Charles H. Reilly

Simulift: a simulation model of human trunk motion

In this paper, the authors present a deterministic simulation model, which they call Simulift, of trunk-muscle activity and intra-abdominal pressure during a sagittally symmetric trunk exertion. Simulift is a descriptive model that quantifies the time-varying loading of the spine based on observed internal forces. Recent findings about the time sequence of events during trunk motion and established equilibrium formulas provide the theoretical bases for the simulation. A profile of electromyographic activity in ten trunk muscles and intra-abdominal pressure is updated as simulated time passes, or as the trunk motion is simulated. Input to the model includes a list of motion-event times and a set of profile-component-behavior data. Simulift is an “impulse” model that computes instantaneous and time-integrated statistics on individual muscle activity, intra-abdominal pressure, compression, lateral shear, and anterior shear as the profile components of the simulated subject change. Computer results for the simulation model are presented.

Networks of internal trunk-loading activities under controlled trunk-motion conditions.

Many attempts have been made to describe the activity of the internal trunk-loading components (muscles and intra-abdominal pressure) in response to external forces acting on the trunk, as is often the case in the workplace. Most models that describe the activity of these internal components are static and do not consider the time series of events that occurs during performance of a task under dynamic conditions. This research has investigated the time sequence activity of ten trunk muscles and intra-abdominal pressure in ten males as they produced sagittally symmetric maximum trunk extension motions (lifting motions) at different velocities. These exertions include an isometric exertion and isokinetic exertions equal to 25, 50, 75 and 100% of a subjects maximum extension velocity. Several event times were noted for each internal trunk-loading component, and hypothesis tests were performed to determine which of these event times were statistically different from each other under the various motion conditions. This information was used to construct networks of internal trunk-loading activities under the various motion conditions. Time-series events that occur under all conditions, as well as those that changed as a function of velocity, have been identified. This information will be useful for the construction of dynamic internal trunk models, and will facilitate the assessment of dynamic loading of the lumbar spine in the workplace.

Efficient multinomial selection in simulation

Abstract : This report considers a simulation experiment consisting of v independent vector observations or replications across k systems, where in any given replication one and only one system is selected as the best performer (i.e., it wins) based on some performance measure. Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM), prescribes a minimum number of replications, denoted as V*, 50 that the probability of correctly selecting the true best system meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system.

Composition for multivariate random variables

We show how to find mixing probabilities, or weights, for composite probability mass functions (pmfs) for k-variate discrete random variables with specified marginal pmfs and a specified, feasible population correlation structure. We characterize a joint pmf that is a composition, or mixture, of 2/sup k-1/ extreme correlation joint pmfs and the joint pmf under independence. Our composition method is also valid for multivariate continuous random variables. We consider the cases where all of the marginal distributions are discrete uniform, negative exponential, or continuous uniform.

Optimization test problems with uniformly distributed coefficients

When an empirical evaluation of a solution method for an optimization problem is conducted, a standard approach is to generate test problems in which all of the coefficients are assumed to be independently and uniformly distributed. However, the performance of algorithms and heuristics can degrade as the correlation among the coefficients in integer programming test problems is strengthened. The author shows how to characterize the joint distribution of two discrete uniform random variables with any feasible correlation and any feasible value for the smallest joint probability when the number of possible values of one random variable is a multiple of the number of possible values of the other. This characterization is used in an experiment with randomly generated 0-1 knapsack problems, and the results of the experiment are summarized.<<ETX>>

Synthetic Optimization Problem Generation: Show Us the Correlations!

In many computational experiments, correlation is induced between certain types of coefficients in synthetic (or simulated) instances of classical optimization problems. Typically, the correlations that are induced are only qualified---that is, described by their presumed intensity. We quantify the population correlations induced under several strategies for simulating 0--1 knapsack problem instances and also for correlation-induction approaches used to simulate instances of the generalized assignment, capital budgeting (or multidimensional knapsack), and set-covering problems. We discuss implications of these correlation-induction methods for previous and future computational experiments on simulated optimization problems.

An investigation of the relationship between problem characteristics and algorithm performance: a case study of the GAP

Abstract We compare synthetic Generalized Assignment Problems (GAP) generated under two correlation-induction strategics: Implicit Correlation Induction (ICI) and Explicit Correlation Induction (ECI). We present computational results for two commercially-available solvers and four heuristics on 590 test problems. We conclude that the solvers’ performances degrade as the population correlation between the objective function and capacity constraint coefficients decreases. However, the heuristics’ performances improved as the absolute value of the same population correlation increases. We find that problems generated under ECI arc more challenging than problems generated under ICI and may lead to a better understanding of the capabilities and limitations of the solution methods being evaluated. We recommend that one consider the purpose(s) of an experiment and types of solution procedures to be evaluated when determining what types of test problems to generate.

Exploiting empirical knowledge for bi-dimensional knapsack problem heuristics

The Multidimensional Knapsack Problem (MKP) has been used to model a variety of practical applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. There have been a variety of heuristics proposed for MKP and a plethora of empirical studies comparing the performance of these heuristics. However, little has been done to garner a deeper understanding of why certain heuristics perform well on certain types of problems and others do not. Using a broad range of practical MKP test problems, we use three representative heuristics and conduct an empirical study aimed at gaining a deeper understanding of heuristic procedure performance as a function of test problem constraint characteristics. Our focus is on the Two-dimensional Knapsack Problem (2KP). New insights developed regarding greedy heuristic performance are exploited to yield two new heuristics whose performance is more robust than that of three legacy heuristics on our test problem set and on benchmark sets of MKP problems. A competitive test of these new heuristics against a set of legacy heuristics, using both existing test problem sets and a new systematically developed test problem set demonstrate the superior, robust performance of our new heuristics.

Generating coefficients for optimization test problems with implicit correlation induction

We consider methods for inducing correlation between the objective function and constraint coefficients in 0-1 Knapsack, generalized assignment, capital budgeting, and set covering problems. Each of the methods that we examine is an implicit correlation-induction (ICI) method that has been featured in the literature. However, the correlation levels used in the corresponding computational experiments are typically neither quantified nor systematically controlled. We present closed-form expressions for the population correlation levels induced with the ICI methods to facilitate the quantification and systematic control of the correlation levels in computational experiments. We also discuss the advantages and disadvantages of ICI methods.

Properties of synthetic optimization problems

We present an approach for measuring certain properties of synthetic optimization problems based on the assumed distribution of coefficient values. We show how to estimate the proportion of all possible solutions that are feasible for the 0-1 Knapsack Problem. We calculate the population variance of the possible solution values and assess the impact of objective constraint correlation on the variability of feasible solution values. We also show how inter-constraint correlation affects the proportion of feasible solutions in the 2-dimensional Knapsack Problem. Finally, we discuss the significance of our findings for designers of computational experiments.