Utilization of the discrete differential evolution for optimization in multidimensional point clouds

The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.Web of Scienceart. no. 632953

Modelo de computación evolutivo para redes sostenibles, eficientes y resistentes.

We present a new approach to adapt the differential evolution (DE) algorithm so that it can be applied in combinatorial optimization problems. The differential evolution algorithm has been proposed as an optimization algorithm for the continuous domain, using real numbers to encode the solutions, and its main operator, the mutation, uses a arithmetic operations to create a mutant using three different random solutions. This mutation operator cannot be used in combinatorial optimization problems, which have a domain of a discrete and finite set of objects. Based on this concept, we present an idea of representing each solution as a set, and replace the arithmetic operators in the classic DE genetic operators by set operators. Using a well known NP-hard problem, the traveling salesman problem (TSP), as an example of a combinatorial optimization problem, we study different possibilities for the mutation operator, presenting the advantages and disadvantages of each, before setting with the best one. We also explain the modifications made to adapt the algorithm for a multiobjective optimization algorithm. Some of these modifications are inherent to the different type of problems, other modification are proposed to improve the algorithm. Amongst the later modification are using more than one population in the evolution process. We also present a new self-adaptive variation of the multiobjective optimization algorithm, although this is not limited to the multi-objective case, and can be used also in the single-objective

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

International audienceABSTRACT: Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. BACKGROUND: There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. RESULTS: Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. CONCLUSIONS: Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations

Modified constrained differential evolution for solving nonlinear global optimization problems

Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolution has shown to be very efficient when solving global optimization problems with simple bounds. In this paper, we propose a modified constrained differential evolution based on different constraints handling techniques, namely, feasibility and dominance rules, stochastic ranking and global competitive ranking and compare their performances on a benchmark set of problems. A comparison with other solution methods available in literature is also provided. The convergence behavior of the algorithm to handle discrete and integer variables is analyzed using four well-known mixed-integer engineering design problems. It is shown that our method is rather effective when solving nonlinear optimization problems.Fundação para a Ciência e a Tecnologia (FCT

Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper,we address the practical testing of aheuristic-based FA (HBFA) for computing optimaof discrete nonlinear optimization problems,where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid ‘erf’ function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid ‘erf’ function with ‘movements in continuous space’ is the best, both in terms of computational requirements and accuracy.Fundação para a Ciência e a Tecnologia (FCT

Set-Based Adaptive Distributed Differential Evolution for Anonymity-Driven Database Fragmentation

By breaking sensitive associations between attributes, database fragmentation can protect the privacy of outsourced data storage. Database fragmentation algorithms need prior knowledge of sensitive associations in the tackled database and set it as the optimization objective. Thus, the effectiveness of these algorithms is limited by prior knowledge. Inspired by the anonymity degree measurement in anonymity techniques such as k-anonymity, an anonymity-driven database fragmentation problem is defined in this paper. For this problem, a set-based adaptive distributed differential evolution (S-ADDE) algorithm is proposed. S-ADDE adopts an island model to maintain population diversity. Two set-based operators, i.e., set-based mutation and set-based crossover, are designed in which the continuous domain in the traditional differential evolution is transferred to the discrete domain in the anonymity-driven database fragmentation problem. Moreover, in the set-based mutation operator, each individual’s mutation strategy is adaptively selected according to the performance. The experimental results demonstrate that the proposed S-ADDE is significantly better than the compared approaches. The effectiveness of the proposed operators is verified

Integrating continuous differential evolution with discrete local search for meander line RFID antenna design

The automated design of meander line RFID antennas is a discrete self-avoiding walk(SAW) problem for which efficiency is to be maximized while resonant frequency is to beminimized. This work presents a novel exploration of how discrete local search may beincorporated into a continuous solver such as differential evolution (DE). A prior DE algorithmfor this problem that incorporates an adaptive solution encoding and a bias favoringantennas with low resonant frequency is extended by the addition of the backbite localsearch operator and a variety of schemes for reintroducing modified designs into the DEpopulation. The algorithm is extremely competitive with an existing ACO approach and thetechnique is transferable to other SAW problems and other continuous solvers. The findingsindicate that careful reintegration of discrete local search results into the continuous populationis necessary for effective performance

A fully continuous individual-based model of tumor cell invasion

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar