A quadratic programming problem with positive definite Hessian subject to box constraints is solved, using an active-set approach. Convex quadratic programming (QP) problems with box constraints appear quite frequently in various real-world applications. The proposed method employs an active-set strategy with Lagrange multipliers, demonstrating rapid convergence. The algorithm, at each iteration, modifies both the minimization parameters in the primal space and the Lagrange multipliers in the dual space. The algorithm is particularly well suited for machine learning, scientific computing, and engineering applications that require solving box constraint QP subproblems efficiently. Key use cases include Support Vector Machines (SVMs), reinforcement learning, portfolio optimization, and trust-region methods in non-linear programming. Extensive numerical experiments demonstrate the method’s superior performance in handling large-scale problems, making it an ideal choice for contemporary optimization tasks. To encourage and facilitate its adoption, the implementation is available in multiple programming languages, ensuring easy integration into existing optimization frameworks.

We report results concerning the functionalization of graphene-based nanoplatelets for improving the thermal energy storage capacity of commonly used phase change materials (PCMs). The goal of this study was to enhance the low thermal conductivity of the PCMs, while preserving their specific and latent heats. We focused on wax-based PCMs, and we tested several types of graphene nanoparticles (GNPs) at a set of different concentrations. Both the size and shape of the GNPs were found to be important factors affecting the PCM’s thermal properties. These were evaluated using differential scanning calorimetry measurements and a modified enthalpy-based water bath method. We found that a small addition of GNPs (1% weight) with high aspect ratio is sufficient to double the thermal conductivity of several widely used PCMs. Our results suggest a simple and efficient procedure for improving the thermal properties of PCMs used in thermal energy storage applications.

Given a {features , target} dataset, we introduce an incremental algorithm that constructs an aggregate regressor, using an ensemble of neural networks. It is well known that ensemble methods suffer from the multicollinearity issue, which is the manifestation of redundancy arising mainly due to the common training-dataset. In the present incremental approach, at each stage we optimally blend the aggregate regressor with a newly trained neural network under a convexity constraint which, if necessary, induces negative correlations. Under this framework, collinearity issues do not arise at all, rendering so the method both accurate and robust.

Determining the thermal conductivity of a material from temperature measurements in a cooling or heating process belongs to the class of inverse problems. In this article, we present a method for a simple experimental setup, consisting of a glass tube containing the material under investigation, two thermistors for temperature monitoring (one at the central axis and the other attached on the outer surface of the tube), and a water heat bath maintained at a desired temperature. We solve the direct problem, i.e., the transient heat conduction equation, treating the thermal conductivity as a parameter whose value is determined by minimizing the difference between the calculated and the experimentally measured temperatures. The method is based on the numerical solution of the one-dimensional transient heat conduction equation in cylindrical coordinates that accurately describes the temperature evolution of a material in a narrow, long glass tube. The technique has been validated by applying it to the lauric and capric acids, whose thermal conductivities are accurately known and therefore it could be a valuable tool for the determination of the thermal properties of phase change materials suitable for thermal storage applications.

Stochastic Gradient Descent (SGD) is perhaps the most frequently used method for large scale training. A common example is training a neural network over a large data set, which amounts to minimizing the corresponding mean squared error (MSE). Since the convergence of SGD is rather slow, acceleration techniques based on the notion of “Mini-Batches” have been developed. All of them however, mimicking SGD, impose diminishing step-sizes as a means to inhibit large variations in the MSE objective. In this article, we introduce random sets of mini-batches instead of individual mini-batches. We employ an objective function that minimizes the average MSE and its variance over these sets, eliminating so the need for the systematic step size reduction. This approach permits the use of state-of-the-art optimization methods, far more efficient than the gradient descent, and yields a significant performance enhancement.

Although micro-anastomosis is the most commonly performed procedure for reconnecting two blood vessels through sutures, thrombus formation and subsequently anastomotic failure remains one of the most serious clinical complications. An important stimulus to thrombus formation is the altered hemodynamics with abnormal Wall Shear Stress (WSS) distribution on endothelial cells generated by the presence of sutures. Computational simulation is a valid tool to examine the local hemodynamics of micro-anastomosed vessels, allowing for the calculation of the WSS, a factor that could otherwise not directly possible to be measured in vivo. The aim of this study is to perform Fluid-Structure Interaction (FSI) analysis of micro-anastomosis in order to examine the effects of the wall compliance on the hemodynamic quantities.

A parallel memetic global optimization algorithm suitable for shared memory multicore systems is proposed and analyzed. The considered algorithm combines two well-known and widely used population-based stochastic algorithms, namely Particle Swarm Optimization and Differential Evolution, with two efficient and parallelizable local search procedures. The sequential version of the algorithm was first introduced as MEMPSODE (MEMetic Particle Swarm Optimization and Differential Evolution) and published in the CPC program library. We exploit the inherent and highly irregular parallelism of the memetic global optimization algorithm by means of a dynamic and multilevel approach based on the OpenMP tasking model. In our case, tasks correspond to local optimization procedures or simple function evaluations. Parallelization occurs at each iteration step of the memetic algorithm without affecting its searching efficiency. The proposed implementation, for the same random seed, reaches the same solution irrespectively of being executed sequentially or in parallel. Extensive experimental evaluation has been performed in order to illustrate the speedup achieved on a shared-memory multicore server.Program summaryProgram title: p-MEMPSODECatalogue identifier: AEXJ_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEXJ_v1_0.htmlProgram obtainable from: CPCProgram Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9950No. of bytes in distributed program, including test data, etc.: 141503Distribution format: tar.gzProgramming language: ANSI C.Computer: Workstation.Operating system: Developed under the Linux operating system using the GNU compilers v.4.4.3 (or higher). Uses the OpenMP API and runtime system.RAM: The code uses O(n x N) internal storage, n being the dimension of the problem and N the maximum population size. The required memory is dynamically allocated.Word size: 64Classification: 4.9.Nature of problem: Numerical global optimization of real valued functions is an indispensable methodology for solving a multitude of problems in science and engineering. Many problems exhibit a number of local and/or global minimizers, expensive function evaluations or require real-time response. In addition, discontinuities of the objective function, non-smooth and deceitful landscapes constitute challenging obstacles for most optimization algorithms.Solution method: We implement a memetic global optimization algorithm that combines stochastic, population-based methods with deterministic local search procedures. More specifically, the Unified Particle Swarm Optimization and the Differential Evolution algorithms are harnessed with the derivative-free Torczon's Multi-Directional Search and the gradient-based BFGS method. The produced hybrid algorithms possess inherent parallelism that is exploited efficiently by means of the OpenMP tasking model. Given the same random seed, the proposed implementation reaches the same solution irrespective of being executed sequentially or in parallel.Restrictions: The current version of the software uses only double precision arithmetic. An OpenMP-enabled (version 3.0 or higher) compiler is required.Unusual features: The software requires bound constraints on the optimization variables.Running time: The running time depends on the complexity of the objective function (and its derivatives if used) as well as on the number of available cores. Extensive experimental results demonstrate that the speedup closely approximates ideal values. (C) 2015 Elsevier B.V. All rights reserved.

We propose an adaptive Memetic Particle Swarm Optimization algorithm where local search is selected from a pool of different algorithms. The choice of local search is based on a probabilistic strategy that uses a simple metric to score the efficiency of local search. Our study investigates whether the pool size affects the memetic algorithm's performance, as well as the possible benefit of using the adaptive strategy against a baseline static one. For this purpose, we employed the memetic algorithms framework provided in the recent MEMPSODE optimization software, and tested the proposed algorithms on the Benchmarking Black Box Optimization (BBOB 2012) test suite. The obtained results lead to a series of useful conclusions.

Memetic algorithms are hybrid schemes that usually integrate metaheuristics with classical local search techniques, in order to attain more balanced intensification/diversification trade--off in the search procedure. MEMPSODE is a recently published software that implements such memetic schemes, based on the Particle Swarm Optimization and Differential Evolution algorithms, as well as on the Merlin optimization environment that offers a variety of local search methods. The present study aims at investigating the impact of the selected local search algorithm in the memetic schemes produced by MEMPSODE. Our interest was focused on gradient--free local search methods. We applied the derived memetic schemes on the noiseless testbed of the Black--Box Optimization Benchmarking 2012 workshop. The obtained results can offer significant insight to optimization practitioners with respect to the most promising approaches.

We present MEMPSODE, a global optimization software tool that integrates two prominent population-based stochastic algorithms, namely Particle Swarm Optimization and Differential Evolution, with well established efficient local search procedures made available via the Merlin optimization environment. The resulting hybrid algorithms, also referred to as Memetic Algorithms, combine the space exploration advantage of their global part with the efficiency asset of the local search, and as expected they have displayed a highly efficient behavior in solving diverse optimization problems. The proposed software is carefully parametrized so as to offer complete control to fully exploit the algorithmic virtues. It is accompanied by comprehensive examples and a large set of widely used test functions, including tough atomic cluster and protein conformation problems.Program summaryProgram title: MEMPSODE (MEMetic Particle Swarm Optimization and Differential Evolution)Catalogue identifier: AELM_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program. including test data, etc.: 14 877No. of bytes in distributed program, including test data, etc.: 592 244Distribution format: tar.gzProgramming language: ANSI C, ANSI Fortran-77Computer: WorkstationsOperating system: Developed under the Linux operating system using the GNU compilers v.4.4.3. It has also been tested under Solaris and the Cygwin environment.RAM: The code uses O (n x N) internal storage, n being the dimension of the problem and N the maximum population size. The required memory is dynamically allocated.Word size: 64 bitsClassification: 4.9Subprograms used:Cat Id Title ReferenceAAXW_v4_0 MERLIN-3.1.1 CPC 159 (2004) 70Nature of problem: Optimization is a valuable mathematical tool for solving a plethora of scientific and engineering problems. Usually, the underlying problems are modeled with objective functions whose minimizers (or maximizers) correspond to the desired solutions of the original problem. In many cases, there is a multitude of such minimizers that correspond to solutions either locally, i.e., in their close neighborhood, or globally, i.e., with respect to the whole search space. There is a significant number of efficient algorithms for addressing optimization problems. One can distinguish two main categories, based on their adequacy in performing better global (exploration) or local (exploitation) search. Standard local optimization algorithms have the ability to rapidly converge towards local minimizers but they are also prone to get easily trapped in their vicinity. These algorithms usually exploit local information of the objective function, including first- and second-order derivatives. On the other hand, global optimization algorithms are designed to perform better exploration, although at the cost of questionable convergence properties. Typically, these approaches integrate stochastic operations. The form of the optimization problem at hand plays a crucial role in the selection of the most appropriate algorithm. Objective functions that lack nice mathematical properties (such as differentiability, continuity etc.) may raise applicability issues for algorithms that require derivatives. On the other hand, applications that require high accuracy may be laborious for stochastic algorithms. The existence of a multitude of local and/or global minimizers can render these problems even harder for any single optimization algorithm.Solution method: Evolutionary Algorithms and Swarm Intelligence approaches have been established as effective global optimization algorithms that make minor assumptions about the objective function. Particle Swarm Optimization (PSO) and Differential Evolution (DE) possess a salient position among the most successful algorithms of these categories. Numerous studies indicate that their performance can be radically improved when combined with efficient local optimization schemes. The resulting hybrid algorithms offer more balanced search intensification/diversification than the original ones, thereby increasing both their efficiency and effectiveness. Such hybrid schemes are called Memetic Algorithms, and they have gained a rapidly growing interest over the past few years.We present MEMPSODE (MEMetic, PSO and DE), a global optimization software that implements memetic PSO and DE within a unified framework. The software utilizes local search procedures from the established Merlin optimization environment. The performance of the implemented approaches is illustrated on several examples, including hard optimization tasks such as atomic cluster and protein conformation problems.Restrictions: The current version of the software uses double precision arithmetic. However, it can be easily adapted by the user to handle integer or mixed-integer problems.Unusual features: The software takes into account only bound constraints. General constraints may be tackled by user-defined penalty or barrier functions that can be easily incorporated in the source code of the objective function.Additional comments: The use of the Merlin Optimization Environment 3.1.1 (see subprograms above) is optional.A comprehensive user manual is provided that covers in detail the installation procedure and provides detailed examples of operation.Running time: The running time depends solely on the complexity of the objective function (and its derivatives, if used) as well as on the available computational budget (number of function evaluations). The test run provided (Rastrigin function n = 10), requires 2.5 x 10(6) function evaluations (2.8 seconds on an i7-920 CPU). (c) 2012 Elsevier B.V. All rights reserved.

This paper presents a software infrastructure for high performance numerical optimization on clusters of multicore systems. At the core, a runtime system implements a programming and execution environment for irregular and adaptive task-based parallelism. Building on this, we extract and exploit the parallelism of a global optimization application at multiple levels, which include Hessian calculations and Newton-based local optimizations. We discuss parallel implementations details and task distribution schemes for managing nested parallelism. Finally, we report experimental performance results for all the components of our software system on a multicore cluster.

A method based on the solution of the one-dimensional single channel inverse scattering is proposed for the design of quantum filters having specific reflection and transmission properties. The inversion procedure allows one, via modifications of a prefabricated prototype system, to reach the desired filter properties. The feasibility of the method is demonstrated on several examples, where filter properties are requested in different energy ranges. The shape and range of the corresponding potential are smooth and therefore they render themselves to applications in microelectronics, nanostractures and in quantum devices.

The use of global optimization (GO) techniques in few-body systems is discussed. Their usefulness is demonstrated by applying them to solve the two-body bound state problem by casting the wave function as an artificial neural network (ANN) as well as by employing them to locate zeros of the Jost function in the complex k-plane corresponding to bound and resonance states.

In this article we present an incremental method for building a mixture model. Given the desired number of clusters K ≥ 2, we start with a two-component mixture and we optimize the likelihood by repeatedly applying a Split-Merge operation. When an optimum is obtained, we add a new component to the model by splitting in two, a properly chosen cluster. This goes on until the number of components reaches a preset limiting value. We have performed numerical experiments on several data–sets and report a performance comparison with other rival methods.

A novel method for solving ordinary and partial differential equations, based on grammatical evolution is presented. The method forms generations of trial solutions expressed in an analytical closed form. Several examples are worked out and in most cases the exact solution is recovered. When the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. We report results on several problems to illustrate the potential of this approach.

A modification of the standard Simulated Annealing (SA) algorithm is presented for finding the global minimum of a continuous multidimensional, multimodal function. We report results of computational experiments with a set of test functions and we compare to methods of similar structure. The accompanying software accepts objective functions coded both in Fortran 77 and C++.

A method for automatic arrhythmic beat classification is proposed. The method is based in the analysis of the RR interval signal, extracted from ECG recordings. Classification is made using support vector machines methodology to formulate a quadratic programming problem, subject to simple constraints, which is solved using the BOXCQP method. Four types of cardiac rhythms beats are classified: (1) beats belonging to ventricular flutter/fibrillation episodes, (2) premature ventricular contractions, (3) normal sinus rhythm and (4) beats belonging to 2 o heart block episodes. The method is evaluated using the ECG recordings from the MIT-BIH arrhythmia database and results are presented.

We introduce the Neural Spline, that is a mathematical model built by combining a neural network and an associated Obreshkov polynomial. The neural spline has finite support and can be used as the basic element in constructing continuous modular neural-based models. These models are suitable for function approximation in partitioned domains and are also amenable to efficient parallel or distributed implementation. Experimental results are presented for test problems in one and two dimensions which illustrate the effectiveness of the proposed function approximation scheme.