47 research outputs found
Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers
In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover
Geometric particle swarm optimization for the sudoku puzzle
Geometric particle swarm optimization (GPSO) is a recently introduced generalization of traditional particle swarm optimization (PSO) that applies to all combinatorial spaces. The aim of this paper is to demonstrate the applicability of GPSO to non-trivial combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as a nontrivial constrained combinatorial problem. We apply GPSO to solve the sudoku puzzle
Decomposition and enumeration in partially ordered sets
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.Includes bibliographical references (p. 123-126).by Patricia Hersh.Ph.D
Optimal prefix codes for pairs of geometrically-distributed random variables
Optimal prefix codes are studied for pairs of independent, integer-valued
symbols emitted by a source with a geometric probability distribution of
parameter , . By encoding pairs of symbols, it is possible to
reduce the redundancy penalty of symbol-by-symbol encoding, while preserving
the simplicity of the encoding and decoding procedures typical of Golomb codes
and their variants. It is shown that optimal codes for these so-called
two-dimensional geometric distributions are \emph{singular}, in the sense that
a prefix code that is optimal for one value of the parameter cannot be
optimal for any other value of . This is in sharp contrast to the
one-dimensional case, where codes are optimal for positive-length intervals of
the parameter . Thus, in the two-dimensional case, it is infeasible to give
a compact characterization of optimal codes for all values of the parameter
, as was done in the one-dimensional case. Instead, optimal codes are
characterized for a discrete sequence of values of that provide good
coverage of the unit interval. Specifically, optimal prefix codes are described
for (), covering the range , and
(), covering the range . The described codes produce the expected
reduction in redundancy with respect to the one-dimensional case, while
maintaining low complexity coding operations.Comment: To appear in IEEE Transactions on Information Theor
EGAC: a genetic algorithm to compare chemical reaction networks
Discovering relations between chemical reaction networks (CRNs)
is a relevant problem in computational systems biology for model
reduction, to explain if a given system can be seen as an abstraction
of another one; and for model comparison, useful to establish an evolutionary
path from simpler networks to more complex ones. This
is also related to foundational issues in computer science regarding
program equivalence, in light of the established interpretation of a
CRN as a kernel programming language for concurrency. Criteria
for deciding if two CRNs can be formally related have been recently
developed, but these require that a candidate mapping be provided.
Automatically finding candidate mappings is very hard in general
since the search space essentially consists of all possible partitions
of a set. In this paper we tackle this problem by developing a genetic
algorithm for a class of CRNs called influence networks, which can
be used to model a variety of biological systems including cell-cycle
switches and gene networks. An extensive numerical evaluation
shows that our approach can successfully establish relations between
influence networks from the literature which cannot be found
by exact algorithms due to their large computational requirements
Prospects for Declarative Mathematical Modeling of Complex Biological Systems
Declarative modeling uses symbolic expressions to represent models. With such
expressions one can formalize high-level mathematical computations on models
that would be difficult or impossible to perform directly on a lower-level
simulation program, in a general-purpose programming language. Examples of such
computations on models include model analysis, relatively general-purpose
model-reduction maps, and the initial phases of model implementation, all of
which should preserve or approximate the mathematical semantics of a complex
biological model. The potential advantages are particularly relevant in the
case of developmental modeling, wherein complex spatial structures exhibit
dynamics at molecular, cellular, and organogenic levels to relate genotype to
multicellular phenotype. Multiscale modeling can benefit from both the
expressive power of declarative modeling languages and the application of model
reduction methods to link models across scale. Based on previous work, here we
define declarative modeling of complex biological systems by defining the
operator algebra semantics of an increasingly powerful series of declarative
modeling languages including reaction-like dynamics of parameterized and
extended objects; we define semantics-preserving implementation and
semantics-approximating model reduction transformations; and we outline a
"meta-hierarchy" for organizing declarative models and the mathematical methods
that can fruitfully manipulate them
Evolutionary optimisation of network flow plans for emergency movement in the built environment
Planning for emergency evacuation, and, more generally, for emergency movement involving
both evacuation (egress) of occupants and ingress of first responders, presents
important and challenging problems. A number of the current issues that arise during
emergency incidents are due to the uncertainty and transiency of environmental conditions.
In general, movement plans are formulated at building design-time, and those
involved, such as building occupants and emergency responders, are left to adapt routing
plans to actual events as they unfold. In the context of next-generation emergency
response systems, it has been proposed to dynamically plan and route individuals during
an emergency event, replanning to take account of changes in the environment.
In this work, an emergency movement problem, the Maximal Safest Escape (MSE)
problem, is formulated in terms that model the uncertain and transient environmental
conditions as a flow problem in time-dependent networks with time-varying and
stochastic edge travel-times and capacities (STV Networks). The objective of the MSE
problem is to find flow patterns with the a priori maximal probability of successfully
conveying all supply from the source to the sink in some given STV Network. The
MSE and its deterministic counterpart are proved to be NP-hard. Furthermore, due to
inherent complexity in evaluating the exact quality of candidate solutions, a simulation
approximation method is presented based on well-known Monte-Carlo sampling
methods.
Given the complexity of the problem, and using the approximation method for evaluating
solutions, it is proposed to tackle the MSE problem using a metaheuristic approach
based on an existing framework that integrates Evolutionary Algorithms (EA)
with a state-of-the-art statistical ranking and selection method, the Optimal Computing
Budget Allocation (OCBA). Several improvements are proposed for the framework to
reduce the computational demand of the ranking method. Empirically, the approach
is compared with a simple fitness averaging approach and conditions under which the
integrated framework is more efficient are investigated. The performance of the EA
is compared against upper and lower bounds on optimal solutions. An upper bound
is established through the “wait-and-see” bound, and a lower bound by a naıve random
search algorithm (RSA). An experimental design is presented that allows for a
fair comparison between the EA and the RSA. While there is no guarantee that the
EA will find optimal solutions, this work demonstrates that the EA can still find useful
solutions; useful solutions are those that are at least better than some baseline, here the
lower bound, in terms of solution quality and computational effort. Experimentally, it is demonstrated that the EA performs significantly better than the baseline. Also, the
EA finds solutions relatively close to the upper bound; however, it is difficult to establish
how optimistic the upper bounds. The main approach is also compared against
an existing approach developed for solving a related problem wrapped in a heuristic
procedure in order to apply the approach to the MSE. Empirical results show that the
heuristic approach requires significantly less computation time, but finds solutions of
significantly lower quality.
Overall, this work introduces and empirically verifies the efficacy of a metaheuristic
based on a framework integrating EAs with a state-of-the-art statistical ranking and
selection technique, the OCBA, for a novel flow problem in STV Networks. It is suggested
that the lessons learned during the course of this work, along with the specific
techniques developed, may be relevant for addressing other flow problems of similar
complexity