Abstract: For the past 25 years, NK landscapes have been the classic benchmarks for modeling combinatorial fitness landscapes with epistatic interactions between up to K+1 of N binary features. However, the ruggedness of NK landscapes grows in large discrete jumps as K increases, and computing the global optimum of unrestricted NK landscapes is an NP-complete problem. Walsh polynomials are a superset of NK landscapes that solve some of the problems. In this paper, we propose a new class of benchmarks called NM landscapes, where M refers to the Maximum order of epistatic interactions between N features. NM landscapes are much more smoothly tunable in ruggedness than NK landscapes and the location and value of the global optima are trivially known. For a subset of NM landscapes the location and magnitude of global minima are also easily computed, enabling proper normalization of fitnesses. NM landscapes are simpler than Walsh polynomials and can be used with alphabets of any arity, from binary to real-valued. We discuss several advantages of NM landscapes over NK landscapes and Walsh polynomials as benchmark problems for evaluating search strategies.
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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).