity simulators need minutes, hours or even days to perform one simulation. The goal of global surrogate modeling is to create an approximation model that mimics the original simulator, based on a limited number of expensive simulations, but can be evaluated much faster. The set of simulations performed to create this model is called the experimental design. Traditionally, one-shot designs such as the Latin hypercube and factorial design are used, and all simulations are performed before the first model is built. In order to reduce the number of simulations needed to achieve the desired accuracy, sequential design methods can be employed. These methods generate the samples for the experimental design one by one, without knowing the total number of samples in advance. In this paper, the authors perform an extensive study of new and state-of-the-art space-filling sequential design methods. It is shown that the new sequential methods proposed in this paper produce results comparable to the best one-shot experimental designs available right now.     

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.     

A note on weighing designs

Summary Banerjee [1], [2] has shown that the arrangements afforded by a Balanced Incomplete Block Design can be used as an efficient spring balance design. Such designs suffer from one drawback viz., there are only a few or no degrees of freedom left for the estimation of error-variance,σ ². To overcome this difficulty, it has been suggested that the whole design may be repeated a certain number of times to get an estimate of the error variance. In the present note an attempt has been made to give an alternative design where there is no necessity of such repetition. It has been also shown that these designs give a lesser variance of the estimated weights than the repeated design. Institute of Agricultural Research Statistics     

Compatibility of conditionally specified models

A conditionally specified joint model is convenient to use in fields such as spatial data modeling, Gibbs sampling, and missing data imputation. One potential problem with such an approach is that the conditionally specified models may be incompatible, which can lead to serious problems in applications. We propose an odds ratio representation of a joint density to study the issue and derive conditions under which conditionally specified distributions are compatible and yield a joint distribution. Our conditions are the simplest to verify compared with those proposed in the literature. The proposal also explicitly constructs joint densities that are fully compatible with the conditionally specified densities when the conditional densities are compatible, and partially compatible with the conditional densities when they are incompatible. The construction result is then applied to checking the compatibility of the conditionally specified models. Ways to modify the conditionally specified models based on the construction of the joint models are also discussed when the conditionally specified models are incompatible.     

Quadrature Methods for Bayesian Optimal Design of Experiments With Nonnormal Prior Distributions

Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for nonnormal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients, and any other parameters that are strictly positive or have upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well. Supplementary materials for this article are available online.     

Imprimitive flag-transitive symmetric designs

A recent paper of O'Reilly Regueiro obtained an explicit upper bound on the number of points of a flag-transitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of these parameter sequences.     

A dual local search framework for combinatorial optimization problems with TSP application

In practice, solving realistically sized combinatorial optimization problems to optimality is often too time-consuming to be affordable; therefore, heuristics are typically implemented within most applications software. A specific category of heuristics has attracted considerable attention, namely local search methods. Most local search methods are primal in nature; that is, they start the search with a feasible solution and explore the feasible space for better feasible solutions. In this research, we propose a dual local search method and customize it to solve the traveling salesman problem (TSP); that is, a search method that starts with an infeasible solution, explores the dual space—each time reducing infeasibility, and lands in the primal space to deliver a feasible solution. The proposed design aims to replicate the designs of optimal solution methodologies in a heuristic way. To be more specific, we solve a combinatorial relaxation of a TSP formulation, design a neighborhood structure to repair such an infeasible starting solution, and improve components of intermediate dual solutions locally. Sample-based evidence along with statistically significant t-tests support the superiority of this dual design compared to its primal design counterpart.     

Scheduling flexible machining and assembly systems

Most scheduling papers consider flexible machining and assembly systems as being independent. In this paper, a heuristic two-level scheduling algorithm for a system consisting of a machining and an assembly subsystem is developed. It is shown that the upper level problem is equivalent to the two machine flow shop problem. The algorithm at the lower level schedules jobs according to the established product and part priorities. Related issues, such as batching, due dates, process planning and alternative routes, are discussed. The algorithm and associated concepts are illustrated on a number of numerical examples.     

Towards governance on noise between municipality and terminal operator by the use of simulation modelling

The development of multimodal transport terminals in urban areas generates various serious environmental problems. The available tools for the analyses of the use of such terminals offer insufficient support for decision-making on the location and design of these terminals from the sustainability perspective. New approaches are needed. This article contributes to satisfy this need, triggered by the planning of a new Barge Terminal in the Dutch city of Tilburg (BTT). Presently, the existing terminal in Tilburg is operating near full capacity and the construction of a new terminal is considered the best strategy to cope with steady growth. The main question concerns the optimal design of the new barge terminal to offer a high operational performance, however without exceeding the environmental quality standards, in particular noise. The article presents a simulation approach to assist in the process of finding a balance between the operational performance and the noise effects of alternative designs of the new terminal.     

Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.     

On 2-(45, 12, 3) designs

Under the assumption that the incidence matrix of a 2-(45, 12, 3) design has a certain block structure, we determine completely the number of nonisomorphic designs involved. We discover 1136 such designs with trivial automorphism group. In addition we analyze all 2-(45, 12, 3) designs having an automorphism of order 5 or 11. Altogether, the total number of nonisomorphic 2-(45, 12, 3) designs found in 3752. Many of these designs are self-dual and each of these self-dual designs possess a polarity. Some have polarities with no absolute points, giving rise to strongly regular (45, 12, 3, 3) graphs. In total we discovered 58 pairwise nonisomorphic strongly regular graphs, one of which has a trivial automorphism group. Further, we analyzed completely all the designs for subdesigns with parameters 2-(12, 4, 3), 2-(9, 3, 3), and 2-(5, 4, 3). In the first case, the number of 2-(12, 4, 3) subdesigns that a design possessed, if non-zero, turned out to be a multiple of 3, whereas 2-(9, 3, 3) subdesigns were so abundant it was more unusual to find a design without them. Finally, in the case of 2-(5, 4, 3) subdesigns there is a design, unique amongst the ones discovered, that has precisely 9 such subdesigns and these form a partition of the point set of the design. This design has a transitive group of automorphisms of order 360. © 1996 John Wiley & Sons, Inc.     

LP extreme points and cuts for the fixed-charge network design problem

Many design decisions in transporation, communication, and manufacturing planning can be modeled as problems of routing multiple commodities between various origin and destination nodes of a directed network. Each arc of the network is uncapacitated and carries a fixed charge as well as a cost per unit of flow. We refer to the general problem of selecting a subset of arcs and routing the required multi-commodity flows along the chosen arcs at a minimum total cost as the fixed charge network design problem. This paper focuses on strenghthening the linear programming relaxation of a path-flow formulation for this problem. The considerable success achieved by researchers in solving many related design problems with algorithms that use strong linear programming-based lower bounds motivates this study. We first develop a convenient characterization of fractional extreme points for the network design linear programming relaxation. An auxiliary graph introduced for this characterization also serves to generate two families of cuts that exclude some fractional solutions without eliminating any feasible integer solutions. We discuss a separation procedure for one class of inequalities and demonstrate that many of our results generalize known properties of the plant location problem. Supported in part by grant number ECS-831-6224 of the National Science Foundation.     

A pathsearch damped Newton method for computing general equilibria

Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearch damped Newton method for solving such problems. Our algorithm improves on the typical Newton method (which generates and solves a sequence of LCPs) in both speed and robustness. The underlying complementarity problem is reformulated as a normal map so that standard algorithmic enhancements of Newton's method for solving nonlinear equations can be easily applied. The solver is implemented as a GAMS subsystem, using an interface library developed for this purpose. Computational results obtained from a number of test problems arising in economics are given.This material is based on research supported by the National Science Foundation Grant CCR-9157632 and the Air Force Office of Scientific Research Grant F49620-94-1-0036.     

A robustness approach to uncapacitated network design problems

In this paper, we address uncapacitated network design problems characterised by uncertainty in the input data. Network design choices have a determinant impact on the effectiveness of the system. Design decisions are frequently made with a great degree of uncertainty about the conditions under which the system will be required to operate. Instead of finding optimal designs for a given future scenario, designers often search for network configurations that are “good” for a variety of likely future scenarios. This approach is referred to as the “robustness” approach to system design. We present a formal definition of “robustness” for the uncapacitated network design problem, and develop algorithms aimed at finding robust network designs. These algorithms are adaptations of the Benders decomposition methodology that are tailored so they can efficiently identify robust network designs. We tested the proposed algorithms on a set of randomly generated problems. Our computational experiments showed two important properties. First, robust solutions are abundant in uncapacitated network design problems, and second, the proposed algorithms performance is satisfactory in terms of cost and number of robust network designs obtained.     

Multiple orders per job batch scheduling with incompatible jobs

The multiple orders per job (MOJ) scheduling problem is presented for the batch-processing environment such as that exemplified by diffusion ovens. A mixed-integer programming formulation is presented for the incompatible job family case wherein only jobs that belong to the same family may be grouped together in a production batch. This optimization formulation is tested through an extensive experimental design with the objective of minimizing total weighted tardiness (maximizing on-time delivery performance). Optimal solutions are achievable for this initial set of 6-to-12 order problems, but it is noted that the optimization model takes an unreasonable amount of computation time, which suggests the need for heuristic development to support the analysis of larger, more practical MOJ batch scheduling problems. A number of simple heuristic approaches are investigated in an attempt to find near-optimal solutions in a reasonable amount of computation time. It is seen that a combination of the heuristics produces near-optimal solutions for small order problems. Further testing proves that these heuristic combinations are the best for large order problems as well.     

Higher and lower-level knowledge discovery from Pareto-optimal sets

Innovization (innovation through optimization) is a relatively new concept in the field of multi-objective engineering design optimization. It involves the use of Pareto-optimal solutions of a problem to unveil hidden mathematical relationships between variables, objectives and constraint functions. The obtained relationships can be thought of as essential properties that make a feasible solution Pareto-optimal. This paper proposes two major extensions to innovization, namely higher-level innovization and lower-level innovization. While the former deals with the discovery of common features among solutions from different Pareto-optimal fronts, the latter concerns features commonly occurring among solutions that belong to a specified (or preferred) part of the Pareto-optimal front. The knowledge of such lower-level information is extremely beneficial to a decision maker, since it focuses on a preferred set of designs. On the other hand, higher-level innovization reveals interesting knowledge about the general problem structure. Neither of these crucial aspects concerning multi-objective designs has been addressed before, to the authors’ knowledge. We develop methodologies for handling both levels of innovization by extending the authors’ earlier automated innovization algorithm and apply them to two well-known engineering design problems. Results demonstrate that the proposed methodologies are generic and are ready to be applied to other engineering design problems.