Forrest Stonedahl

Evolving viral marketing strategies

One method of viral marketing involves seeding certain consumers within a population to encourage faster adoption of the product throughout the entire population. However, determining how many and which consumers within a particular social network should be seeded to maximize adoption is challenging. We define a strategy space for consumer seeding by weighting a combination of network characteristics such as average path length, clustering coefficient, and degree. We measure strategy effectiveness by simulating adoption on a Bass-like agent-based model, with five different social network structures: four classic theoretical models (random, lattice, small-world, and preferential attachment) and one empirical (extracted from Twitter friendship data). To discover good seeding strategies, we have developed a new tool, called BehaviorSearch, which uses genetic algorithms to search through the parameter-space of agent-based models. This evolutionary search also provides insight into the interaction between strategies and network structure. Our results show that one simple strategy (ranking by node degree) is near-optimal for the four theoretical networks, but that a more nuanced strategy performs significantly better on the empirical Twitter-based network. We also find a correlation between the optimal seeding budget for a network, and the inequality of the degree distribution.

Finding forms of flocking: evolutionary search in ABM parameter-spaces

While agent-based models (ABMs) are becoming increasingly popular for simulating complex and emergent phenomena in many fields, understanding and analyzing ABMs poses considerable challenges. ABM behavior often depends on many model parameters, and the task of exploring a models parameter space and discovering the impact of different parameter settings can be difficult and time-consuming. Exhaustively running the model with all combinations of parameter settings is generally infeasible, but judging behavior by varying one parameter at a time risks overlooking complex nonlinear interactions between parameters. Alternatively, we present a case study in computer-aided model exploration, demonstrating how evolutionary search algorithms can be used to probe for several qualitative behaviors (convergence, non-convergence, volatility, and the formation of vee shapes) in two different flocking models. We also introduce a new software tool (BehaviorSearch) for performing parameter search on ABMs created in the NetLogo modeling environment.

CrossNet: a framework for crossover with network-based chromosomal representations

We propose a new class of crossover operators for genetic algorithms (CrossNet) which use a network-based (or graph-based) chromosomal representation. We designed CrossNet with the intent of providing a framework for creating crossover operators that take advantage of domain-specific knowledge for solving problems. Specifically, GA users supply a network which defines the epistatic relationships between genes in the genotype. CrossNet-based crossover uses this information with the goal of improving linkage. We performed two experiments that compared CrossNet-based crossover with one-point and uniform crossover. The first experiment involved the density classification problem for cellular automata (CA), and the second experiment involved fitting two randomly generated hyperplane-defined functions (hdfs). Both of these exploratory experiments support the hypothesis that CrossNet-based crossover can be useful, although performance improvements were modest. We discuss the results and remain hopeful about the successful application of CrossNet to other domains. We conjecture that future work with the CrossNet framework will provide a useful new perspective for investigating linkage and chromosomal representations.

When Does Simulated Data Match Real Data? Comparing Model Calibration Functions Using Genetic Algorithms

Agent-based models can be manipulated to replicate real- world datasets, but choosing the best set of parameters to achieve this result can be difficult. To validate a model, the real-world dataset is often divided into a training and test set. The training set is used to calibrate the parameters and the test set is used to determine if the calibrated model represents the real-world data. The difference between the real-world data and the simulated data is determined using an error measure. When using an evolutionary computation technique to choose the parameters, this error measure becomes the fitness function, and choosing the appropriate measure becomes even more crucial for a successful calibration process. We survey the effect of five different error measures in the context of a toy problem and a real world problem (simulating on-line news consumption). We use each error measure in turn to calibrate on the training dataset, and then examine the results of all five error measures on both the training and testing datasets. For the toy problem, one measure was the Pareto-dominant choice for calibration, but no error measure dominated all the others for the real-world problem.

Spatial Competition with Interacting Agents

We generalize Hotelling’s model of spatial competition with more than two firms in a two-dimensional space. Firms choose both price and location to maximize profits. The principle of minimum differentiation does not hold in general. Local duopolies emerge from the interaction between firms. Firms do not spread uniformly across the two-dimensional space, nor do they all charge the same price. Firms in more competitive locations charge lower prices. More product attributes produce more price competition.Using agent-based modeling, we generalize Hotelling?s model of spatial competition with more than two firms in a two-dimensional space. Firms choose both price and location to maximize profits. The principle of minimum differentiation does not hold in general. Local duopolies emerge from the interaction betweenfirms. Firms do not spread uniformly across the two-dimensional space, nor do they all charge the same price. Firms in more competitive locations charge lower prices and generate less profit.

When does simulated data match real data

Agent-based models can replicate real-world patterns, but finding parameters that achieve the best match can be difficult. To validate a model, a real-world dataset is often divided into a training set (to calibrate the parameters) and a test set (to validate the calibrated model). The difference between the training and test data and the simulated data is determined using an error measure. In the context of evolutionary computation techniques, the error measure also serves as a fitness function, and thus affects evolutionary search dynamics. We survey the effect of five different error measures on both a toy problem and a real world problem of matching a model to empirical online news consumption behavior. We use each error measure separately for calibration on the training dataset, and then examine the results of all five error measures on both the training and testing datasets. We show that certain error measures sometimes serve as better fitness functions than others, and in fact using one error measure may result in better calibration (on a different measure) than using the different measure directly. For the toy problem, the Pearsons correlation measure dominated all other measures, but no single error measure was Pareto dominant for the real world problem.

Effect of Heterogeneous Sediment Distributions on Hyporheic Flow in Physical and Numerical Models: S.H. Stonedahl et al. Groundwater x, no. x: x-xx

Variations in permeability have been found to significantly affect the flow of water though hyporheic systems, especially in regions with discontinuous transitions between distinct streambed lithologies. In this study, we probabilistically arranged two sediments (sand and sandy gravel) in a grid framework and imposed a single hyporheic flow cell across the grid to investigate how discontinuous permeability fields influence volumetric flow and residence time distributions. We used both a physical system and computer simulations to model flow through this sediment grid. A solution of blue dye and salt was pumped into the system and used to detect flow. We recorded the dye location using time-lapse photography and measured the electrolytic conductivity levels as the water exited the system as a proxy for salt concentration. We also used a computer simulation to calculate dye-fronts, residence times, and exiting salt concentrations for the modeled system. Comparison between simulations and physical measurements yielded strong agreement. In further simulations with 300 different grids, we found a strong correlation between volumetric flow rate and the placement of high permeability grid cells in regions of high hydraulic head gradients. One implication is that small anomalies in streambed permeability have a disproportionately large influence on hyporheic flows when located near steep head gradients such as steps. We also used moving averages with varying window sizes to investigate the effect of the abruptness of transitions between sediment types. We found that smoother permeability fields increased the volumetric flow rate and decreased the median residence times.

Novelty and Objective-based Neuroevolution of a Physical Robot Swarm.

This paper compares the use of novelty search and objective-based evolution to discover motion controllers for an exploration task wherein mobile robots search for immobile targets inside a bounded polygonal region and stop to mark target locations. We evolved the robots’ neural-network controllers in a custom 2-D simulator, selected the best performing neurocontrollers from both novelty search and objective-based search, and compared performance relative to an unevolved (baseline) controller and a simple human-designed controller. The controllers were also transferred onto physical robots, and the real-world tests provided good empirical agreement with simulation results, showing that both novelty search and objective-based search produced controllers that were comparable or superior to the human-designed controller, and that objective-based search slightly outperformed novelty search. The best controllers had surprisingly low genotypic complexity, suggesting that this task may lack the type of deceptive fitness landscape that has previously favored novelty search over objective-based search.

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation.

Advective exchange between the pore space of sediments and the overlying water column, called hyporheic exchange in fluvial environments, drives solute transport in rivers and many important biogeochemical processes. To improve understanding of these processes through visual demonstration, we created a hyporheic flow simulation in the multi-agent computer modeling platform NetLogo. The simulation shows virtual tracer flowing through a streambed covered with two-dimensional bedforms. Sediment, flow, and bedform characteristics are used as input variables for the model. We illustrate how these simulations match experimental observations from laboratory flume experiments based on measured input parameters. Dye is injected into the flume sediments to visualize the porewater flow. For comparison virtual tracer particles are placed at the same locations in the simulation. This coupled simulation and lab experiment has been used successfully in undergraduate and graduate laboratories to directly visualize river-porewater interactions and show how physically-based flow simulations can reproduce environmental phenomena. Students took photographs of the bed through the transparent flume walls and compared them to shapes of the dye at the same times in the simulation. This resulted in very similar trends, which allowed the students to better understand both the flow patterns and the mathematical model. The simulations also allow the user to quickly visualize the impact of each input parameter by running multiple simulations. This process can also be used in research applications to illustrate basic processes, relate interfacial fluxes and porewater transport, and support quantitative process-based modeling.