Methods for Shape-Constrained Kernel Density Estimation

Nonparametric density estimators are used to estimate an unknown probability density while making minimal assumptions about its functional form. Although the low reliance of nonparametric estimators on modelling assumptions is a benefit, their performance will be improved if auxiliary information about the density\u27s shape is incorporated into the estimate. Auxiliary information can take the form of shape constraints, such as unimodality or symmetry, that the estimate must satisfy. Finding the constrained estimate is usually a difficult optimization problem, however, and a consistent framework for finding estimates across a variety of problems is lacking. It is proposed to find shape-constrained density estimates by starting with a pilot estimate obtained by standard methods, and subsequently adjusting its shape until the constraints are satisfied. This strategy is part of a general approach, in which a constrained estimation problem is defined by an estimator, a method of shape adjustment, a constraint, and an objective function. Optimization methods are developed to suit this approach, with a focus on kernel density estimation under a variety of constraints. Two methods of shape adjustment are examined in detail. The first is data sharpening, for which two optimization algorithms are proposed: a greedy algorithm that runs quickly but can handle a limited set of constraints, and a particle swarm algorithm that is suitable for a wider range of problems. The second is the method of adjustment curves, for which it is often possible to use quadratic programming to find optimal estimates. The methods presented here can be used for univariate or higher-dimensional kernel density estimation with shape constraints. They can also be extended to other estimators, in both the density estimation and regression settings. As such they constitute a step toward a truly general optimizer, that can be used on arbitrary combinations of estimator and constraint

Parallel multi-swarm cooperative particle swarm optimization for protein–ligand docking and virtual screening

BACKGROUND: A high-quality docking method tends to yield multifold gains with half pains for the new drug development. Over the past few decades, great efforts have been made for the development of novel docking programs with great efficiency and intriguing accuracy. AutoDock Vina (Vina) is one of these achievements with improved speed and accuracy compared to AutoDock4. Since it was proposed, some of its variants, such as PSOVina and GWOVina, have also been developed. However, for all these docking programs, there is still large room for performance improvement. RESULTS: In this work, we propose a parallel multi-swarm cooperative particle swarm model, in which one master swarm and several slave swarms mutually cooperate and co-evolve. Our experiments show that multi-swarm programs possess better docking robustness than PSOVina. Moreover, the multi-swarm program based on random drift PSO can achieve the best highest accuracy of protein–ligand docking, an outstanding enrichment effect for drug-like activate compounds, and the second best AUC screening accuracy among all the compared docking programs, but with less computation consumption than most of the other docking programs. CONCLUSION: The proposed multi-swarm cooperative model is a novel algorithmic modeling suitable for protein–ligand docking and virtual screening. Owing to the existing coevolution between the master and the slave swarms, this model in parallel generates remarkable docking performance. The source code can be freely downloaded from https://github.com/li-jin-xing/MPSOVina. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12859-022-04711-0

Identifying preferred solutions for multi-objective aerodynamic design optimization

 Aerodynamic designers rely on high-fidelity numerical models to approximate, within reasonable accuracy, the flow around complex aerodynamic shapes. The ability to improve the flow field behaviour through shape modifications has led to the use of optimization techniques. A significant challenge to the application of evolutionary algorithms for aerodynamic shape optimization is the often excessive number of expensive computational fluid dynamic evaluations required to identify optimal designs. The computational effort is intensified when considering multiple competing objectives, where a host of trade-off designs are possible. This research focuses on the development of control measures to improve efficiency and incorporate the domain knowledge and experience of the designer to facilitate the optimization process. A multi-objective particle swarm optimization framework is developed, which incorporates designer preferences to provide further guidance in the search. A reference point is projected on the objective landscape to guide the swarm towards solutions of interest. This point reflects the preferred compromise and is used to focus all computing effort on exploiting a preferred region of the Pareto front. Data mining tools are introduced to statistically extract information from the design space and confirm the relative influence of both variables and objectives to the preferred interests of the designer. The framework is assisted by the construction of time-adaptive Kriging models, for the management of high-fidelity problems restricted by a computational budget. A screening criterion to locally update the Kriging models in promising areas of the design space is developed, which ensures the swarm does not deviate from the preferred search trajectory. The successful integration of these design tools is facilitated through the specification of the reference point, which can ideally be based on an existing or target design. The over-arching goal of the developmental effort is to reduce the often prohibitive cost of multi-objective design to the level of practical affordability in aerospace problems. The superiority of the proposed framework over more conventional search methods is conclusively demonstrated via a series of experiments and aerodynamic design problems

Evolutionary population dynamics and multi-objective optimisation problems

Griffith Sciences, School of Information and Communication TechnologyFull Tex

Cellular Harmony Search for Optimization Problems

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors.Thememory consideration and population update aremodified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS