We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing ...coordinate descent type algorithms, the SNCD updates a regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the "strong rule" for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultrahigh dimensions. We illustrate the application via a real data example.
Optimization is an important and fundamental challenge to solve optimization problems in different scientific disciplines. In this paper, a new stochastic nature-inspired optimization algorithm ...called Pelican Optimization Algorithm (POA) is introduced. The main idea in designing the proposed POA is simulation of the natural behavior of pelicans during hunting. In POA, search agents are pelicans that search for food sources. The mathematical model of the POA is presented for use in solving optimization issues. The performance of POA is evaluated on twenty-three objective functions of different unimodal and multimodal types. The optimization results of unimodal functions show the high exploitation ability of POA to approach the optimal solution while the optimization results of multimodal functions indicate the high ability of POA exploration to find the main optimal area of the search space. Moreover, four engineering design issues are employed for estimating the efficacy of the POA in optimizing real-world applications. The findings of POA are compared with eight well-known metaheuristic algorithms to assess its competence in optimization. The simulation results and their analysis show that POA has a better and more competitive performance via striking a proportional balance between exploration and exploitation compared to eight competitor algorithms in providing optimal solutions for optimization problems.
Summary
As the aerospace and automotive industries continue to strive for efficient lightweight structures, topology optimization (TO) has become an important tool in this design process. However, ...one ever‐present criticism of TO, and especially of multimaterial (MM) optimization, is that neither method can produce structures that are practical to manufacture. Optimal joint design is one of the main requirements for manufacturability. This article proposes a new density‐based methodology for performing simultaneous MMTO and multijoint TO. This algorithm can simultaneously determine the optimum selection and placement of structural materials, as well as the optimum selection and placement of joints at material interfaces. In order to achieve this, a new solid isotropic material with penalization‐based interpolation scheme is proposed. A process for identifying dissimilar material interfaces based on spatial gradients is also discussed. The capabilities of the algorithm are demonstrated using four case studies. Through these case studies, the coupling between the optimal structural material design and the optimal joint design is investigated. Total joint cost is considered as both an objective and a constraint in the optimization problem statement. Using the biobjective problem statement, the tradeoff between total joint cost and structural compliance is explored. Finally, a method for enforcing tooling accessibility constraints in joint design is presented.
The size and shape of the mechanism working area are one of the most important criteria of its performance. Known approaches to the analysis of the workspace, such as the geometric method or the ...discretization method, have a number of features that limit their effective application. This paper considers the optimization chord method for determining the working areas of various types on the example of a planar parallel mechanism. The simulation results for maximum, constant orientation and dextrous workspaces are presented.
Cellular Genetic Algorithms defines a new class of optimization algorithms based on the concepts of structured populations and Genetic Algorithms (GAs). The authors explain and demonstrate the ...validity of these cellular genetic algorithms throughout the book. This class of genetic algorithms is shown to produce impressive results on a whole range of domains, including complex problems that are epistatic, multi-modal, deceptive, discrete, continuous, multi-objective, and random in nature. The focus of this book is twofold. On the one hand, the authors present new algorithmic models and extensions to the basic class of Cellular GAs in order to tackle complex problems more efficiently. On the other hand, practical real world tasks are successfully faced by applying Cellular GA methodologies to produce workable solutions of real-world applications. These methods can include local search (memetic algorithms), cooperation, parallelism, multi-objective, estimations of distributions, and self-adaptive ideas to extend their applicability. The methods are benchmarked against well-known metaheuristics like Genetic Algorithms, Tabu Search, heterogeneous GAs, Estimation of Distribution Algorithms, etc. Also, a publicly available software tool is offered to reduce the learning curve in applying these techniques. The three final chapters will use the classic problem of ““vehicle routing”” and the hot topics of ““ad-hoc mobile networks”” and ““DNA genome sequencing”” to clearly illustrate and demonstrate the power and utility of these algorithms.
The simulation-driven metaheuristic algorithms have been successful in solving numerous problems compared to their deterministic counterparts. Despite this advantage, the stochastic nature of such ...algorithms resulted in a spectrum of solutions by a certain number of trials that may lead to the uncertainty of quality solutions. Therefore, it is of utmost importance to use a correct tool for measuring the performance of the diverse set of metaheuristic algorithms to derive an appropriate judgment on the superiority of the algorithms and also to validate the claims raised by researchers for their specific objectives. The performance of a randomized metaheuristic algorithm can be divided into efficiency and effectiveness measures. The efficiency relates to the algorithm’s speed of finding accurate solutions, convergence, and computation. On the other hand, effectiveness relates to the algorithm’s capability of finding quality solutions. Both scopes are crucial for continuous and discrete problems either in single- or multi-objectives. Each problem type has different formulation and methods of measurement within the scope of efficiency and effectiveness performance. One of the most decisive verdicts for the effectiveness measure is the statistical analysis that depends on the data distribution and appropriate tool for correct judgments.
•Heap-based optimizer (HBO) inspired by corporate rank hierarchy (CRH) is proposed.•HBO utilizes heap to map the hierarchy and model equations for 3 CRH activities.•A parameter (γ) to escape local ...optima without lacking exploitation is introduced.•Exploration and exploitation are balanced through self-adaptive parameters.•Performance is evaluated on 97 benchmarks and 3 mechanical engineering problems.
In an organization, a group of people working for a common goal may not achieve their goal unless they organize themselves in a hierarchy called Corporate Rank Hierarchy (CRH). This principle motivates us to map the concept of CRH to propose a new algorithm for optimization that logically arranges the search agents in a hierarchy based on their fitness. The proposed algorithm is named as heap-based optimizer (HBO) because it utilizes the heap data structure to map the concept of CRH. The mathematical model of HBO is built on three pillars: the interaction between the subordinates and their immediate boss, the interaction between the colleagues, and self-contribution of the employees. The proposed algorithm is benchmarked with 97 diverse test functions including 29 CEC-BC-2017 functions with very challenging landscapes against 7 highly-cited optimization algorithms including the winner of CEC-BC-2017 (EBO-CMAR). In the first two experiments, the exploitative and explorative behavior of HBO is evaluated by using 24 unimodal and 44 multimodal functions, respectively. It is shown through experiments and Friedman mean rank test that HBO outperforms and secures 1st rank. In the third experiment, we use 29 CEC-BC-2017 benchmark functions. According to Friedman mean rank test HBO attains 2nd position after EBO-CMAR; however, the difference in ranks of HBO and EBO-CMAR is shown to be statistically insignificant by using Bonferroni method based multiple comparison test. Moreover, it is shown through the Friedman test that the overall rank of HBO is 1st for all 97 benchmarks. In the fourth and the last experiment, the applicability on real-world problems is demonstrated by solving 3 constrained mechanical engineering optimization problems. The performance is shown to be superior or equivalent to the other algorithms, which have been used in the literature. The source code of HBO is publicly available athttps://github.com/qamar-askari/HBO.
Performance and energy are the two most important objectives for optimization on heterogeneous high performance computing platforms. This work studies a mathematical problem motivated by the ...bi‐objective optimization of data‐parallel applications on such platforms for performance and energy. First, we formulate the problem and present an exact algorithm of polynomial complexity solving the problem where all the application profiles of objective type one are continuous and strictly increasing, and all the application profiles of objective type two are linear increasing. We then apply the algorithm to develop solutions for two related optimization problems of parallel applications on heterogeneous hybrid platforms, one for performance and dynamic energy and the other for performance and total energy. Our proposed solution methods are then employed to solve the two bi‐objective optimization problems for two data‐parallel applications, matrix multiplication and gene sequencing, on a hybrid platform employing five heterogeneous processors, namely, two different Intel multicore CPUs, an Nvidia K40c GPU, an Nvidia P100 PCIe GPU, and an Intel Xeon Phi.
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