Bastien Chopard

Bastien Chopard
  • University of Geneva

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373
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11,871
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Current institution
University of Geneva

Publications

Publications (373)
Article
Full-text available
We propose a numerical representation of beliefs in social systems based on the so-called SAT problem in computer science. The main idea is that a belief system is a set of true/false values associated with claims or propositions. Each individual assigns these values according to its cognitive system in order to minimize logical contradictions, thu...
Article
Full-text available
The concept of planetary health underscores the intricate relationship between environmental concerns and global health. This interconnection raises an important question related to cross-sectoral policy development: to what extent are environmental issues integrated into global health governance? To address this question, this study examines resol...
Article
MRI, a widespread non-invasive medical imaging modality, is highly sensitive to patient motion. Despite many attempts over the years, motion correction remains a difficult problem and there is no general method applicable to all situations. We propose a retrospective method for motion estimation and correction to tackle the problem of in-plane rigi...
Article
Full-text available
We consider the car following problem for a set of autonomous vehicles following each other on either an infinite or circular road. The behavior of each car is specified by its "speed regulator", a device that decides to increase or decrease the speed of the car as a function of the head-tail distance to its predecessor and the speed of both cars....
Article
Full-text available
The goal of this paper it to explore the possibility to simplify a stochastic complex dynamical system by reducing the number of its degrees of freedom, through a coarse graining procedure. Our objective is to create reduced systems which requires less computational burden to control. In other words, the question is whether one can act on the simpl...
Article
Full-text available
One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient’s bloodstream, which breaks down the thrombi’s fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or...
Chapter
Circulatory models can significantly help develop new ways to alleviate the burden of stroke on society. However, it is not always easy to know what hemodynamics conditions to impose on a numerical model or how to simulate porous media, which ineluctably need to be addressed in strokes. We propose a validated open-source, flexible, and publicly ava...
Preprint
Full-text available
One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient's bloodstream, which breaks down the thrombi's fibrin fibers: intravenous or intravascular thrombolysis. Unfortunately, however, the successful outcome of this procedure is still more of an exception than the rule. Underst...
Presentation
The gravitational settling of crystals in magmas plays a major role in their chemical differentiation. The overall reduction in segregation velocity between the crystals or bubbles and the melt with increasing particle volume fraction is commonly referred to as hindered settling. Hindered settling is generally parameterized empirically through sepa...
Article
Full-text available
From a complexity perspective on governance, multilateral diplomacy is based on interactions between people, ideas, norms, policies and institutions. This article uses a computer-assisted methodology to better understand governance systems as a network of norms. All World Health Assembly (WHA) resolutions that were available from 1948 to 2022 were...
Article
The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with...
Article
Full-text available
The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation with a diffusion constant given by the so-called Zydney-Colton theory. Here we reconsider this hypothesis based on experimental observations and numerical simulations including a fully resolved suspension of red blood cells and platelets subject to a she...
Article
Full-text available
MRI is a non-invasive medical imaging modality that is sensitive to patient motion, which constitutes a major limitation in most clinical applications. Solutions may arise from the reduction of acquisition times or from motion-correction techniques, either prospective or retrospective. Benchmarking the latter methods requires labeled motion-corrupt...
Article
Full-text available
IntroductionThe flow diverter stent (FDS) has become a first-line treatment for numerous intra-cranial aneurysms (IAs) by promoting aneurysm thrombosis. However, the biological phenomena underlying its efficacy remain unknown. We proposed a method to collect in situ blood samples to explore the flow diversion effect within the aneurysm sac. In this...
Article
Full-text available
A novel mesh refinement sensor is proposed for lattice Boltzmann methods (LBMs) applicable to either static or dynamic mesh refinement algorithms. The sensor exploits the kinetic nature of LBMs by evaluating the departure of distribution functions from their local equilibrium state. This sensor is first compared, in a qualitative manner, to three s...
Chapter
We consider the auto-organization of a set of autonomous vehicles following each other on either an infinite or circular road. The behavior of each car is specified by its “speed regulator”, a device that decides to increase or decrease the speed of the car as a function of the head-tail distance to its predecessor and the speed of both cars. A col...
Chapter
The problem of cellular automata coarse-graining is considered. The case of 1D boolean cellular automata (CA) is investigated. Probabilistic rules for 1D CA are parameterized. Then the coarse-graining procedure and the reduced probabilistic CA are defined in the general case. The reduction procedure is illustrated on the example of the Wolfram CA d...
Article
Parallel iterative applications often suffer from load imbalance, one of the most critical performance degradation factors. Hence, load balancing techniques are used to distribute the workload evenly to maximize performance. A key challenge is to know when to use load balancing techniques. In general, this is done through load balancing criteria, w...
Article
Various numerical methods for modeling wave propagation are presented in the literature. These models are specified by the inclusion of nonlinearity and dispersion. The nonlinear Shallow Water Equations (SWEs) and Boussinesq equations are two main sets for wave-based problems. Lattice Boltzmann Method (LBM) is a productive method for solving variou...
Article
Full-text available
Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present pathology tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-indiv...
Article
Most parallel applications suffer from load imbalance, a crucial performance degradation factor. In particle simulations, this is mainly due to the migration of particles between processing elements, which eventually gather unevenly and create workload imbalance. Dynamic load balancing is used at various iterations to mitigate load imbalance, emplo...
Article
Full-text available
In cardiovascular disorders, the study of thrombocytes, commonly known as platelets, is highly important since they are involved in blood clotting, essential in hemostasis, and they can in pathological situations affect the blood circulation. In this paper, single deposited platelets are measured using interferometric digital holographic microscopy...
Article
Full-text available
This perspective paper considers thrombolysis in the context of ischemic strokes, intending to build eventually a numerical model capable of simulating the thrombolytic treatment and predicting patient outcomes. Numerical modeling is a scientific methodology based on an abstraction of a system but requires understanding their spatio-temporal intera...
Article
Full-text available
Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for dispersal and associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gr...
Presentation
Full-text available
This talk summarizes recent efforts dedicated to the porting of the open-source software Palabos to GPUs. More information is available at: https://palabos.unige.ch/community/cpu-gpu-80-days/
Article
There is a discrepancy between successful recanalization and good clinical outcome after endovascular treatment (EVT) in acute ischemic stroke patients. During removal of a thrombus, a shower of microemboli may release and lodge to the distal circulation. The objective of this study was to determine the extent of damage on brain tissue caused by mi...
Article
Full-text available
The increase of computer power and the development of new algorithms is currently pushing the scientific investigation to new frontiers. is is particularly promising in the field of diplomacy where the complexification of international relations calls for new approaches to understand how humanity can collectively address contemporary global challen...
Preprint
Most parallel applications suffer from load imbalance, a crucial performance degradation factor. In particle simulations, this is mainly due to the migration of particles between processing elements, which eventually gather unevenly and create workload imbalance. Dynamic load balancing is used at various iterations to mitigate load imbalance, emplo...
Article
It has been observed in vitro that complete clot lysis is generally preceded by a slow phase of lysis during which the degradation seems to be inefficient. However, this slow regime was merely notified but not yet quantitatively discussed. In our experiments we observed that the lysis ubiquitously occurred in two distinct regimes, a slow and a fast...
Article
Full-text available
An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs and treatment. in silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, namely clinical trials and animal testing. We present the...
Presentation
Full-text available
This talk then aims at comparing the most common collision models, in a comprehensive manner, through standard validation testcases. To do so, we relied on the unified formalism [1,2]to implement these collision models in both the open-source code Palabos [3], and in the hardware agnostic framework STLBM [4]. Results obtained with D2Q9-LBMs are pro...
Article
Full-text available
Palabos-npFEM is a computational framework for the simulation of blood flow with fully resolved constituents. The software resolves the trajectories and deformed state of blood cells, such as red blood cells and platelets, and the complex interaction between them. The tool combines the lattice Boltzmann solver Palabos for the simulation of blood pl...
Preprint
Full-text available
Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gravitationally-...
Article
We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations....
Preprint
It has been observed in vitro that complete clot lysis is generally preceded by a period of latency during which the degradation seems to be inefficient. However, this latency was merely notified but not yet quantitatively discussed. In our experiments we observed that the lysis ubiquitously occurred in two distinct regimes, a slow and a fast lysis...
Preprint
Parallel iterative applications often suffer from load imbalance, one of the most critical performance degradation factors. Hence, load balancing techniques are used to distribute the workload evenly to maximize performance. A key challenge is to know \textit{when} to use load balancing techniques. In general, this is done through load balancing cr...
Article
Full-text available
In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical process that are at work during the growth and the organization of multi-cell tissues. As compared to in vivo experiments, computer based frameworks dedicated to tissue modeling allow us to easily t...
Article
Full-text available
•A detailed, practical description of a 2D lattice Boltzmann (LB) free-surface model and its coupling with a 1D LB shallow water model is provided. •A Python code is provided, that implements the Gaussian droplet benchmark of the research article [1] corresponding to this method article. •Particular attention is given to the details of the free-sur...
Chapter
In this paper, we show that the theory of information offers some tools to detect changes in the interaction topology of a dynamical system defined on a graph. As an illustrative example, the system we consider is a probabilistic voter model defined on a scale-free network. We show that, using time-delayed mutual-information, the interaction topolo...
Preprint
Full-text available
In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical process that are at work during the growth and the organization of multi-cell tissues. As compared to in vivo experiments, computer based frameworks dedicated to tissue modeling allow us to easily t...
Preprint
Full-text available
In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical process that are at work during the growth and the organization of multi-cell tissues. As compared to in vivo experiments, computer based frameworks dedicated to tissue modeling allow us to easily t...
Article
Full-text available
We propose a highly versatile computational framework for the simulation of cellular blood flow focusing on extreme performance without compromising accuracy or complexity. The tool couples the lattice Boltzmann solver Palabos for the simulation of blood plasma, a novel finite-element method (FEM) solver for the resolution of deformable blood cells...
Preprint
Full-text available
Palabos-npFEM is a computational framework for the simulation of blood flow with fully resolved constituents. The software resolves the trajectories and deformed state of blood cells, such as red blood cells and platelets, and the complex interaction between them. The tool combines the lattice Boltzmann solver Palabos for the simulation of blood pl...
Preprint
Full-text available
Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present clinical tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-indivi...
Article
Full-text available
Red blood cells (RBCs) in pathological situations undergo biochemical and conformational changes, leading to alterations in rheology involved in cardiovascular events. The shape of RBCs in volunteers and stable and exacerbated chronic obstructive pulmonary disease (COPD) patients was analyzed. The effects of RBC spherization on platelet transport (...
Preprint
We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well established Bouzidi, Firdaouss and Lallemand (20...
Article
Full-text available
Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding req...
Presentation
Full-text available
Abstract submitted: 29th DSFD conference (Viterbo, Italy, 13-17 July, 2020)
Article
Full-text available
The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization...
Preprint
Full-text available
The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation. Here we propose a disruptive view, by showing that the random part of their velocity is governed by a fat-tailed probability distribution, usually referred to as a L\'evy flight. Although for small spatio-temporal scales, it is hard to distinguish it fr...
Article
The fibrin clot is gelatinous matter formed upon injury to stop blood loss and is later destroyed by fibrinolysis, an enzymatic cascade with feedback. Pharmacological fibrinolysis stimulation is also used to destroy pathological, life-threatening clots and thrombi (thrombolysis). The regulation of the nonlinear spatially nonuniform fibrinolytic pro...
Article
Full-text available
We address the link between the controllability or observability of a stochastic complex system and concepts of information theory. We show that the most influential degrees of freedom can be detected without acting on the system, by measuring the time-delayed multi-information. Numerical and analytical results support this claim, which is develope...
Preprint
Full-text available
Rationale: There are important interactions between Red Blood Cells (RBCs) and platelets in the bloodstream. These interactions lead to a phenomenon called margination. RBCs in pathological situations undergo biochemical and conformational changes leading to alterations in blood rheology. Aim: RBCs shape in volunteers (21), stable (42) and exacerba...
Article
Full-text available
We present the scope, concepts, data structures and application programming models of the open-source Lattice Boltzmann library Palabos. Palabos is a C++ software platform developed since 2010 for Computational Fluid Dynamics simulations and Lattice Boltzmann modeling, which specifically targets applications with complex, coupled physics. The softw...
Preprint
The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its associated local dynamics. Delayed mutual information is also used to solve the community detection problem. A prob...
Preprint
The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization...
Article
Full-text available
Approximate Bayesian computation (ABC) provides us with a way to infer parameters of models, for which the likelihood function is not available, from an observation. Using ABC, which depends on many simulations from the considered model, we develop an inferential framework to learn parameters of a stochastic numerical simulator of volcanic eruption...
Article
The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its associated local dynamics. Delayed mutual information is also used to solve the community detection problem. A prob...
Preprint
Full-text available
We address the link between the controllability or observability of a stochastic complex system and concepts of information theory. We show that the most influential degrees of freedom can be detected without acting on the system, by measuring the time-delayed multi-information. Numerical and analytical results support this claim, which is develope...
Preprint
Full-text available
We propose a highly versatile computational framework for the simulation of cellular blood flow focusing on extreme performance without compromising accuracy or complexity. The tool couples the lattice Boltzmann solver Palabos for the simulation of the blood plasma, a novel finite element method (FEM) solver for the resolution of the deformable blo...
Article
Full-text available
By exploiting the kinetic nature of the lattice Boltzmann scheme, a novel criterion for automatic grid refinement is presented, in which the local refinement level is explicitly based on the local Knudsen number of the simulated system. This criterion can be applied to the non-thermal, weakly compressible Lattice Boltzmann Method. A striking advant...
Article
Full-text available
Flow diverters stents (FDS) are a family of stents commonly used by clinicians to treat cerebral aneurysms. The purpose of a FDS is to modify the blood flow within the aneurysmal cavity and induce thrombosis and tissue remodeling. To predict the success of a given FDS in a patient specific situation, or to design more effective FDS, numerical simul...
Preprint
Full-text available
We present the scope, concepts, data structures and application programming models of the open-source Lattice Boltzmann library Palabos. Palabos is a C++ software platform developed since 2010 for Computational Fluid Dynamics simulations and Lattice Boltzmann modeling, which specifically targets applications with complex, coupled physics. The softw...
Preprint
Approximate Bayesian computation (ABC) provides us with a way to infer parameters of models, for which the likelihood function is not available, from an observation. Using ABC, which depends on many simulations from the considered model, we develop an inferential framework to learn parameters of a stochastic numerical simulator of volcanic eruption...
Preprint
In parallel iterative applications, computational efficiency is essential for addressing large problems. Load imbalance is one of the major performance degradation factors of parallel applications. Therefore, distributing, cleverly, and as evenly as possible, the workload among processing elements (PE) maximizes application performance. So far, the...
Article
Full-text available
Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. This article proposes a formalism that describes all these methods within a common mathematical framework, and in this way allows us to draw direct links...
Article
We present a computational framework for the simulation of blood flow with fully resolved red blood cells (RBCs) using a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel finite element based solver for the deformable bodies and an immersed boundary method for the fluid-solid interaction. For the RBCs, we pr...
Data
This Supplemental Material aims at helping the reader with the coding of collision models considered in ''Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations''.
Presentation
Full-text available
Abstract submitted to the DSFD conference (Bangalore, 22-26 July, 2019)
Preprint
Full-text available
We present a computational framework for the simulation of blood flow with fully resolved red blood cells (RBCs) using a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel finite element based solver for the deformable bodies and an immersed boundary method for the fluid-solid interaction. For the RBCs, we pr...
Article
Full-text available
In this position paper, we discuss two relevant topics: (i) generic multiscale computing on emerging exascale high-performing computing environments, and (ii) the scaling of such applications towards the exascale. We will introduce the different phases when developing a multiscale model and simulating it on available computing infrastructure, and a...
Preprint
Full-text available
Many organs, such as the gut or the spine are formed through folding of an epithelium. Whereas genetic regulation of epithelium folding has been investigated extensively, the nature of the mechanical forces driving this process remain largely unknown. Here we show that monolayers of identical cells proliferating on the inner surface of elastic sphe...
Preprint
Full-text available
Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. The present article proposes a formalism that describes all these methods within a common mathematical framework, and in this way allows to draw direct l...
Article
Full-text available
Tissue folding is a frequently observed phenomenon, from the cerebral cortex gyrification, to the gut villi formation and even the crocodile head scales development. Although its causes are not yet well understood, some hypotheses suggest that it is related to the physical properties of the tissue and its growth under mechanical constraints. In ord...
Article
Full-text available
We present a scheme for coupling a 2D lattice Boltzmann free-surface solver with a 1D lattice Boltzmann shallow water solver, allowing to save computational effort and efficiently realize multiscale systems. The accuracy of the coupling is validated with two tests. First, we compare the numerical and analytical solutions in a setup with fixed inflo...
Article
Full-text available
We consider a multi-agent model of a simple economical system and study the impacts of a wave of immigrants on the stability of the system. Our model couples a labor market with a goods market. We first create a stable economy with N agents and study the impact of adding n new workers in the system. The time to reach a new equilibrium market is fou...
Article
Full-text available
In dynamical systems, local interactions between dynamical units generate correlations which are stored and transmitted throughout the system, generating the macroscopic behavior. However a framework to quantify and study this at the microscopic scale is missing. Here we propose an 'information processing' framework based on Shannon mutual informat...
Article
Full-text available
Many important scientific problems are inherently multi scale. This is, for instance, the case in models in material science or environmental science. A big challenge is to formulate generic frameworks for multiscale modeling and simulation. Despite its importance, the scientific community still lacks a well-accepted generic methodology to address...
Article
We present a lattice Boltzmann model designed for the simulation of dilute and dense finite-sized rigid particle suspensions under applied shear. We use a bottom-up approach and fully resolve the mechanical interaction between fluid and particles. Our model consists in coupling a lattice Boltzmann scheme for Newtonian and incompressible fluid flows...
Article
Numerical modeling of the blood flow through flow diverters in intracranial aneurysms is a crucial tool to personalize and optimize endovascular stenting procedures in the treatment of aneurysms. However, large computational meshes are needed to resolve the difference of scale between the struts of a flow diverter and the blood vessel leads, leadin...
Chapter
In this chapter we take up again the notion of an optimization problem from the point of view of the structure of the search space associated with its instances, an idea that has been only mentioned in the previous chapter. These concepts are a prerequisite to understand all the metaheuristics that will follow in later chapters. For the sake of cla...
Chapter
In this chapter we shall present some newer metaheuristics for optimization that are loosely based on analogies with the biological world. In contrast with the metaheuristics described in the previous chapters, these algorithms have been around for a comparatively short time and it is difficult to know whether they are going to be as successful as...
Chapter
The goal of this chapter, which is based on reference [63], is to better characterize the nature of the search space of particular problems where the number of optimal solutions, and the difficulty of finding them, varies as a function of a parameter that can be modified at will. According to the value of the parameter, the system goes from a situa...
Chapter
Inspired by animal behavior, Eberhart and Kennedy [49, 22] proposed in 1995 an optimization method called Particle Swarm Optimization (PSO). In this approach, a swarm of particles simultaneously explore a problem’s search space with the goal of finding the global optimum configuration.
Chapter
Evolutionary algorithms (EAs) are a set of optimization and machine learning techniques that find their inspiration in the biological processes of evolution established by Darwin [27] and other scientists in the ninenteenth century. Starting from a population of individuals that represent admissible solutions to a given problem through a suitable c...
Chapter
In this chapter we give a more detailed description of genetic operators, and in particular of selection. We will also introduce a more advanced evolutionary method called Genetic Programming, which makes use of complex, variable-sized individual representations. Finally, we will discuss the possibilities that arise when there is a topological stru...
Chapter
Tabu search was proposed in 1986 by F. Glover [36]. This metaheuristic gives good results on combinatorial optimization problems such as quadratic assignment.
Chapter
Metaheuristics are a family of algorithmic techniques that are useful for solving difficult problems. Roughly speaking, the difficulty or hardness of a problem is the quantity of computational resources needed to find the solution. When this quantity increases at a high rate with increasing problem size, in a way that will be defined precisely late...
Chapter
The metaheuristic called the ant colony method has been inspired by entomology, the science of insect behavior. An interesting observation is that ants are apparently capable of solving what we would call optimization problems, such as finding a short path between the nest and a source of food. This result will be discussed in detail in Section 5.2...
Chapter
In contrast with exact algorithms whose worst-case time complexity is known (see Chapter 1), metaheuristics do not provide that kind of bound. They can be very effective on a given instance of a problem and, at the same time, show long running times on another without finding a satisfactory solution. On the other hand, for example, the selection so...
Chapter
In contrast to the classical theoretical computational complexity point of view summarized in Chapter 1 according to which a given problem belongs to a certain complexity class, the common practice in the metaheuristics community is to consider the specific search space of a given problem instance or class of problem instances (see Chapter 2). This...
Chapter
The method of simulated annealing (SA) draws its inspiration from the physical process of metallurgy and uses terminology that comes from that field. When a metal is heated to a sufficiently high temperature, its atoms undergo disordered movements of large amplitude. If one now cools the metal down progressively, the atoms reduce their movement and...

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