251 research outputs found
Multi-objective Evolutionary Algorithms are Still Good: Maximizing Monotone Approximately Submodular Minus Modular Functions
As evolutionary algorithms (EAs) are general-purpose optimization algorithms,
recent theoretical studies have tried to analyze their performance for solving
general problem classes, with the goal of providing a general theoretical
explanation of the behavior of EAs. Particularly, a simple multi-objective EA,
i.e., GSEMO, has been shown to be able to achieve good polynomial-time
approximation guarantees for submodular optimization, where the objective
function is only required to satisfy some properties but without explicit
formulation. Submodular optimization has wide applications in diverse areas,
and previous studies have considered the cases where the objective functions
are monotone submodular, monotone non-submodular, or non-monotone submodular.
To complement this line of research, this paper studies the problem class of
maximizing monotone approximately submodular minus modular functions (i.e.,
) with a size constraint, where is a non-negative monotone
approximately submodular function and is a non-negative modular function,
resulting in the objective function being non-monotone non-submodular. We
prove that the GSEMO can achieve the best-known polynomial-time approximation
guarantee. Empirical studies on the applications of Bayesian experimental
design and directed vertex cover show the excellent performance of the GSEMO
Interactive Camera Network Design using a Virtual Reality Interface
Traditional literature on camera network design focuses on constructing
automated algorithms. These require problem specific input from experts in
order to produce their output. The nature of the required input is highly
unintuitive leading to an unpractical workflow for human operators. In this
work we focus on developing a virtual reality user interface allowing human
operators to manually design camera networks in an intuitive manner. From real
world practical examples we conclude that the camera networks designed using
this interface are highly competitive with, or superior to those generated by
automated algorithms, but the associated workflow is much more intuitive and
simple. The competitiveness of the human-generated camera networks is
remarkable because the structure of the optimization problem is a well known
combinatorial NP-hard problem. These results indicate that human operators can
be used in challenging geometrical combinatorial optimization problems given an
intuitive visualization of the problem.Comment: 11 pages, 8 figure
Parameterized Complexity Analysis of Randomized Search Heuristics
This chapter compiles a number of results that apply the theory of
parameterized algorithmics to the running-time analysis of randomized search
heuristics such as evolutionary algorithms. The parameterized approach
articulates the running time of algorithms solving combinatorial problems in
finer detail than traditional approaches from classical complexity theory. We
outline the main results and proof techniques for a collection of randomized
search heuristics tasked to solve NP-hard combinatorial optimization problems
such as finding a minimum vertex cover in a graph, finding a maximum leaf
spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of
Evolutionary Computation: Recent Developments in Discrete Optimization",
edited by Benjamin Doerr and Frank Neumann, published by Springe
Maximum n-times Coverage for Vaccine Design
We introduce the maximum -times coverage problem that selects overlays
to maximize the summed coverage of weighted elements, where each element must
be covered at least times. We also define the min-cost -times coverage
problem where the objective is to select the minimum set of overlays such that
the sum of the weights of elements that are covered at least times is at
least . Maximum -times coverage is a generalization of the multi-set
multi-cover problem, is NP-complete, and is not submodular. We introduce two
new practical solutions for -times coverage based on integer linear
programming and sequential greedy optimization. We show that maximum -times
coverage is a natural way to frame peptide vaccine design, and find that it
produces a pan-strain COVID-19 vaccine design that is superior to 29 other
published designs in predicted population coverage and the expected number of
peptides displayed by each individual's HLA molecules.Comment: 10 pages, 5 figure
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