Abstract: Important progress has been made by many researchers in extracting fundamental designprinciples from patterns in design parameters along the nondominated front generated by evolutionary algorithms in biobjective optimization problems. However, to the best of our knowledge, no attention has been given to discovering design principles from the wealth of additional information available from patterns in dominated solutions. To explore the same, we use heatmaps of dominated solutions to visualize how relevant variables self-organize with respect to the objectives throughout the feasible region. We overlay ceteris paribus lines on these heatmaps to show how the objective values change when a given design variable is varied while all others are held constant. We use three biobjective optimization problems to demonstrate various ways in which these visualization techniques can provide additional useful information beyond that which can be determined from the nondominated front. Specically, we investigate a simple two-member truss design problem, a simple welded beam design problem, and a real-world watershed management design problem to illustrate: 1) how principles derived from the nondominated front alone can be misleading; 2) how new principles can be derived from the dominated solutions; and 3) how nondominated solutions can often be fragile with respect to assumptions about uncertain external forcing conditions, whereas solutions a short distance inside the front are often much more robust.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).