Static Penalty Functions Research Articles

Developing a hybrid system for stock selection and portfolio optimization with many-objective optimization based on deep learning and improved NSGA-III

Portfolio management is a critical aspect of investment strategies, with the goal to balance the low-risk and high-return investments. Despite this, existing portfolios frequently overlook the integration of stock selection outcomes and underutilize data from listed companies, leading to suboptimal portfolio performance. Addressing these shortcomings, this paper introduces a hybrid system involving stock selection and portfolio optimization. In stock selection, the system employs a combination of convolutional neural network and bi-directional recurrent neural network to predict stock trends. This approach enables the identification of stocks likely to appreciate in value, setting the stage for their inclusion in the subsequent optimization process. For portfolio optimization, the study formulates a five-objective optimization problem that incorporates mean, variance, skewness, kurtosis, and distance-to-default as key considerations. To solve the many-objective constrained optimization problem, an advanced strategy employing a static penalty function and an improved Non-dominated Sorting Genetic Algorithm III (NSGA-III) based on tent chaotic mapping is utilized. The efficacy of the proposed hybrid system is rigorously tested through three sets of ablation experiments alongside two discussions focused on its robustness and computational efficiency. The findings from these investigations reveal that the hybrid system outperforms traditional approaches, reducing risks and improving returns for investors.

A novel solution to optimal power flow problems using composite differential evolution integrating effective constrained handling techniques

Optimal power flow is a complex and highly non-linear problem in which steady-state parameters are needed to find a network’s efficient and economical operation. In addition, the difficulty of the Optimal power flow problem becomes enlarged when new constraints are added, and it is also a challenging task for the power system operator to solve the constrained Optimal power flow problems efficiently. Therefore, this paper presents a constrained composite differential evolution optimization algorithm to search for the optimum solution to Optimal power flow problems. In the last few decades, numerous evolutionary algorithm implementations have emerged due to their superiority in solving Optimal power flow problems while considering various objectives such as cost, emission, power loss, etc. evolutionary algorithms effectively explore the solution space unconstrainedly, often employing the static penalty function approach to address the constraints and find solutions for constrained Optimal power flow problems. It is a drawback that combining evolutionary algorithms and the penalty function approach requires several penalty parameters to search the feasible space and discard the infeasible solutions. The proposed a constrained composite differential evolution algorithm combines two effective constraint handling techniques, such as feasibility rule and ɛ constraint methods, to search in the feasible space. The proposed approaches are recognized on IEEE 30, 57, and 118-bus standard test systems considering 16 study events of single and multi-objective optimization functions. Ultimately, simulation results are examined and compared with the many recently published techniques of Optimal power flow solutions owing to show the usefulness and performance of the proposed a constrained composite differential evolution algorithm.

Optimization of advanced manufacturing processes using socio inspired cohort intelligence algorithm

The demand of Advanced Machining Processes (AMP) is continuously increasing owing to the technological advancement. The problems based on AMP are complex in nature as it consisted of parameters which are interdependent. These problems also consisted of linear and nonlinear constraints. This makes the problem complex which may not be solved using traditional optimization techniques. The optimization of process parameters is indispensable to use AMP's at its aptness and to make it economical to use. This paper states the optimization of process parameters of Ultrasonic machining (USM) and Abrasive water jet machining (AWJM) processes to maximize the Material Removal Rate (MRR) using a socio inspired Cohort Intelligent (CI) algorithm. The constraints involved with these problems are handled using static penalty function approach. The solutions are compared with other contemporary techniques such as Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Modified Harmony Search (HS_M) and Genetic Algorithm (GA).

Minimization of Torque Ripple in the Brushless DC Motor Using Constrained Cuckoo Search Algorithm

This paper presents the application of the cuckoo search (CS) algorithm in attempts to the minimization of the commutation torque ripple in the brushless DC motor (BLDC). The optimization algorithm was created based on the cuckoo’s reproductive behavior. The lumped-parameters mathematical model of the BLDC motor was developed. The values of self-inductances, mutual inductances, and back-electromotive force waveforms applied in the mathematical model were calculated by the use of the finite element method. The optimization algorithm was developed in Python 3.8. The CS algorithm was coupled with the static penalty function. During the optimization process, the shape of the voltage supplying the stator windings was determined to minimize the commutation torque ripple. Selected results of computer simulation are presented and discussed.

Optimum Design of Combined Rectangular RCC Footing using GA

The paper presents an estimation of the optimum cost of an isolated and combined footing following the safety and serviceability guidelines of Indian Standard (IS) 456:2000. The optimization methods, i.e., genetic algorithm, with static penalty function approach is developed in MATLAB compliant for optimal design of isolated and combined rectangular footing. The objective function formulated is based on the total cost of footing which includes the cost of concrete, steel and formwork. The influence design variables the total cost of footing are length, width and depth of footing and area of steel(flexural) reinforcement for moment at critical sections. The footing design algorithm is developed according to the biaxial-isolated and biaxial-combined rectangular footing as per IS codes. The constraints, e.g., dimension of footing, restriction on bending, shear stresses and displacements, are considered in the footing design algorithm which acted as a subroutine to the developed optimization programs. Five numerical examples have been taken to solved and evaluate the versatility of the developed method and observe the efficacy of method.

Optimization of Fuel Cost in Electric Power Systems using Harmony Search Algorithm

Fuel Cost Optimization emerges as an important issue in electrical load distribution systems. In this study, the performance of Harmony Search Algorithm, which has a significant place in the literature, has been observed for a sample problem in the field of fuel cost optimization. It is aimed to distribute the load provided by a three-unit power plant with minimum cost. Three restricted functions are defined in order to calculate the energy production cost per hour of three thermal power plants. For this reason, the problem has been solved by using equal weighted scalarization, one of the multi-objective optimization techniques and static penalty function with Harmony Search Algorithm. The obtained results are presented in comparison with the Lagrange solution and Artificial Bee Colony Algorithm, which were used to solve the same problem.

Constraint-handling techniques within differential evolution for solving process engineering problems

A wide range of process systems engineering problems involve an optimisation formulation that is difficult to solve due to sources of discontinuity and non-convexity and a high number of constraints to satisfy. Differential Evolution algorithm (DE) has proven to be robust for the solution of highly non-convex and mixed-integer problems; nevertheless, its performance greatly depends on the constraint-handling technique used. In this study, numerical comparisons of some state-of-the-art constraint-handling techniques are performed: static penalty function, stochastic ranking, feasibility rules, ε constrained method and gradient-based repair. The obtained results show that the gradient-based repair technique deserves a special attention when solving highly constrained problems. This technique enables to efficiently satisfy both inequality and equality constraints, which makes it particularly adapted for the solution of process engineering optimization problems.

Cost optimization of rectangular RC footing using GA and UPSO

The paper presents an estimation of the optimum cost of an isolated foundation following the safety and serviceability guidelines of Indian Standard (IS) 456:2000. Two adaptable optimization algorithms are developed for the first time to optimize the cost of any type of isolated footing design. Two optimization methods, i.e., constrained binary-coded genetic algorithm, with static penalty function approach and unified particle swarm optimization are developed in MATLAB compliant for optimal design of any isolated foundations. The objective function formulated is based on the total cost of footing. This includes the cost of concrete, the cost of steel and cost of formwork. The design variables which influence the total cost of footing are plan area and depth of footing and area of flexural reinforcement at moment critical sections. The footing design algorithm is developed according to the biaxial-isolated rectangular footing as per IS codes. The constraints, e.g., dimension of footing, restriction on bending, shear stresses and displacements, are considered in the footing design algorithm which acted as a subroutine to the developed optimization programs. Four different numerical examples have been solved to evaluate the versatility of the developed method. A comparison study has been done to observe the efficacy of both the optimization methods.

Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms

In power systems, optimal power flow (OPF) is a complex and constrained optimization problem in which quite often multiple and conflicting objectives are required to be optimized. The traditional way of dealing with multi-objective OPF (MOOPF) is the weighted sum method which converts the multi-objective OPF into a single-objective problem and provides a single solution from the set of Pareto solutions. This paper presents MOOPF study applying multi-objective evolutionary algorithm based on decomposition (MOEA/D) where a set of non-dominated solutions (Pareto solutions) can be obtained in a single run of the algorithm. OPF is formulated with two or more objectives among fuel (generation) cost, emission, power loss and voltage deviation. The other important aspect in OPF problem is about satisfying power system constraints. As the search process adopted by evolutionary algorithms is unconstrained, for a constrained optimization problem like OPF, static penalty function approach has been extensively employed to discard infeasible solutions. This approach requires selection of a suitable penalty coefficient, largely done by trial-and-error, and an improper selection may often lead to violation of system constraints. In this paper, an effective constraint handling method, superiority of feasible solutions (SF), is used in conjunction with MOEA/D to handle network constraints in MOOPF study. The algorithm MOEA/D-SF is applied to standard IEEE 30-bus and IEEE 57-bus test systems. Simulation results are analyzed, especially for constraint violation and compared with recently reported results on OPF.

Optimization procedure to minimize fuel consumption of a four-stroke marine turbocharged diesel engine

A numerical optimization model is developed to simulate the performance of a large four-stroke marine turbocharged diesel engine along the entire operating range by finding the optimal value of the adjustable parameters: speed of the turbocharger, start angle of injection, intake valve timing and amount of injected fuel. This numerical model assists to find the optimal values of these different parameters together without performing any experimental trials for different engine speeds and loads by minimizing the fuel consumption and by verifying the exhaust emissions limitation. This model couples a nonlinear optimization procedure implemented in Matlab/Simulink and 1D engine simulation software. Firstly, the marine diesel engine model is established and calibrated using data from the manufacturer, and the nonlinear optimization model is constructed using the fitness function, static penalty functions and boundary conditions. The optimizer adopted showed a good computing performance even when running in normal computers. The model is used to calculate the BSFC and to compute the amount of CO2 and NOx emissions for different working conditions. The results are important because in marine diesel engines, the values of the parameters of the turbocharger, injection system and valves timings and thus the amount of BSFC, CO2 and NOx emissions are not provided by the manufacturer along the entire operating range, although these data are required in different marine applications either during the preliminary stage of ship design or to be used in ship routing code. This simulation environment based optimization scheme can be further used to compute the performance of any marine diesel engine and to be a part of a numeric model of the complete propulsion system.

An adaptive multi-objective evolutionary algorithm for constrained workflow scheduling in Clouds

The Cloud workflow scheduling is to find proper Cloud resources for the execution of workflow tasks to efficiently utilize resources and meet different user’s quality of service requirements. Cloud workflow scheduling is a constrained and NP-complete problem and multi-objective evolutionary algorithms have shown their excellent ability to solve such problem. But most existing works simply use static penalty function to handle constraints which usually result in premature when the constraints become strict. On the other hand, with the search space being more tremendous and chaotic, how to balance the ability of exploring the entire search space and exploiting the important regions during the evolutionary process is increasingly important. In this paper, an adaptive individual-assessment scheme based on evolutionary states is proposed to handle the constraints in multi-objective optimization problems. In addition, the evolutionary parameters are also adjusted accordingly to balance the exploration and exploitation ability. These are distinguishable from most previous studies that directly incorporate multi-objective evolutionary algorithm to search excellent solutions for Cloud workflow scheduling. Experimental results demonstrate the proposed algorithm outperforms other state-of-the-art methods in convergence and diversity, and it also achieves better optimization ability when it is applied to solve Cloud workflow scheduling problem.

Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques

Optimal power flow (OPF) is a highly non-linear complex optimization problem where the steady state parameters of an electrical network need to be determined for its economical and efficient operation. The complexity of the problem escalates with ubiquitous presence of constraints in the problem. Solving OPF remains a popular but challenging task among power system researchers. In last couple of decades, numerous evolutionary algorithms (EAs) have been applied to find optimal solutions with different objectives of OPF. However, the search method adopted by EAs is unconstrained. An extensively used methodology to discard infeasible solutions found during the search process is the static penalty function approach. The process requires appropriate selection of penalty coefficients decided largely by tedious trial and error method. This paper presents performance evaluation of proper constraint handling (CH) techniques — superiority of feasibly solutions (SF), self-adaptive penalty (SP) and an ensemble of these two constraint handling techniques (ECHT) with differential evolution (DE) being the basic search algorithm, on the problem of OPF. The methods are tested on standard IEEE 30, IEEE 57 and IEEE 118-bus systems for several OPF objectives such as cost, emission, power loss, voltage stability etc. Single objective and weighted sum multi-objective cases of OPF are studied under the scope of this literature. Simulation results are analyzed and compared with most recent studies on the problem.

Constrained Nonnegative Matrix Factorization Based on Particle Swarm Optimization for Hyperspectral Unmixing

Spectral unmixing is an important part of hyperspectral image processing. In recent years, constrained nonnegative matrix factorization (CNMF) has been successfully applied for unmixing without the pure-pixel assumption and the result is physically meaningful. However, traditional CNMF algorithms always have two limitations: 1) Most of them are based on gradient methods and usually get trapped in a local optimum. 2) As they adopt static penalty function as the constraint handling method, it's difficult to choose a proper regularization parameter that can balance the tradeoff between reconstruction error and constraint well, which leads to the decreased accuracy. In this paper, we introduce particle swarm optimization (PSO) combined with two types of progressive constraint handling approaches for spectral unmixing in the framework of CNMF. A basic method called high-dimensional double-swarm PSO (HDPSO) algorithm is first proposed. It divides the original high-dimension problem into a series of easier subproblems and adopts two interactive swarms to search endmembers and abundances, respectively. Then, adaptive PSO (APSO) and multiobjective PSO algorithms are proposed by respectively incorporating adaptive penalty function and multiobjective optimization approaches into HDPSO. Experiments with both simulated data and real hyperspectral images are used to compare these methods with traditional algorithms and results validate that the proposed methods give better performance for spectral unmixing.

Constrained cohort intelligence using static and dynamic penalty function approach for mechanical components design

Most of the metaheuristics can efficiently solve unconstrained problems; however, their performance may degenerate if the constraints are involved. This paper proposes two constraint handling approaches for an emerging metaheuristic of Cohort Intelligence (CI). More specifically CI with static penalty function approach (SCI) and CI with dynamic penalty function approach (DCI) are proposed. The approaches have been tested by solving several constrained test problems. The performance of the SCI and DCI have been compared with algorithms like GA, PSO, ABC, d-Ds. In addition, as well as three real world problems from mechanical engineering domain with improved solutions. The results were satisfactory and validated the applicability of CI methodology for solving real world problems.

Data-driven RLV multi-objective reentry trajectory optimization based on new QABC algorithm

In recent years, big data and cloud technology have been widely used in information extraction and optimization decision. An improved artificial bees colony (ABC) algorithm called QABC is proposed for optimum design of the reusable launch vehicle (RLV) reentry trajectory. Because of poor convergence property of classical ABC algorithm in solving constrained nonlinear optimization problems (CNOPs), several modifications are carried out in this paper. The modifications include a quantum delta potential well model, two dynamic tolerance mechanisms, and a general generation mechanism of selection probability which is associated with the fitness of food source. In this paper, taking RLV three-dimension reentry trajectory design as an application example, a single-objective/multi-constraints optimization model was established with physical programming (PP) method and static penalty function method, in which four objectives (maximum range, minimum heat load, minimum heat flux (MHF), minimum oscillation) and five constraints (dynamic pressure, overload, heat flow, terminal altitude, and terminal velocity) were taken into account. Four single objective trajectory designs and two typical multi-objective trajectory designs with different preference structures were resolved, and the results showed that the optimization model founded by PP method was effective and flexible to reflect the designers preference. The improved algorithm, QABC, show excellent performance in solving RLV reentry trajectory optimization problem and a good prospect in other engineering applications.

Optimal design of submarine pipeline routes by genetic algorithm with different constraint handling techniques

This work deals with optimization methods for the selection of submarine pipeline routes, employed to carry the oil & gas from offshore platforms. The main motives are related to the assessment of constraint-handling techniques, an important issue in the application of genetic algorithms and other nature-inspired algorithms to such complex, real-world engineering problems.Several methods associated to the modeling and solution of the optimization problem are addressed, including: the geometrical parameterization of candidate routes; their encoding in the context of the genetic algorithm; and, especially, the incorporation into the objective function of the several design criteria involved in the route evaluation. Initially, we propose grouping the design criteria as either “soft” or “hard”, according to the practical consequences of their violation. Then, the latter criteria are associated to different constraint-handling techniques: the classical static penalty function method, and more advanced techniques such as the Adaptive Penalty Method, the ε-Constrained method, and the Ho-Shimizu technique.Case studies are presented to compare the performance of these methods, applied to actual offshore scenarios. The results indicate the importance of clearly characterizing feasible and infeasible solutions, according to the classification of design criteria as “soft” or “hard” respectively. They also indicate that the static penalty approach is not adequate, while the other techniques performed better, especially the ε-Constrained and the Ho-Shimizu methods. Finally, it is seen that the optimization tool may reduce the design time to assess an optimal route, providing accurate results, and minimizing the costs of installation and operation of submarine pipelines.

CONSTRAINT-BASED SYNTHESIS OF LINEAR ANTENNA ARRAY USING MODIFIED INVASIVE WEED OPTIMIZATION

This paper presents a novel technique for the synthesis of unequally spaced linear antenna array. The modifled Invasive Weed Optimization (IWO) algorithm is applied to optimize the antenna element positions for suppressing peak side lobe level (PSLL) and for achieving nulls in specifled directions. The novelty of the proposed approach is in the application of a constraint-based static penalty function during optimization of the array. The static penalty function is able to put selective pressure on the PSLL, the flrst null beam width (FNBW) or the accurate null positioning as desired by the application at hand lending a high degree of ∞exibility to the synthesis process. Various design examples are considered and the obtained results are validated by comparing with the results obtained using Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO) and Cat Swarm Optimization (CSO). Results demonstrate that the proposed method outperforms the previously published methods in terms of a signiflcant reduction in peak side lobe level while maintaining strong nulls in desired directions. The ∞exibility and ease of implementation of the modifled IWO algorithm in handling the constraints using static penalty function is evident from this analysis, showing the usefulness of the constraint based method in electromagnetic optimization problems.

A modified imperialist competitive algorithm for constrained optimization of plate-fin heat exchangers

In this study, to handle the design optimization of plate-fin heat exchangers, a constrained version of a newly introduced evolutionary algorithm, the imperialist competitive algorithm, is proposed. Imperialist competitive algorithm was initially established for unconstrained optimization problems and different strategies such as penalty functions were employed to handle the constraints in the previous studies. In the proposed constrained imperialist competitive algorithm, a feasibility-based ranking is employed in the imperialist competitive algorithm method. Seven design parameters and various constraints are considered for the design optimization in which minimum weight and minimum total annual cost were considered as the autonomous objective functions. The results are compared with those obtained by a genetic algorithm approach combined with a static penalty function scheme. Also, a comparison between the proposed algorithm and the original imperialist competitive algorithm is performed. The simulation results show that both the proposed algorithm and imperialist competitive algorithm are of higher accuracy than the genetic algorithm, which is commonly used. Also, the numerical experiment indicates that the modification in the imperialist competitive algorithm leads to better performance of the algorithm.

A memetic approach to the automatic design of high-performance analog integrated circuits

This article introduces an evolution-based methodology, named memetic single-objective evolutionary algorithm (MSOEA), for automated sizing of high-performance analog integrated circuits. Memetic algorithms may achieve higher global and local search ability by properly combining operators from different standard evolutionary algorithms. By integrating operators from the differential evolution algorithm, from the real-coded genetic algorithm, operators inspired by the simulated annealing algorithm, and a set of constraint handling techniques, MSOEA specializes in handling analog circuit design problems with numerous and tight design constraints. The method has been tested through the sizing of several analog circuits. The results show that design specifications are met and objective functions are highly optimized. Comparisons with available methods like genetic algorithm and differential evolution in conjunction with static penalty functions, as well as with intelligent selection-based differential evolution, are also carried out, showing that the proposed algorithm has important advantages in terms of constraint handling ability and optimization quality.

Genetic algorithm with adaptive and dynamic penalty functions for the selection of cleaner production measures: a constrained optimization problem

This paper presents a new approach of genetic algorithm (GA) to solve the constrained optimization problem. In a constrained optimization problem, feasible and infeasible regions occupy the search space. The infeasible regions consist of the solutions that violate the constraint. Oftentimes classical genetic operators generate infeasible or invalid chromosomes. This situation takes a turn for the worse when infeasible chromosomes alone occupy the whole population. To address this problem, dynamic and adaptive penalty functions are proposed for the GA search process. This is a novel strategy because it will attempt to transform the constrained problem into an unconstrained problem by penalizing the GA fitness function dynamically and adaptively. New equations describing these functions are presented and tested. The effects of the proposed functions developed have been investigated and tested using different GA parameters such as mutation and crossover. Comparisons of the performance of the proposed adaptive and dynamic penalty functions with traditional static penalty functions are presented. The result from the experiments show that the proposed functions developed are more accurate, efficient, robust and easy to implement. The algorithms developed in this research can be applied to evaluate environmental impacts from process operations.