Globally convergent hybridization of particle swarm optimization using line search-based derivative-free techniques

The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are not provided. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a test function and for two real-world optimization problems in ship hydrodynamics.The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are often not available. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a specific test function and for two real-world optimization problems in ship hydrodynamics

Globally convergent evolution strategies for constrained optimization

International audienceIn this paper we propose, analyze, and test algorithms for constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function.The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints.The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses the particular cases of bounds on the variables and linear constraints. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness

Modelling Blood Flow and Metabolism in the Preclinical Neonatal Brain during and Following Hypoxic-Ischaemia

Hypoxia-ischaemia (HI) is a major cause of neonatal brain injury, often leading to long-term damage or death. In order to improve understanding and test new treatments, piglets are used as preclinical models for human neonates. We have extended an earlier computational model of piglet cerebral physiology for application to multimodal experimental data recorded during episodes of induced HI. The data include monitoring with near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS), and the model simulates the circulatory and metabolic processes that give rise to the measured signals. Model extensions include simulation of the carotid arterial occlusion used to induce HI, inclusion of cytoplasmic pH, and loss of metabolic function due to cell death. Model behaviour is compared to data from two piglets, one of which recovered following HI while the other did not. Behaviourally-important model parameters are identified via sensitivity analysis, and these are optimised to simulate the experimental data. For the non-recovering piglet, we investigate several state changes that might explain why some MRS and NIRS signals do not return to their baseline values following the HI insult. We discover that the model can explain this failure better when we include, among other factors such as mitochondrial uncoupling and poor cerebral blood flow restoration, the death of around 40% of the brain tissue. Copyright

Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems.Fundação para a Ciência e a Tecnologia (FCT) - PTDC/MAT/64838/2006, PTDC/MAT/098214/200

Path generation, control, and monitoring

A critical issue in additive manufacturing (AM) is the control of the printer actuators such that the deposition of material (or a few different materials) takes place in an organized way. Typically, the actuators are connected with a low-level controller that can receive computer numerical control (CNC) instruction. A 3D printer controller is, usually, expected to receive a set of CNC instructions in a format called G-Code, where a set of control instructions is provided. These instructions include the necessary settings for the printer to work (e.g., a temperature setup) and printer head movement instructions (e.g., the x-, y-, and z-positions in reference axes). The set of the printer actuators positions, where some operations take place, is called the printer path. Path planning or generation corresponds to the computation of the printer head trajectory during a period of time where the object is to be built. A five-degree of freedom/5-axis 3D printer that considers a hybrid process based on additive manufacturing of composites with long or short fibers reinforced thermoplastic matrix is being addressed in this book. The 5-axis printer considers the three usual degrees of freedom plus two additional degrees of freedom, located at the printer table. While software for 3D printing is still possible to be used, full advantage of the printer potential demands for new path generation strategies. We start in Sect. 6.1 by introducing the reader to the optimal orientation of objects, where object orientation is optimal w.r.t. some objective functions that measure the printing performance. Since we are majorly interested in a 5-axis printer control, we present a printer emulator in Sect. 6.2, which allows us to monitor the printing process. Path generation is addressed in Sect. 6.3. We aim to provide flat and curved path planning to take advantage on the 5-axis printer, and in Sect. 6.4, we provide a strategy to print complex objects. The proposed approach for path planning can also be used for inspecting the printed objects by a non-destructive test, and we introduce this topic in Sect. 6.5.(undefined

Population-based optimization of cytostatic/cytotoxic combination cancer chemotherapy

This article studies the suitability of modern population based algorithms for designing combination cancer chemotherapies. The problem of designing chemotherapy schedules is expressed as an optimization problem (an optimal control problem) where the objective is to minimize the tumor size without compromising the patient's health. Given the complexity of the underlying mathematical model describing the tumor's progression (considering two types of drugs, the cell cycle and the immune system response), analytical and classical optimization methods are not suitable, instead, stochastic heuristic optimization methods are the right tool to solve the optimal control problem. Considering several solution quality and performance metrics, we compared three powerful heuristic algorithms for real-parameter optimization, namely, CMA evolution strategy, differential evolution, and particle swarm pattern search method. The three algorithms were able to successfully solve the posed problem. However, differential evolution outperformed its counterparts both in quality of the obtained solutions and efficiency of search