Search results for "Mathematica"
showing 10 items of 7971 documents
Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations
2014
Abstract The present paper is concerned with a nonlinear initial–boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by two parameters: its degree of maturity μ and its maturation velocity v . At mitosis, the daughter cells and mother cells are related by a general reproduction rule. We prove existence and uniqueness results in the case where the total cross-section and the boundary conditions are depending on the total density of population. Local and nonlocal reproduction rules are discussed.
An existence and uniqueness principle for a nonlinear version of the Lebowitz-Rubinow model with infinite maximum cycle length
2017
The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.
Multi-modal search for multiobjective optimization: an application to optimal smart grids management
2012
This paper studies the possibility to use efficient multimodal optimizers for multi-objective optimization. In this paper, the application area considered for such new approach is the optimal dispatch of energy sources in smart microgrids. The problem indeed shows a non uniform Pareto front and requires efficient optimal search methods. The idea is to exploit the potential of agents in population-based heuristics to improve diversity in the Pareto front, where solutions show the same rank and are thus equally weighted. Since Pareto dominance is at the basis of the theory of multi-objective optimization, most algorithms show the non dominance ranking as quality indicator, with some problem i…
Scatter search for an uncapacitated p-hub median problem
2015
Scatter search is a population-based method that has been shown to yield high-quality outcomes for combinatorial optimization problems. It uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation for an NP -hard variant of the classic p-hub median problem. Specifically, we tackle the uncapacitated r-allocation p-hub median problem, which consists of minimizing the cost of transporting the traffics between nodes of a network through special facilities that act as transshipment points. This problem has a significant number of applications in practice, such as the design of transportati…
A hybrid evolution strategy for the open vehicle routing problem
2010
This paper presents a hybrid evolution strategy (ES) for solving the open vehicle routing problem (OVRP), which is a well-known combinatorial optimization problem that addresses the service of a set of customers using a homogeneous fleet of non-depot returning capacitated vehicles. The objective is to minimize the fleet size and the distance traveled. The proposed solution method manipulates a population of @m individuals using a (@m+@l)-ES; at each generation, a new intermediate population of @l offspring is produced via mutation, using arcs extracted from parent individuals. The selection and combination of arcs is dictated by a vector of strategy parameters. A multi-parent recombination …
A two-point boundary value formulation of a mean-field crowd-averse game
2014
Abstract We consider a population of “crowd-averse” dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem. Such a result has a value in that it turns a set of coupled partial differential equations into ordinary differential equations.
Scheduling a cellular manufacturing system with GA
2002
The flexible manufacturing cell scheduling problem is considered with a multi-objective approach, pursuing together makespan minimisation and the in process job wait minimisation. The formulation of the scheduling problem is discussed, analysing how to generate well suited sequences, like generalised permutation sequences, and the proper construction of a JIT timing of activities. An evolutionary sequencing algorithm based on both classic genetic operators and hybrid operators is then proposed. The hybrid operators have been introduced to construct highly fit initial population, to perform periodically a local search on the population and to maintain enough genetical diversity in the actual…
A hybrid genetic algorithm with local search
2001
Abstract A hybrid genetic algorithm with internal local search was developed for optimisations involving continuous variables. The reproduction probabilities were enhanced using the fitness values obtained when a local method was applied to each individual in the population. These estimations are more realistic, since consider not the apparent but the hidden, latent quality of each individual. The information gathered in the local search was also used to build an auxiliary population recording the successfully enhanced individuals, which allowed to detect the convergence and self-adapt the search limits. The size of this auxiliary population was kept constant by a cluster analysis strategy.…
Opinion dynamics and stubbornness through mean-field games
2013
This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach epsilon-consensus in a neighborhood of the stubborn agent's opinion.
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.