Self-adaptive Penalty Function Research Articles

Maximizing energy efficiency and system throughput using a self-adaptive penalty function with a whale optimization algorithm in social-aware device-to-device communications

Device-to-device (D2D) communication is an emerging approach for 5 G networks. It allows for high capacity, low latency, and increased bandwidth. These features have prompted several research studies to focus on meeting customers’ expectations. This research concentrates on obtaining optimal resource and power allocation, better quality of service, and reliable connectivity between D2D clients through a whale optimization algorithm (WOA). The WOA possesses greater stability, faster integration speeds, a powerful global search ability, and greater accuracy than traditional methods. The WOA utilizes an unconstrained objective function obtained through a self-adaptive penalty function. This unconstrained objective function yields optimal solutions for the resource as well as power allocation, higher throughputs, and energy and spectral efficiencies in D2D communications. For D2D communications, the energy efficiency of the WOA is 47.12 % higher than a genetic algorithm (GA) and 70.33 % higher than particle swarm optimization (PSO), and it yields high spectral efficiency and system throughput. Obviously, the WOA in this proposal is more efficient than a GA or PSO and shows the advantages of combining physical and social parameters for improved wireless network performance.

Mesh antenna cable net form finding optimization by an improved NSGA-II

The tension uniformity and surface accuracy of mesh antenna cable net are two well-accepted evaluation criteria for form finding. Traditional form finding techniques often rely on single-objective optimization and weighting factors. Although the Non-dominated Sorting Genetic Algorithm II (NSGA-II) can address the limitation, there are still challenges of wide distribution and insufficient precision of solutions. In the present work, a novel multi-objective optimization method based on an improved NSGA-II is introduced to conduct mesh antenna cable net form finding optimization. Based on the preference region (PR), a self-adaptive penalty function is proposed. The function is designed to steer the optimization process toward the PR, and enhancing the precision of the solutions. The extent of penalization for an individual solution depends on its positioning relative to the PR and is modified by a penalty coefficient that adapts dynamically to the population number within the PR. Additionally, a form finding method considering flexible frames is developed. The initial population for the flexible frame optimization is sourced from results of rigid frames, with the maximum truss node position error as the convergence criterion. Benchmark tests and case studies confirm that the improved NSGA-II enhances distributivity and convergence, while also providing form-finding results with higher surface accuracy and more uniform tension distribution.

Optimum Design of Reinforced Concrete Beams with Large Opening Using Neural Network Algorithm

It is quite rare to find researches in the literature connecting neural networks to design challenges in civil engineering, particularly with regard to beam with large openings. Therefore, to ascertain the best cost design for such a beam, an optimization technique is developed, written using MATLAB functions, and verified in this study. Because of the efficiency and dependability of the iterative Particle Swarm Optimization (PSO) process, the ACI 318-19 code method is adopted via this algorithm. Using four beam design (decision) variables, which are: beam width b, longitudinal tension reinforcement area As, longitudinal compression reinforcement area A’s, and vertical shear reinforcement area Av; the objective is to minimize the overall beam cost function. The constraints for each of the 60 randomly chosen particles are handled using the self-adaptive penalty function technique, which is applied in all the 100 iterations for each of the four proposed beam design case studies with identical openings. For the developed method, completing all iterations serves as a stopping criterion. Comparative studies are conducted to demonstrate how the compressive strength of concrete and the live load scheme affect the optimal overall beam cost and the associated design variables. The relations between cost of beams and the four design variables, which are presented through graphs and tables, indicate that the beam’s cost is significantly impacted by the loading condition. This is shown by increasing the cost of beam B1, with no sustained live loads, from 722 US dollars to 984 US dollars for beam B4, which has concentrated and distributed sustained live loads. Future research is advised to include modern strengthening techniques for beams with openings, and apply this research to a PSO algorithm with several objectives.

The Successive Approximation Genetic Algorithm (SAGA) for Optimization Problems with Single Constraint

A limited feasible region restricts individuals from evolving optionally and makes it more difficult to solve constrained optimization problems. In order to overcome difficulties such as introducing initial feasible solutions, a novel algorithm called the successive approximation genetic algorithm (SAGA) is proposed; (a) the simple genetic algorithm (SGA) is the main frame; (b) a self-adaptive penalty function is considered and the penalty factor is adjusted automatically by the proportion of feasible and infeasible solutions; (c) a generation-by-generation approach and a three-stages evolution are introduced; and (d) dynamically enlarging and reducing the tolerance error of the constraint violation makes it much easier to generate initial feasible solutions. Then, ten benchmarks and an engineering problem were adopted to evaluate the SAGA in detail. It was compared with the improved dual-population genetic algorithm (IDPGA) and eight other algorithms, and the results show that SAGA finds the optimum in 5 s for an equality constraint and 1 s for an inequality constraint. The largest constraint violation can be accurate to at least three decimal fractions for most problems. SAGA obtains a better value, of 1.3398, than the eight other algorithms for the engineering problem. In conclusion, SAGA is very suitable for solving nonlinear optimization problems with a single constraint, accompanied by more accurate solutions, but it takes a longer time. In reality, SAGA searched for a better solution along the bound after several iterations and converged to an acceptable solution in early evolution. It is critical to improve the running speed of SAGA in the future.

A self-adaptive strategy based firefly algorithm for constrained engineering design problems

Firefly algorithm (FA) is an effective meta-heuristic method, which has drawn extensive attentions and inspired many variants. However, it is difficult to balance the relation of the exploration and exploitation of FA. To this end, FA with self-adaptive strategy (SAFA) is proposed to improve the performance of the algorithm for constrained engineering design problems. Firstly, the characteristics of the standard FA are analyzed, and the essence of FA easily trapped into the local optima is revealed by theory analysis and case study. Secondly, a self-adaptive strategy for attraction model is proposed to improve the exploitation ability, and another self-adaptive strategy for stochastic model is developed to ensure a better balance between the exploration and exploitation. Thirdly, a self-adaptive penalty function is presented to treat constraint conditions. Then, the initial parameter setting is investigated, and the proper initial parameter value corresponding to the optimal performance of SAFA is obtained. And then, SAFA and other FA variants are used to optimize a set of classical and Congress on Evolutionary Computation (CEC) 2015 benchmark functions. Meanwhile, the contributions of self-adaptive strategies for attraction model and stochastic model are investigated with experimental analysis, respectively Finally, SAFA and other meta-heuristic methods are employed to solve constrained engineering design problems. The effects of SAFA with standard and self-adaptive penalty function are compared. Numerical experimental results show that self-adaptive strategies for attraction model and stochastic model improve the performance of FA, and SAFA obtains the best solutions on most of the benchmark functions. In addition, SAFA has the advantage in solving problems with different kind of dimensions, and maintains reasonable population diversity throughout the iteration compared with the other FA variants. Meanwhile, SAFA can reduce the computational complexity and ensure the solution accuracy in solving constrained optimization problems.

A Dual-Population-Based Evolutionary Algorithm for Constrained Multiobjective Optimization

The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> . In c-DPEA, a novel self-adaptive penalty function, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">saPF</i> , is designed to preserve competitive infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> . On the other hand, infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bCAD</i> , is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.

Cohort intelligence with self-adaptive penalty function approach hybridized with colliding bodies optimization algorithm for discrete and mixed variable constrained problems

Recently, several socio-/bio-inspired algorithms have been proposed for solving a variety of problems. Generally, they perform well when applied for solving unconstrained problems; however, their performance degenerates when applied for solving constrained problems. Several types of penalty function approaches have been proposed so far for handling linear and non-linear constraints. Even though the approach is quite easy to understand, the precise choice of penalty parameter is very much important. It may further necessitate significant number of preliminary trials. To overcome this limitation, a new self-adaptive penalty function (SAPF) approach is proposed and incorporated into socio-inspired Cohort Intelligence (CI) algorithm. This approach is referred to as CI–SAPF. Furthermore, CI–SAPF approach is hybridized with Colliding Bodies Optimization (CBO) algorithm referred to as CI–SAPF–CBO algorithm. The performance of the CI–SAPF and CI–SAPF–CBO algorithms is validated by solving discrete and mixed variable problems from truss structure domain, design engineering domain, and several problems of linear and nonlinear in nature. Furthermore, the applicability of the proposed techniques is validated by solving two real-world applications from manufacturing engineering domain. The results obtained from CI–SAPF and CI–SAPF–CBO are promising and computationally efficient when compared with other nature inspired optimization algorithms. A non-parametric Wilcoxon’s rank sum test is performed on the obtained statistical solutions to examine the significance of CI–SAPF–CBO. In addition, the effect of the penalty parameter on pseudo-objective function, penalty function and constrained violations is analyzed and discussed along with the advantages over other algorithms.

Genetic Algorithm-Based Energy Efficiency Maximization for Social-Aware Device-to-Device Communications

In this paper, we propose a novel energy efficiency maximization scheme for social-aware device-to-device (D2D) communications based on a genetic algorithm (GA). The proposed scheme incorporates both social and physical parameters of users to model the energy efficiency maximization problem. The formulated problem considers the spectral reuse, spectral efficiency, and the transmit power constraints of both cellular and D2D users to satisfy their quality of service requirements. Moreover, an algorithm based on the self-adaptive penalty function is applied to convert the constrained problem into an unconstrained problem. Next, GA is utilized to maximize the unconstrained problem. The feasibility of the proposed scheme is shown by computing its time complexity in terms of big- $O$ notation. Moreover, the convergence of the proposed scheme is analyzed by comparing the maximum and average values of the overall energy efficiencies for different iterations. Likewise, the performance is evaluated in terms of overall energy efficiency and system throughput for various D2D communications scenarios. To demonstrate the efficiency of the proposed scheme, the results are compared with those for a static penalty-based GA algorithm. Furthermore, to demonstrate the significance of combining the two types of parameters (i.e., social and physical), the performance of the proposed scheme is compared with schemes based on only social or physical parameters.

Design of Reinforced Concrete Deep Beams using Particle Swarm Optimization Technique

Researches available in literature interrelating neural networks to civil engineering design problems, especially for beep beams, are very rare. Therefore, an optimization algorithm is developed and verified in this study and coded using MATLAB functions to determine the optimum cost design of reinforced concrete deep beams. ACI 318-14 code method is used benefiting from iterative particle swarm optimization technique due to its efficiency and reliability. Minimizing total cost is used as the objective function in terms of four decision variables. Self-adaptive penalty function technique is used to handle constraints for each of the 300 randomly selected particles, and in each of the 50 total iterations followed for each one of four suggested deep beam design case studies. Performing all iterations is used as a stopping criteria for the developed algorithm. Comparative studies are made to show the effect of concrete compressive strength, live load scheme, and length of deep beam, on the optimum total cost and the corresponding decision variables. Results presented in the form of graphs and tables show that the loading condition has a significant effect on the total cost of deep beams. The cost increase is accompanied by deep beam length increase, height increase, longitudinal reinforcement area increase and vertical shear reinforcement area decrease. The calculated optimum cost is noticed for beam DB1, which is 1255 US$, with 1.29 m beam height, 0.01445 m2 vertical shear reinforcement, 0.00914 m2 horizontal shear reinforcement and 0.00238 m2 main longitudinal reinforcement. The results show a relatively less difference in total cost between all the four beams at 4 m length compared to 8 m length. Also, a relatively mild increase in total cost is happened for beams DB3 and DB4 as the height increases, especially above 1.7 m height. As the main longitudinal reinforcement increases, cost of DB4 is affected more significantly than others, and as the vertical shear reinforcement increases, DB4 curve shows a relatively low degradation in cost.

Fixture layout optimization in multi-station sheet metal assembly considering assembly sequence and datum scheme

One of the most influential causes of dimensional inaccuracy in automotive bodies is the inescapable fixture deviation, which is propagated in a Multi-Station Assembly (MSA) process. Therefore, a robust fixture design is necessary to increase product quality. The aim of this paper is to present a methodology for simultaneous optimization of fixture layout and assembly configuration, including assembly sequence and datum shift scheme, in MSA. To model the accumulated variation from one station to the downstream stations, a non-linear state-space representation is adopted. Feasible assembly sequences are automatically generated using a liaison graph and Breadth-First Search algorithm, and also all datum scheme options are provided based on a permutation method that is dependent on the number of parts and stations. Further, the sum of squared standard deviations for key product characteristics to be minimized is an optimization object. Part boundaries, design requirements, and assembly configuration feasibility are the constraints. This constrained problem is converted into an unconstrained one by two strategies: (i) Geometry boundaries and assembly configuration constraints are fulfilled through removing infeasible solutions from the design space and (ii) Design requirements are met by using a self-adaptive penalty function. Finally, the unconstrained problem is optimized using a genetic algorithm. The proposed methodology improved assembly process capability by 68 to 84% for an automotive body side in a case study.

Handling time-varying constraints and objectives in dynamic evolutionary multi-objective optimization

Abstract Recently, several researchers within the evolutionary and swarm computing community have been interested in solving dynamic multi-objective problems where the objective functions, the problem's parameters, and/or the constraints may change over time. According to the related literature, most works have focused on the dynamicity of objective functions, which is insufficient since also constraints may change over time along with the objectives. For instance, a feasible solution could become infeasible after a change occurrence, and vice versa. Besides, a non-dominated solution may become dominated, and vice versa. Motivated by these observations, we devote this paper to focus on the dynamicity of both: (1) problem's constraints and (2) objective functions. To achieve our goal, we propose a new self-adaptive penalty function and a new feasibility driven strategy that are embedded within the NSGA-II and that are applied whenever a change is detected. The feasibility driven strategy is able to guide the search towards the new feasible directions according to the environment changes. The empirical results have shown that our proposal is able to handle various challenges raised by the problematic of dynamic constrained multi-objective optimization. Moreover, we have compared our new dynamic constrained NSGA-II version, denoted as DC-MOEA, against two existent dynamic constrained evolutionary algorithms. The obtained results have demonstrated the competitiveness and the superiority of our algorithm on both aspects of convergence and diversity.

Constraint genetic algorithm and its application in sintering proportioning

This paper puts forward a method for constrained optimization problems based on self-adaptive penalty function and improved genetic algorithm. In order to improve the speed of convergence and avoid premature convergence, a method based on good-point set theory has been proposed. By using good point set method for generating initial population, the initial population is uniformly distributed in the solution space. This paper Designs an elite reverse learning strategy, and proposes a mechanism to automatically adjust the crossover probability according to the individual advantages and disadvantages. The tests indicate that the proposed constrained genetic algorithm is efficient and feasible.

Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.

Regularized machine learning through constraint swarm and evolutionary computation applied to regression problems

Purpose – 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). Design/methodology/approach – 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. Findings – 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. Originality/value – 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 Great Salmon Run Metaheuristic for Robust Shape and Size Design of Truss Structures with Dynamic Constraints

In this investigation, the authors intend to demonstrate the applicability of a recent spotlighted metaheuristic called the great salmon run (TGSR) algorithm for shape and size design of truss structures. The algorithmic functioning of TGSR emulates the annual migration of salmons together with dangers laid through their pathways. In a previous study by the authors, it has been proved that the method is as effective as most of the state-of-the-art metaheuristics for a wide range of numerical benchmark problems. Here, the authors utilize TGSR together with some rival metaheuristics, i.e. bee algorithm (BA), scale factor local search differential evolutionary algorithm (SFLSDEA), chaotic particle swarm optimization (CPSO) algorithm, self adaptive penalty function genetic algorithm (SAPFGA) and mutable smart bee algorithm (MSBA), for optimal design of truss structures with dynamic frequency constraints. To effectively handle the constraints, the authors take the advantage of self-adaptive penalty function (SAPF) constraint handling technique to free the user from any priori penalty coefficient tuning. Therefore, an algorithm for automation of constraint shape and size design of truss structures is proposed here. Furthermore, for more elaboration, the authors consider the results of some previous reports for same problems to find out whether TGSR is capable of yielding comparative results as compared to other metaheuristics. Through the experiments, the exploration/exploitation capabilities of TGSR for truss design are investigated. It is proved that TGSR is not only able to handle the nonlinearities and decision making difficulties associated with shape and size optimization of truss structures but also can show comparative results as compared to powerful state-of-the-art metaheuristics.

A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems

In this paper, a new dynamic self-adaptive multi-objective particle swarm optimization (DSAMOPSO) method is proposed to solve binary-state multi-objective reliability redundancy allocation problems (MORAPs). A combination of penalty function and modification strategies is used to handle the constraints in the MORAPs. A dynamic self-adaptive penalty function strategy is utilized to handle the constraints. A heuristic cost-benefit ratio is also supplied to modify the structure of violated swarms. An adaptive survey is conducted using several test problems to illustrate the performance of the proposed DSAMOPSO method. An efficient version of the epsilon-constraint (AUGMECON) method, a modified non-dominated sorting genetic algorithm (NSGA-II) method, and a customized time-variant multi-objective particle swarm optimization (cTV-MOPSO) method are used to generate non-dominated solutions for the test problems. Several properties of the DSAMOPSO method, such as fast-ranking, evolutionary-based operators, elitism, crowding distance, dynamic parameter tuning, and tournament global best selection, improved the best known solutions of the benchmark cases of the MORAP. Moreover, different accuracy and diversity metrics illustrated the relative preference of the DSAMOPSO method over the competing approaches in the literature.

A robust learning based evolutionary approach for thermal-economic optimization of compact heat exchangers

This paper presents a robust, efficient and parameter-setting-free evolutionary approach for the optimal design of compact heat exchangers. A learning automata based particle swarm optimization (LAPSO) is developed for optimization task. Seven design parameters, including discreet and continuous ones, are considered as optimization variables. To make the constraint handling straightforward, a self-adaptive penalty function method is employed. The efficiency and the accuracy of the proposed method are demonstrated through two illustrative examples that include three objectives, namely minimum total annual cost, minimum weight and minimum number of entropy generation units. Numerical results indicate that the presented approach generates the optimum configuration with higher accuracy and a higher success rate when compared with genetic algorithms (GAs) and particle swarm optimization (PSO).

Optimization of plate-fin heat exchangers by an improved harmony search algorithm

This study explores the use of a proposed variant of harmony search algorithm for design optimization of plate-fin heat exchangers. The algorithm deals with a large number of continuous and discrete variables. To handle the constraints in the optimization problem, a self-adaptive penalty function scheme is used. The efficiency and accuracy of the proposed method are demonstrated through an illustrative example taken from previous studies. Numerical results indicate that the presented approach can generate optimum solutions with higher accuracy when compared to Genetic algorithms (GAs), Particle Swarm Optimization (PSO) and GA hybrids with PSO (GAHPSO).

Optimising maximum power output and minimum entropy generation of Atkinson cycle using mutable smart bees algorithm

The purpose of this article is optimising maximum power output (MPO) and minimum entropy generation (MEG) of an Atkinson cycle as a multi-objective constraint thermodynamic problem by a new improved artificial bee colony algorithm which utilises 'mutable smart bee' (MSB) instead of conventional bees. The results have been checked with some of the most common optimising algorithms like Karaboga's original artificial bee colony, bees algorithm (BA), improved particle swarm optimisation (IPSO), Lukasik firefly algorithm (LFFA) and self-adaptive penalty function genetic algorithm (SAPF-GA). Mutable smart bee (MSB) is able to maintain its historical memories for the location and quality of food sources and also a little chance of mutation during the searching process is considered for this bee. These features were found as strong elements for mining data in constraint areas and the results will prove this claim.

Multiobjective Optimization of Irreversible Thermal Engine Using Mutable Smart Bee Algorithm

A new method called mutable smart bee (MSB) algorithm proposed for cooperative optimizing of the maximum power output (MPO) and minimum entropy generation (MEG) of an Atkinson cycle as a multiobjective, multi-modal mechanical problem. This method utilizes mutable smart bee instead of classical bees. The results have been checked with some of the most common optimizing algorithms like Karaboga’s original artificial bee colony, bees algorithm (BA), improved particle swarm optimization (IPSO), Lukasik firefly algorithm (LFFA), and self-adaptive penalty function genetic algorithm (SAPF-GA). According to obtained results, it can be concluded that Mutable Smart Bee (MSB) is capable to maintain its historical memory for the location and quality of food sources and also a little chance of mutation is considered for this bee. These features were found as strong elements for mining data in constraint areas and the results will prove this claim.