Performance analyses of weighted superposition attraction-repulsion algorithms in solving difficult optimization problems.

The purpose of this paper is to test the performance of the recently proposed weighted superposition attraction-repulsion algorithms (WSA and WSAR) on unconstrained continuous optimization test problems and constrained optimization problems. WSAR is a successor of weighted superposition attraction algorithm (WSA). WSAR is established upon the superposition principle from physics and mimics attractive and repulsive movements of solution agents (vectors). Differently from the WSA, WSAR also considers repulsive movements with updated solution move equations. WSAR requires very few algorithm-specific parameters to be set and has good convergence and searching capability. Through extensive computational tests on many benchmark problems including CEC'2015 and CEC'2020 performance of the WSAR is compared against WSA and other metaheuristic algorithms. It is statistically shown that the WSAR algorithm is able to produce good and competitive results in comparison to its predecessor WSA and other metaheuristic algorithms.

Nested Markov chain hyper-heuristic (NMHH): a hybrid hyper-heuristic framework for single-objective continuous problems.

This article introduces a new hybrid hyper-heuristic framework that deals with single-objective continuous optimization problems. This approach employs a nested Markov chain on the base level in the search for the best-performing operators and their sequences and simulated annealing on the hyperlevel, which evolves the chain and the operator parameters. The novelty of the approach consists of the upper level of the Markov chain expressing the hybridization of global and local search operators and the lower level automatically selecting the best-performing operator sequences for the problem. Numerical experiments conducted on well-known benchmark functions and the comparison with another hyper-heuristic framework and six state-of-the-art metaheuristics show the effectiveness of the proposed approach.

Pflacco: Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems in Python.

The herein proposed Python package pflacco provides a set of numerical features to characterize single-objective continuous and constrained optimization problems. Thereby, pflacco addresses two major challenges in the area optimization. Firstly, it provides the means to develop an understanding of a given problem instance, which is crucial for designing, selecting, or configuring optimization algorithms in general. Secondly, these numerical features can be utilized in the research streams of automated algorithm selection and configuration. While the majority of these landscape features is already available in the R package flacco, our Python implementation offers these tools to an even wider audience and thereby promotes research interests and novel avenues in the area of optimization.

An enhanced ant colony optimizer with Cauchy-Gaussian fusion and novel movement strategy for multi-threshold COVID-19 X-ray image segmentation.

The novel coronavirus pneumonia (COVID-19) is a respiratory disease of great concern in terms of its dissemination and severity, for which X-ray imaging-based diagnosis is one of the effective complementary diagnostic methods. It is essential to be able to separate and identify lesions from their pathology images regardless of the computer-aided diagnosis techniques. Therefore, image segmentation in the pre-processing stage of COVID-19 pathology images would be more helpful for effective analysis. In this paper, to achieve highly effective pre-processing of COVID-19 pathological images by using multi-threshold image segmentation (MIS), an enhanced version of ant colony optimization for continuous domains (MGACO) is first proposed. In MGACO, not only a new move strategy is introduced, but also the Cauchy-Gaussian fusion strategy is incorporated. It has been accelerated in terms of convergence speed and has significantly enhanced its ability to jump out of the local optimum. Furthermore, an MIS method (MGACO-MIS) based on MGACO is developed, where it applies the non-local means, 2D histogram as the basis, and employs 2D Kapur's entropy as the fitness function. To demonstrate the performance of MGACO, we qualitatively analyze it in detail and compare it with other peers on 30 benchmark functions from IEEE CEC2014, which proves that it has a stronger capability of solving problems over the original ant colony optimization for continuous domains. To verify the segmentation effect of MGACO-MIS, we conducted a comparison experiment with eight other similar segmentation methods based on real pathology images of COVID-19 at different threshold levels. The final evaluation and analysis results fully demonstrate that the developed MGACO-MIS is sufficient to obtain high-quality segmentation results in the COVID-19 image segmentation and has stronger adaptability to different threshold levels than other methods. Therefore, it has been well-proven that MGACO is an excellent swarm intelligence optimization algorithm, and MGACO-MIS is also an excellent segmentation method.

Improved intelligent clonal optimizer based on adaptive parameter strategy.

The intelligent clonal optimizer (ICO) is a new evolutionary algorithm, which adopts a new cloning and selection mechanism. In order to improve the performance of the algorithm, quasi-opposition-based and quasi-reflection-based learning strategy is applied according to the transition information from exploration to exploitation of ICO to speed up the convergence speed of ICO and enhance the diversity of the population. Furthermore, to avoid the stagnation of the optimal value update, an adaptive parameter method is designed. When the update of the optimal value falls into stagnation, it can adjust the parameter of controlling the exploration and exploitation in ICO to enhance the convergence rate of ICO and accuracy of the solution. At last, an improved intelligent chaotic clonal optimizer (IICO) based on adaptive parameter strategy is proposed. In this paper, twenty-seven benchmark functions, eight CEC 2104 test functions and three engineering optimization problems are used to verify the numerical optimization ability of IICO. Results of the proposed IICO are compared to ten similar meta-heuristic algorithms. The obtained results confirmed that the IICO exhibits competitive performance in convergence rate and accurate convergence.

Estimation in the partially nonlinear model by continuous optimization.

A useful model for data analysis is the partially nonlinear model where response variable is represented as the sum of a nonparametric and a parametric component. In this study, we propose a new procedure for estimating the parameters in the partially nonlinear models. Therefore, we consider penalized profile nonlinear least square problem where nonparametric components are expressed as a B-spline basis function, and then estimation problem is expressed in terms of conic quadratic programming which is a continuous optimization problem and solved interior point method. An application study is conducted to evaluate the performance of the proposed method by considering some well-known performance measures. The results are compared against parametric nonlinear model.

AnAnaS: Software for Analytical Analysis of Symmetries in Protein Structures.

Symmetry is very common among proteins found in structural databases such as the Protein Data Bank (PDB). We present novel software, called AnAnaS, that finds positions and orientations of the symmetry axes in all types of symmetrical protein assemblies. It deals with five symmetry groups: cyclic, dihedral, tetrahedral, octahedral, and icosahedral. The software also assesses the quality of symmetry and can detect symmetries in incomplete cyclic assemblies. Internally, AnAnaS comprises discrete and continuous optimization steps and is applicable to assemblies with multiple chains in the asymmetric subunits or to those with pseudosymmetry. The method is very fast as most of the steps are performed analytically.

Generating New Space-Filling Test Instances for Continuous Black-Box Optimization.

This article presents a method to generate diverse and challenging new test instances for continuous black-box optimization. Each instance is represented as a feature vector of exploratory landscape analysis measures. By projecting the features into a two-dimensional instance space, the location of existing test instances can be visualized, and their similarities and differences revealed. New instances are generated through genetic programming which evolves functions with controllable characteristics. Convergence to selected target points in the instance space is used to drive the evolutionary process, such that the new instances span the entire space more comprehensively. We demonstrate the method by generating two-dimensional functions to visualize its success, and ten-dimensional functions to test its scalability. We show that the method can recreate existing test functions when target points are co-located with existing functions, and can generate new functions with entirely different characteristics when target points are located in empty regions of the instance space. Moreover, we test the effectiveness of three state-of-the-art algorithms on the new set of instances. The results demonstrate that the new set is not only more diverse than a well-known benchmark set, but also more challenging for the tested algorithms. Hence, the method opens up a new avenue for developing test instances with controllable characteristics, necessary to expose the strengths and weaknesses of algorithms, and drive algorithm development.

Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning.

In this article, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focusing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that, compared to the portfolio's single best solver, on average requires less than half of the resources for solving a given problem. Therefore, there is a huge gain in efficiency compared to classical ensemble methods combined with an increased insight into problem characteristics and algorithm properties by using informative features. The model acts on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications. The model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial population of an evolutionary (optimization) algorithm so that even the feature costs become negligible.

Peculiarities in the Material Design of Buckling Resistance for Tensioned Laminated Composite Panels with Elliptical Cut-Outs.

The results of analytical and numerical studies of the buckling behavior of laminated multilayered tensioned sheets with circular and elliptical openings are presented. The analysis shows the significant influence of stress concentration effects on buckling modes and loads, particularly taking into consideration variations in the E1/E2 and E1/G12 ratios. The results of finite element (FE) computations prove that the buckling mode cannot be described by a single buckle localized at the apex of the hole. The optimal design of such structures seems to be much more complicated than classical buckling problems of compressed laminated panels without holes. However, the obtained results indicate that the optimal laminate configurations occur at the boundaries of the feasible regions of the introduced design space. Both continuous and discrete fibre orientations are considered. For continuous fibre orientations, the optimal stacking sequence corresponds to angle-ply symmetric laminates.

Analytical symmetry detection in protein assemblies. II. Dihedral and cubic symmetries.

Protein assemblies are often symmetric, as this organization has many advantages compared to individual proteins. Complex protein structures thus very often possess high-order symmetries. Detection and analysis of these symmetries has been a challenging problem and no efficient algorithms have been developed so far. This paper presents the extension of our cyclic symmetry detection method for higher-order symmetries with multiple symmetry axes. These include dihedral and cubic, i.e., tetrahedral, octahedral, and icosahedral, groups. Our method assesses the quality of a particular symmetry group and also determines all of its symmetry axes with a machine precision. The method comprises discrete and continuous optimization steps and is applicable to assemblies with multiple chains in the asymmetric subunits or to those with pseudo-symmetry. We implemented the method in C++ and exhaustively tested it on all 51,358 symmetric assemblies from the Protein Data Bank (PDB). It allowed us to study structural organization of symmetric assemblies solved by X-ray crystallography, and also to assess the symmetry annotation in the PDB. For example, in 1.6% of the cases we detected a higher symmetry group compared to the PDB annotation, and we also detected several cases with incorrect annotation. The method is available at http://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available at http://samson-connect.net.

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries.

Symmetry in protein, and, more generally, in macromolecular assemblies is a key point to understand their structure, stability and function. Many symmetrical assemblies are currently present in the Protein Data Bank (PDB) and some of them are among the largest solved structures, thus an efficient computational method is needed for the exhaustive analysis of these. The cyclic symmetry groups represent the most common assemblies in the PDB. These are also the building blocks for higher-order symmetries. This paper presents a mathematical formulation to find the position and the orientation of the symmetry axis in a cyclic symmetrical protein assembly, and also to assess the quality of this symmetry. Our method can also detect symmetries in partial assemblies. We provide an efficient C++ implementation of the method and demonstrate its efficiency on several examples including partial assemblies and pseudo symmetries. We also compare the method with two other published techniques and show that it is significantly faster on all the tested examples. Our method produces results with a machine precision, its cost function is solely based on 3D Euclidean geometry, and most of the operations are performed analytically. The method is available athttp://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available athttp://samson-connect.net.

Performance Analysis of Continuous Black-Box Optimization Algorithms via Footprints in Instance Space.

This article presents a method for the objective assessment of an algorithm's strengths and weaknesses. Instead of examining the performance of only one or more algorithms on a benchmark set, or generating custom problems that maximize the performance difference between two algorithms, our method quantifies both the nature of the test instances and the algorithm performance. Our aim is to gather information about possible phase transitions in performance, that is, the points in which a small change in problem structure produces algorithm failure. The method is based on the accurate estimation and characterization of the algorithm footprints, that is, the regions of instance space in which good or exceptional performance is expected from an algorithm. A footprint can be estimated for each algorithm and for the overall portfolio. Therefore, we select a set of features to generate a common instance space, which we validate by constructing a sufficiently accurate prediction model. We characterize the footprints by their area and density. Our method identifies complementary performance between algorithms, quantifies the common features of hard problems, and locates regions where a phase transition may lie.

Continuous Optimization of Drug Storage Position Management in Automatic Dispensing Machine by Or-bital Utilization Rate Algorithm / 中国药房

OBJECTIVE:To optimize the drug storage position management in automatic dispensing machine,and improve the dispensing efficiency. METHODS:The orbital utilization rate of drugs in automatic dispensing machine was calculated,the opti-mum value of orbital utilization rate was set up to adjust the drug varieties and numbers of storage tracks for continually optimizing the storage position management. Dispensing rates of automatic dispensing machines and real-time dispensing windows with fully automated deployment before (Mar.-Jun. 2016) and after (Jul.-Oct. 2016) optimization were statistically analyzed and compared. RESULTS:The optimum value of orbital utilization rate was set up as 67%. Drugs more than the value were increased the num-bers of storage tracks,while drugs less than the value was decreased the numbers of storage tracks or removed out of dispensing machines. From Mar. to Oct. 2016,2 dispensing machines in our hospital adjusted 75 varieties and 127 orbits in total,storage num-bers was increased by 158 boxes. Compared with before optimization (Mar.),dispensing rate of automatic dispensing machines was increased from 73.7% to 81.3% after optimization(Oct.),dispensing rate of real-time dispensing window was increased from 39.8% to 51.8%(P<0.05). CONCLUSIONS:Applying the orbital utilization rate algorithm for adjusting drug variety and track number in machine can effectively and continually optimize the drug storage position,increase the storage capacity in machine, make full use of automatic equipments and improve the dispensing efficiency.

Continuous Optimization of Drug Storage Position Management in Automatic Dispensing Machine by Or-bital Utilization Rate Algorithm / 中国药房

OBJECTIVE:To optimize the drug storage position management in automatic dispensing machine,and improve the dispensing efficiency. METHODS:The orbital utilization rate of drugs in automatic dispensing machine was calculated,the opti-mum value of orbital utilization rate was set up to adjust the drug varieties and numbers of storage tracks for continually optimizing the storage position management. Dispensing rates of automatic dispensing machines and real-time dispensing windows with fully automated deployment before (Mar.-Jun. 2016) and after (Jul.-Oct. 2016) optimization were statistically analyzed and compared. RESULTS:The optimum value of orbital utilization rate was set up as 67%. Drugs more than the value were increased the num-bers of storage tracks,while drugs less than the value was decreased the numbers of storage tracks or removed out of dispensing machines. From Mar. to Oct. 2016,2 dispensing machines in our hospital adjusted 75 varieties and 127 orbits in total,storage num-bers was increased by 158 boxes. Compared with before optimization (Mar.),dispensing rate of automatic dispensing machines was increased from 73.7% to 81.3% after optimization(Oct.),dispensing rate of real-time dispensing window was increased from 39.8% to 51.8%(P<0.05). CONCLUSIONS:Applying the orbital utilization rate algorithm for adjusting drug variety and track number in machine can effectively and continually optimize the drug storage position,increase the storage capacity in machine, make full use of automatic equipments and improve the dispensing efficiency.

Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem.

This paper analyzes a (1, λ)-Evolution Strategy, a randomized comparison-based adaptive search algorithm optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are investigated: first, the case where the step-size is constant, and second, the case where the step-size is adapted using cumulative step-size adaptation. We exhibit for each case a Markov chain describing the behavior of the algorithm. Stability of the chain implies, by applying a law of large numbers, either convergence or divergence of the algorithm. Divergence is the desired behavior. In the constant step-size case, we show stability of the Markov chain and prove the divergence of the algorithm. In the cumulative step-size adaptation case, we prove stability of the Markov chain in the simplified case where the cumulation parameter equals 1, and discuss steps to obtain similar results for the full (default) algorithm where the cumulation parameter is smaller than 1. The stability of the Markov chain allows us to deduce geometric divergence or convergence, depending on the dimension, constraint angle, population size, and damping parameter, at a rate that we estimate. Our results complement previous studies where stability was assumed.

A self adaptive hybrid enhanced artificial bee colony algorithm for continuous optimization problems.

The artificial bee colony (ABC) algorithm is one of popular swarm intelligence algorithms that inspired by the foraging behavior of honeybee colonies. To improve the convergence ability, search speed of finding the best solution and control the balance between exploration and exploitation using this approach, we propose a self adaptive hybrid enhanced ABC algorithm in this paper. To evaluate the performance of standard ABC, best-so-far ABC (BsfABC), incremental ABC (IABC), and the proposed ABC algorithms, we implemented numerical optimization problems based on the IEEE Congress on Evolutionary Computation (CEC) 2014 test suite. Our experimental results show the comparative performance of standard ABC, BsfABC, IABC, and the proposed ABC algorithms. According to the results, we conclude that the proposed ABC algorithm is competitive to those state-of-the-art modified ABC algorithms such as BsfABC and IABC algorithms based on the benchmark problems defined by CEC 2014 test suite with dimension sizes of 10, 30, and 50, respectively.