Constrained Design Problems Research Articles

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Engineering Design Problems

Metaheuristic optimization algorithms (Nature-Inspired Optimization Algorithms) are a class of algorithms that mimic the behavior of natural systems such as evolution process, swarm intelligence, human activity and physical phenomena to find the optimal solution. Since the introduction of meta-heuristic optimization algorithms, they have shown their profound impact in solving the high-scale and non-differentiable engineering problems. This paper presents a comparative study of the most widely used nature-inspired optimization algorithms for solving engineering classical design problems, which are considered challenging. The teen metaheuristic algorithms employed in this study are, namely, Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Biogeography Based Optimization Algorithm (BBO), Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES), Cuckoo Search algorithm (CS), Differential Evolution (DE), Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), Gravitational Search Algorithm (GSA) and Particle Swarm Optimization (PSO). The efficiency of these algorithms is evaluated on teen popular engineering classical design problems using the solution quality and convergence analysis, which verify the applicability of these algorithms to engineering classical constrained design problems. The experimental results demonstrated that all the algorithms provide a competitive solution.

A novel hybrid Fick’s law algorithm-quasi oppositional–based learning algorithm for solving constrained mechanical design problems

AbstractIn this article, a recently developed physics-based Fick’s law optimization algorithm is utilized to solve engineering optimization challenges. The performance of the algorithm is further improved by incorporating quasi-oppositional–based techniques at the programming level. The modified algorithm was applied to optimize the rolling element bearing system, robot gripper, planetary gear system, and hydrostatic thrust bearing, along with shape optimization of the vehicle bracket system. Accordingly, the algorithm realizes promising statistical results compared to the rest of the well-known algorithms. Furthermore, the required number of iterations was comparatively less required to attain the global optimum solution. Moreover, deviations in the results were the least even when other optimizers provided better or more competitive results. This being said that this optimization algorithm can be adopted for a critical and wide range of industrial and real-world challenges optimization.

Multi-joint topology optimization for stiffness constrained design problems

Multi-joint topology optimization for stiffness constrained design problems

Bayesian optimization with active learning of design constraints using an entropy-based approach

The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints. Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures, as well as possess low density, high thermal conductivity, narrow solidification range, high solidus temperature, and a small linear thermal expansion coefficient. Traditional Integrated Computational Materials Engineering (ICME) methods are not sufficient for exploring combinatorially-vast alloy design spaces, optimizing for multiple objectives, nor ensuring that multiple constraints are met. In this work, we propose an approach for solving a constrained multi-objective materials design problem over a large composition space, specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy (MPEA) for potential use in next-generation gas turbine blades. Our approach is able to learn and adapt to unknown constraints in the design space, making decisions about the best course of action at each stage of the process. As a result, we identify 21 Pareto-optimal alloys that satisfy all constraints. Our proposed framework is significantly more efficient and faster than a brute force approach.

Finite-time velocity-free adaptive neural constrained cooperative control of Euler–Lagrange systems

This paper addresses a new constrained control design problem to develop the trajectory-tracking specifications of the cooperative control of Euler–Lagrange systems with respect to the convergence rate and steady-state errors by constraining the limited bounds on the trajectory-tracking errors in the leader–follower formation control problem. A control design based on an asymmetric barrier Lyapunov function is proposed for the leader–follower formation control of Euler–Lagrange systems in the presence of unknown parameters and unmodeled dynamics that progresses to the infinity when its arguments attain to the predefined bounds. These constrained output states are considered in the leader–follower formation control problem to cope with the system restrictions such as limited sensing ranges. The Lyapunov stability is pursued to assure that all the signals of the closed-loop system are bounded and the leader–follower formation errors are finite-time semi-globally uniformly ultimately bounded. Finally, computer simulation results represent the impression of the newly proposed constrained leader–follower formation control for the Euler–Lagrange systems.

Chaotic enhanced teaching-based differential evolution algorithm applied to discrete truss optimization

In this paper, we develop a discrete chaotic enhanced hybrid teaching-based differential evolution algorithm (CETDE) that can deal with realistic yet challenging constrained discrete truss design problems more efficiently. CETDE adaptively executes multiple mutation operators to quickly search for the solution, but at the same time, premature convergence, a common issue in discrete optimization, is also prevented by embedding the chaotic logistic rule into the mutations. An improved logical strategy that only allows potential mutants to go through structural analysis is introduced to reduce computation. An enhanced chaotic local search strategy and a one-component change technique are also developed for further efficiency. Besides, CETDE simultaneously keeps continuous and discrete population throughout the evolution, which is distinguishable from existing discrete optimizers, to preserve the stochastic nature. Compared to other state-of-the-art performers in the literature, CETDE illustrates both higher efficiency and solution optimality.

Reinforcement Learning for Efficient Design Space Exploration With Variable Fidelity Analysis Models

Abstract Reinforcement learning algorithms can autonomously learn to search a design space for high-performance solutions. However, modern engineering often entails the use of computationally intensive simulation, which can lead to slower design timelines with highly iterative approaches such as reinforcement learning. This work provides a reinforcement learning framework that leverages models of varying fidelity to enable an effective solution search while reducing overall computational needs. Specifically, it utilizes models of varying fidelity while training the agent, iteratively progressing from low- to high fidelity. To demonstrate the effectiveness of the proposed framework, we apply it to two multimodal multi-objective constrained mixed integer nonlinear design problems involving the components of a ground and aerial vehicle. Specifically, for each problem, we utilize a high-fidelity and a low-fidelity deep neural network surrogate model, trained on performance data generated from underlying ground truth models. A tradeoff between solution quality and the proportion of low-fidelity surrogate model usage is observed. Specifically, high-quality solutions are achieved with substantial reductions in computational expense, showcasing the effectiveness of the framework for design problems where the use of just a high-fidelity model is infeasible. This solution quality-computational efficiency tradeoff is contextualized by visualizing the exploration behavior of the design agents.

Chaotic marine predators algorithm for global optimization of real-world engineering problems

A novel metaheuristic called Chaotic Marine Predators Algorithm (CMPA) is proposed and investigated for the optimization of engineering problems. CMPA integrates the exploration merits of the recently proposed Marine Predators Algorithm (MPA) with the chaotic maps exploitation capabilities. Several chaotic maps were applied in the proposed CMPA to govern MPA parameters that eventually led to controlled exploration and exploitation of search. This study makes an initial attempt to explore and employ CMPA in decoding complex and challenging design and manufacturing problems. For performance evaluation of the proposed algorithm, CEC 2020 numerical problems having different dimensions and five widely adopted constrained design problems were solved. For all problems, both qualitative and qualitative results are examined and discussed. Moreover, two case studies of multi-pass turning were examined by the proposed CMPA algorithm to optimize the cutting operation with a minimum cost of production per unit objective. Furthermore, the suggested CMPA algorithm has been investigated for solving a real-world structural topology optimization problem. Statistical analysis is performed, and the results of CMPA are compared with twelve distinguished algorithms. Outcomes of the proposed variant algorithm on the benchmarks demonstrate its significantly improved performance relative to other optimizers including a variant of MPA and two state-of-the-art IEEE CEC competitions winners algorithms. Findings from the manufacturing process exhibit CMPA proficiency in solving arduous real-world design problems.

Constraint handling methods for a generative envelope design using genetic algorithms: The case of a highly constrained problem

The use of genetic algorithms as generative and performance design techniques often involves, in practice, constraint handling, which can be a complex task. Moreover, environmental simulations are computationally expensive and managing constraints can avoid wasting time on infeasible solutions. Despite these two incentives, and the benefits of an immense literature, both applied and theorical, on constrained optimization, there are only few guidelines and tools directly applicable by architects to address this issue. This paper proposes to fill this gap by identifying, classifying, and implementing different constraint management techniques available to architects. Seven methods have been tested for a highly constrained envelope design problem, consisting in the optimization of a sun-shading system. Three of them are easily replicable to different types of projects while the four others need to find a problem-specific heuristic. It appears that the second category is more efficient but implies the use of generative techniques that are more difficult to implement than parametric models.

A simplified non-equidistant grey prediction evolution algorithm for global optimization

Grey prediction evolution algorithm, which is receiving more and more attention, considers the population sequence of evolutionary algorithms as an equidistant time series. In fact, the average fitness value of each generation population decreases at a variable speed during almost any evolution process. Therefore, the population sequence with the property of variable speed evolution should be modeled more properly as a non-equidistant time series. Along this way, this paper proposes a novel evolutionary algorithm based on a non-equidistant grey model, called simplified non-equidistant grey prediction evolution algorithm. The proposed algorithm is identified by its reproduction operator which is developed by the following three steps. Firstly, a non-equidistant grey model based on the average fitness value of each generation population is modeled. Secondly, the interval in the fitting stage of the non-equidistant grey model is simplified to an approximately equidistant time interval. Finally, a simplified reproduction operator which employs a parameter to preserve the non-equidistant nature in the prediction stage of the non-equidistant grey model is developed. The comprehensive performance of the proposed algorithm is evaluated on CEC2014 and CEC2019, as well as six engineering constrained design problems. Experimental results show that the proposed algorithm ranks first in CEC2014 and CECE2019 benchmark functions. The proposed algorithm can achieve a better solution with fewer computational overhead than some state-of-the-art algorithms on six engineering constrained design problems.The Matlab code of this paper is available onhttps://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE.

An efficient arc-search interior-point algorithm for convex quadratic programming with box constraints

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.

Overview of Degrees of Freedom in the Design of PM Synchronous Machines

This contribution discusses the degrees of freedom that could be advantageously exploited in the conception of permanent magnet (PM) machines in the context of very demanding applications, such as electrical vehicle traction. The aim is to inventory degrees of freedom identified in scientific and technical literatures. Identifying these additional degrees of freedom will help positively respond to highly constrained design problems, which are appearing due to the higher usage of electrical energy in many industrial and consumer products. The goal is also to stimulate new ideas in the design of PM synchronous machines.

Information Design for Differential Privacy

Firms and statistical agencies that publish aggregate data face practical and legal requirements to protect the privacy of individuals. Increasingly, these organizations meet these standards by using publication mechanisms which satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that this is equivalent to a constrained information design problem, and characterize its solution. Moreover, we use a novel result on the comparison of information structures to show that the simple geometric mechanism is optimal whenever data users face supermodular decision problems.

Application of ameliorated Harris Hawks optimizer for designing of low-power signed floating-point MAC architecture

Recently established Harris Hawks optimization (HHO) has natural behaviour for finding an optimum solution in global search space without getting trapped in previous convergence. However, the exploitation phase of the current Harris Hawks optimizer algorithm is poor. In the present research, an improved version of the Harris Hawks optimization algorithm, which combined HHO with Particle Swarm Optimization and named as ameliorated Harris Hawks optimizer algorithm, has been proposed to find the solution of various optimization problems such as nonlinear, non-convex and highly constrained engineering design problem. In the proposed research, the exploitation phase of the existing HHO algorithm is improved using a particle swarm optimization algorithm and its performance tested for CEC2005, CECE2017 and CEC2018 benchmark problems. Also, discrete algorithms such as FFT algorithms, convolution and image processing algorithm use multiply and accumulate (MAC) unit as a critical component. The efficiency of a MAC is mainly dependent upon the speed of operation, power dissipation and chip area along with the complexity level of the circuit. In this research paper, a power-efficient signed floating-point MAC (SFMAC) is proposed using universal compressor-based multiplier (UCM). Instead of having a complex design architecture, a simple multiplexer-based circuit is used to achieve signed floating output. The 8 × 8 SFMAC can take 8-bit mantissa and 3-bit exponent. And therefore, the input to the SFMAC can be in the range of − (7.96875)10 to + (7.96875)10. The design and implementation of the proposed architecture is done on the Cadence Spectre tool in GPDK 90 nm and TSMC 130 nm technologies. The analysis has proved that the proposed SFMAC architecture has consumed the least power than the recent MAC architectures available in the literature.

Optimization of Engineering Design Problems Using Atomic Orbital Search Algorithm

In this paper, optimum design of engineering problems is considered by means of the Atomic Orbital Search (AOS), a recently proposed metaheuristic optimization algorithm. The mathematical development of the algorithm is based on principles of quantum mechanics focusing on the act of electrons around the nucleus of an atom. For numerical investigation, 20 of well-known constrained design problems in different engineering fields are considered; some of which have been benchmarked by the 2020 Competitions on Evolutionary Computation (CEC 2020) for real-world optimization purposes. Statistical results including the best, mean, worst and standard deviation of multiple optimization runs are reported for the AOS algorithm. These results are compared to similar data from previous metaheuristic algorithms found in the literature to establish the efficiency and usefulness of the AOS. It is concluded that the AOS has acceptable behavior in dealing with all the considered constrained optimization problems while the maximum difference of about 40% between the best optimum values of the AOS and other approaches is noted for the robot gripper benchmark problem.

A Canis lupus inspired upgraded Harris hawks optimizer for nonlinear, constrained, continuous, and discrete engineering design problem

AbstractRecently established Harris hawks optimization (HHO) has natural behavior for finding an optimum solution in global search space without getting trapped in previous convergence. However, the exploitation phase of the current Harris hawks optimizer algorithm is poor. In the present research, an improved version of the HHO algorithm, which combines Harris hawks optimizer with Canis lupus inspire grey wolf optimizer (GWO) and named as hHHO‐GWO algorithm, has been proposed to find the solution of various optimization problems such as nonlinear, nonconvex, and highly constrained engineering design problem. In the proposed research, the phase of exploration and exploitation of the existing HHO algorithm has been further improved using GWO algorithm and its performance has been tested for various benchmarks problems including CEC2005 (unimodal, multimodal, and fixed dimensions functions), multimodal functions with variable dimensions, and CEC‐BC‐2017 test functions. Further, the developed hybrid optimizer has been tested for 11 different engineering design and optimization problems and experimental results of hHHO‐GWO have been compared with other optimizer.

A symbiotic organisms search algorithm-based design optimization of constrained multi-objective engineering design problems

PurposeIn 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.Design/methodology/approachThough 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.FindingsFour 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.Originality/valueThe 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.

Optimization methods for magnetic resonance imaging gradient waveform design.

The development and implementation of novel MRI pulse sequences remains challenging and laborious. Gradient waveforms are typically designed using a combination of analytical and ad hoc methods to construct each gradient waveform axis independently. This strategy makes coding the pulse sequence complicated, in addition to being time inefficient. As a consequence, nearly all commercial MRI pulse sequences fail to maximize use of the available gradient hardware or efficiently mitigate physiological effects. This results in expensive MRI systems that underperform relative to their inherent hardware capabilities. To address this problem, a software solution is proposed that incorporates numerical optimization methods into MRI pulse sequence programming. Examples are shown for rotational variant vs. invariant waveform designs, acceleration nulled velocity encoding gradients, and mitigation of peripheral nerve stimulation for diffusion encoding. The application of optimization methods to MRI pulse sequence design incorporates gradient hardware limits and the prescribed MRI protocol parameters (e.g. field-of-view, resolution, gradient moments, and/or b-value) to simultaneously construct time-optimal gradient waveforms. In many cases, the resulting constrained gradient waveform design problem is convex and can be solved on-the-fly on the MRI scanner. The result is a set of multi-axis time-optimal gradient waveforms that satisfy the design constraints, thereby increasing SNR-efficiency. These optimization methods can also be used to mitigate imaging artifacts (e.g. eddy currents) or account for peripheral nerve stimulation. The result of the optimization method is to enable easier pulse sequence gradient waveform design and permit on-the-fly implementation for a range of MRI pulse sequences.

Water strider algorithm: A new metaheuristic and applications

The present paper proposes a novel nature-inspired optimization paradigm, which is called the Water Strider Algorithm (WSA). The WSA is a population-based optimizer inspired by the life cycle of water strider bugs. The WSA mimics territorial behavior, intelligent ripple communication, mating style, feeding mechanisms and succession of water striders. The algorithm is mathematically formulated and benchmarked on forty-four numerical problems, four classic examples, two large scale structural size optimization and one structural damage identifying applications. In two phases, the algorithm is investigated to prove its promising performance against possible biases. Different parametric and nonparametric tests, as well as comparison with well-established and state of the art algorithms, indicate the efficient performance of the proposed WSA. The algorithm is applied to classical constrained, unconstrained, continuous and discrete structural design problems confirming its capability of tackling various challenging problems. The paper also presents a real application of the proposed method in structural health monitoring, in which the WSA effectively identified the damage scenarios.

Constrained Transmit Beampattern Design Using a Correlated LFM-PC Waveform Set in MIMO Radar.

This paper considers the design of a desired transmit beampattern under the good ambiguity function constraint using a correlated linear frequency modulation-phase coded (LFM-PC) waveform set in multiple-input-multiple-output (MIMO) radar. Different from most existing beampattern design approaches, we propose using the LFM-PC waveform set to conquer the challenging problem of synthesizing waveforms with constant-envelope and easy-generation properties, and, meanwhile, solve the hard constraint of a good ambiguity behaviour. First, the ambiguity function of the LFM-PC waveform set is derived, and the superiority of LFM-PC waveforms over LFM and PC waveforms is verified. The temporal and spatial characteristic analysis of the LFM-PC waveform set demonstrates that both the transmit beampattern and sidelobe level are mainly affected by the frequency intervals, bandwidths, and phase-coded sequences of the LFM-PC waveform set. Finally, the constrained beampattern design problem is formulated by optimizing these parameters for desired beampatterns and low sidelobes at different doppler frequencies, which is a bi-objective optimization problem. To solve this, we propose a joint optimization strategy followed by a mandatory optimization, where the sequence quadratic programming (SQP) algorithm and adaptive clonal selection (ACS) algorithm are exploited iteratively. The simulation results demonstrate the efficiency of our proposed method.