47 research outputs found

    Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

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    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

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    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

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    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

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    Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter qq, 0<q<10{<}q{<}1. 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 qq cannot be optimal for any other value of qq. This is in sharp contrast to the one-dimensional case, where codes are optimal for positive-length intervals of the parameter qq. Thus, in the two-dimensional case, it is infeasible to give a compact characterization of optimal codes for all values of the parameter qq, as was done in the one-dimensional case. Instead, optimal codes are characterized for a discrete sequence of values of qq that provide good coverage of the unit interval. Specifically, optimal prefix codes are described for q=21/kq=2^{-1/k} (k1k\ge 1), covering the range q1/2q\ge 1/2, and q=2kq=2^{-k} (k>1k>1), covering the range q<1/2q<1/2. 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

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    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

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    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

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    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

    Annales Mathematicae et Informaticae (44.)

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