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The purpose of this paper is to demonstrate the applicability of swarm and evolutionary techniques for regularized machine learning. Generally, by defining a proper penalty function, regularization laws are embedded into the structure of common least square solutions to increase the numerical stability, sparsity, accuracy and robustness of regression weights. Several regularization techniques have been proposed so far which have their own advantages and disadvantages. Several efforts have been made to find fast and accurate deterministic solvers to handle those regularization techniques. However, the proposed numerical and deterministic approaches need certain knowledge of mathematical programming, and also do not guarantee the global optimality of the obtained solution. In this research, the authors propose the use of constraint swarm and evolutionary techniques to cope with demanding requirements of regularized extreme learning machine (ELM).

To implement the required tools for comparative numerical study, three steps are taken. The considered algorithms contain both classical and swarm and evolutionary approaches. For the classical regularization techniques, Lasso regularization, Tikhonov regularization, cascade Lasso-Tikhonov regularization, and elastic net are considered. For swarm and evolutionary-based regularization, an efficient constraint handling technique known as self-adaptive penalty function constraint handling is considered, and its algorithmic structure is modified so that it can efficiently perform the regularized learning. Several well-known metaheuristics are considered to check the generalization capability of the proposed scheme. To test the efficacy of the proposed constraint evolutionary-based regularization technique, a wide range of regression problems are used. Besides, the proposed framework is applied to a real-life identification problem, i.e. identifying the dominant factors affecting the hydrocarbon emissions of an automotive engine, for further assurance on the performance of the proposed scheme.

Through extensive numerical study, it is observed that the proposed scheme can be easily used for regularized machine learning. It is indicated that by defining a proper objective function and considering an appropriate penalty function, near global optimum values of regressors can be easily obtained. The results attest the high potentials of swarm and evolutionary techniques for fast, accurate and robust regularized machine learning.

The originality of the research paper lies behind the use of a novel constraint metaheuristic computing scheme which can be used for effective regularized optimally pruned extreme learning machine (OP-ELM). The self-adaption of the proposed method alleviates the user from the knowledge of the underlying system, and also increases the degree of the automation of OP-ELM. Besides, by using different types of metaheuristics, it is demonstrated that the proposed methodology is a general flexible scheme, and can be combined with different types of swarm and evolutionary-based optimization techniques to form a regularized machine learning approach.

The purpose of this paper is to present a new constrained optimization algorithm based on a particle swarm optimization (PSO) algorithm approach.

This paper introduces a hybrid approach based on a modified ring neighborhood with two new perturbation operators designed to keep diversity. A constraint handling technique based on feasibility and sum of constraints violation is adopted. Also, a special technique to handle equality constraints is proposed.

The paper shows that it is possible to improve PSO and keeping the advantages of its social interaction through a simple idea: perturbing the PSO memory.

The proposed algorithm shows a competitive performance against the state‐of‐the‐art constrained optimization algorithms.

The proposed algorithm can be used to solve single objective problems with linear or non‐linear functions, and subject to both equality and inequality constraints which can be linear and non‐linear. In this paper, it is applied to various engineering design problems, and for the solution of state‐of‐the‐art benchmark problems.

A new neighborhood structure for PSO algorithm is presented. Two perturbation operators to improve PSO algorithm are proposed. A special technique to handle equality constraints is proposed.

The purpose of this paper is the presentation of a technique to be integrated in a numerical airfoil optimization scheme, for the exact satisfaction of a strict equality cross-sectional area constraint.

An airfoil optimization framework is presented, based on Area-Preserving Free-Form Deformation (AP FFD) technique. A parallel metamodel-assisted differential evolution (DE) algorithm is used as an optimizer. In each generation of the DE algorithm, before the evaluation of the fitness function, AP FFD is applied to each candidate solution, via coupling a classic B-Spline-based FFD with an area correction step. The area correction step is achieved by solving a sub problem, which consists of computing and applying the minimum possible offset to each one of the free-to-move control points of the FFD lattice, subject to the area preservation constraint.

The proposed methodology is able to obtain better values of the objective function, compared to both a classic penalty function approach and a generic framework for handling constraints, which suggests the separation of constraints and objectives (separation-sub-swarm), without any loss of the convergence capabilities of the DE algorithm, while it also guarantees an exact area preservation. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the sub problem is possible by using the method of Lagrange multipliers.

AP FFD can be easily incorporated into any 2D shape optimization/design process, as it is a time-saving and easy-to-implement repair algorithm, independent from the nature of the problem at hand.

The proposed methodology proved to be an efficient tool in facing airfoil design problems, enhancing the rigidity of the optimal airfoil by preserving its cross-sectional area to a predefined value.

For one thing, despite the fact that it is popular to research the minimization of the power losses in power systems, the optimization of single objective seems insufficient to fully improve the performance of power systems. Multi-objective VAR Dispatch (MVARD) generally minimizes two objectives simultaneously: power losses and voltage deviation. The purpose of this paper is to propose Multi-Objective Enhanced PSO (MOEPSO) algorithm that achieves a good performance when applied to solve MVARD problem. Thus, the new algorithm is worthwhile to be known by the public.

Motivated by differential evolution algorithm, cross-over operator is introduced to increase particle diversity and reinforce global searching capacity in conventional PSO. In addition to that, a constraint-handling approach considering Constrain-prior Pareto-Dominance (CPD) is presented to handle the inequality constraints on dependent variables. Constrain-prior Nondominated Sorting (CNS) and crowding distance methods are considered to maintain well-distributed Pareto optimal solutions. The method combining CPD approach, CNS technique, and cross-over operator is called the MOEPSO method.

The IEEE 30 node and IEEE 57 node on power systems have been used to examine and test the presented method. The simulation results show the MOEPSO method can achieve lower power losses, smaller voltage deviation, and better-distributed Pareto optimal solutions comparing with the Multi-Objective PSO approach.

The most original parts include: the presented MOEPSO algorithm, the CPD approach that is used to handle constraints on dependent variables, and the CNS method which is considered to maintain a well-distributed Pareto optimal solutions. The performance of the proposed algorithm successfully reflects the value of this paper.

In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.

Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.

Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.

The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

The purpose of this paper is to propose variants of an adaptive penalty scheme for steady-state genetic algorithms applied to constrained engineering optimization problems.

For each constraint a penalty parameter is adaptively computed along the evolution according to information extracted from the current population such as the existence of feasible individuals and the level of violation of each constraint. The adaptive penalty method (APM), as originally proposed, computes the constraint violations of the initial population, and updates the penalty coefficient of each constraint after a given number of new individuals are inserted in the population. A second variant, called sporadic APM with constraint violation accumulation, works by accumulating the constraint violations during a given insertion of new offspring into the population, updating the penalty coefficients, and fixing the penalty coefficients for the next generations. The APM with monotonic penalty coefficients is the third variation, where the penalty coefficients are calculated as in the original method, but no penalty coefficient is allowed to have its value reduced along the evolutionary process. Finally, the penalty coefficients are defined by using a weighted average between the current value of a coefficient and the new value predicted by the method. This variant is called the APM with damping.

The paper checks new variants of an APM for evolutionary algorithms; variants of an APM, for a steady-state genetic algorithm based on an APM for a generational genetic algorithm, largely used in the literature previously proposed by two co-authors of this manuscript; good performance of the proposed APM in comparison with other techniques found in the literature; innovative and general strategies to handle constraints in the field of evolutionary computation.

The proposed algorithm has no limitations and can be applied in a large number of evolutionary algorithms used to solve constrained optimization problems.

The proposed algorithm can be used to solve real world problems in engineering as can be viewed in the references, presented in this manuscript, that use the original (APM) strategy. The performance of these variants is examined using benchmark problems of mechanical and structural engineering frequently discussed in the literature.

It is the first extended analysis of the variants of the APM submitted for possible publication in the literature, applied to real world engineering optimization problems.

The purpose of this paper is to present the application of an adaptive bacterial foraging (BF) algorithm for the design optimization of an energy efficient induction motor.

The induction motor design problem is formulated as a mixed integer nonlinear optimization problem. A set of nine independent variables is selected, and to make the machine feasible and practically acceptable, six constraints are imposed on the design. Two different objective functions are considered, namely, the annual active material cost, and the sum of the annual active material cost, annual cost of the active power loss of the motor and annual energy cost required to supply such power loss. A new adaptive BF algorithm is used for solving the optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling.

The adaptive BF algorithm is validated for two sample motors and benchmarked with the genetic algorithm, particle swarm optimization, simple BF algorithm, and conventional design methods. The results show that the proposed algorithm outperforms the other methods in both the solution quality and convergence rate. The annual cost of the induction motor is remarkably reduced when designed on the basis of minimizing its annual total cost, instead of minimizing its material cost only.

To the best of the knowledge, none of the existing work has applied the BF algorithms for electrical machine design problems. Therefore, the solution to this problem constitutes the main contribution of the paper. According to the huge number of induction motors operating all over the world, the BF techniques used in their design, on minimum annual cost basis, will lead to a tremendous saving in global energy consumption.

The purpose of the paper is to solve hydrothermal scheduling (HTS) problem for energy-efficient management by allocating the optimal real power outputs for thermal and hydroelectric generators.

HTS can be formulated as a complex and non-linear optimization problem which minimizes the total fuel cost and emissions of thermal generators subject to various physical and operational constraints. As the artificial bee colony algorithm has proven its ability to solve various engineering optimization problems, it has been used as a main optimization tool to solve the fixed-head HTS problem.

A meta-heuristic search technique-based algorithm has been implemented for hydrothermal energy management, and the simulation results show that this approach can provide trade-off between conflict objectives and keep a rapid convergence speed.

The proposed methodology is implemented on the standard test system, and the numerical results comparison indicates a considerable saving in total fuel cost and reduction in emission.

Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly.

This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation.

An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach.

An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.