Optimizing reliability-based robust design model using multi-objective genetic algorithm

Reliability-based robust design optimization (RBRDO) is one of the most important tools developed in recent years to improve both quality and reliability of the products at an early design stage. This paper presents a comparative study of different formulation approaches of RBRDO models and their performances. The paper also proposes an evolutionary multi-objective genetic algorithm (MOGA) to one of the promising hybrid quality loss functions (HQLF)-based RBRDO model. The enhanced effectiveness of the HQLF-based RBRDO model is demonstrated by optimizing suitable examples.     

Robust Design using Pareto type optimization: A genetic algorithm with arithmetic crossover

In dual response systems (DRSs) optimization restrictions on the secondary response may rule out better conditions, since an acceptable value for the secondary response is usually unknown. In fact, process conditions that result in a smaller standard deviation are often preferable. Recently, several authors stated that the standard deviation of any performance property could be treated as a new property in its own right as far as Pareto optimizer was concerned. By doing this, there will be many alternative solutions (i.e., the trade-offs between the mean and standard deviation responses) of the DRS problem and Pareto optimization can explore them all. Such analysis is useful, and that is required in order to achieve an improved understanding of the problem before searching for a final optimal solution. In this paper, we again follow this new philosophy and solve the DRS problem by using a genetic algorithm with arithmetic crossover. The genetic algorithm is applied to the printing process problem for improving the quality of a printing process. Genetic algorithms, in contrast to the one-solution-at-a-time approach of most optimization algorithms, maintain a population of hundreds, or thousands, of solutions in speedy manner.     

Reliability-based robust design optimization: A general methodology using genetic algorithm

In this paper, we present an improved general methodology including four stages to design robust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simultaneously to propose the new formulation of reliability-based robust design optimization (RBRDO) problems. In order to generate reliable and robust Pareto-optimal solutions, the combination of genetic algorithm with reliability assessment loop based on the performance measure approach is applied as the second stage. Next, we develop two criteria to select a solution from obtained Pareto-optimal set to achieve the best possible implementation. Finally, the result verification is performed with Monte Carlo Simulations and also the quality improvement during manufacturing process is considered by identifying and controlling the critical variables. The effectiveness and applicability of this new proposed methodology is demonstrated through a case study.     

Pareto optimization of a five-degree of freedom vehicle vibration model using a multi-objective uniform-diversity genetic algorithm (MUGA)

In this paper, a new multi-objective uniform-diversity genetic algorithm (MUGA) with a diversity preserving mechanism called the ε-elimination algorithm is used for Pareto optimization of a five-degree of freedom vehicle vibration model considering the five conflicting functions simultaneously. The important conflicting objective functions that have been considered in this work are, namely, seat acceleration, forward tire velocity, rear tire velocity, relative displacement between sprung mass and forward tire and relative displacement between sprung mass and rear tire. Further, different pairs of these objective functions have also been selected for 2-objective optimization processes. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work. It is shown that the results of 5-objective optimization include those of 2-objective optimization and, therefore, provide more choices for optimal design of a vehicle vibration model.     

A Pareto-optimal genetic algorithm for warehouse multi-objective optimization

The automated warehouse management requires to fulfill objectives that are usually conflicting with each other. The decisions taken must ensure optimized usage of resources, cost reduction and better customer service. The warehouse replenishment task is a typical example of multi-objective optimization. In this paper, a genetic algorithm with a new crossover operator is developed to solve the replenishment problem. This algorithm is applied to real warehouse data and produces Pareto-optimal permutations of the stored products. A fuzzy rule-base is proposed to increase the diversity of the optimal solutions.     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.     

Multi-objective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization

A novel and generic multi-objective design paradigm is proposed which utilizes quantum-behaved PSO (QPSO) for deciding the optimal configuration of the LQR controller for a given problem considering a set of competing objectives. There are three main contributions introduced in this paper as follows. (1) The standard QPSO algorithm is reinforced with an informed initialization scheme based on the simulated annealing algorithm and Gaussian neighborhood selection mechanism. (2) It is also augmented with a local search strategy which integrates the advantages of memetic algorithm into conventional QPSO. (3) An aggregated dynamic weighting criterion is introduced that dynamically combines the soft and hard constraints with control objectives to provide the designer with a set of Pareto optimal solutions and lets her to decide the target solution based on practical preferences. The proposed method is compared against a gradient-based method, seven meta-heuristics, and the trial-and-error method on two control benchmarks using sensitivity analysis and full factorial parameter selection and the results are validated using one-tailed T-test. The experimental results suggest that the proposed method outperforms opponent methods in terms of controller effort, measures associated with transient response and criteria related to steady-state.     

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

There is an ever increasing need to use optimization methods for thermal design of data centers and the hardware populating them. Airflow simulations of cabinets and data centers are computationally intensive and this problem is exacerbated when the simulation model is integrated with a design optimization method. Generally speaking, thermal design of data center hardware can be posed as a constrained multi-objective optimization problem. A popular approach for solving this kind of problem is to use Multi-Objective Genetic Algorithms (MOGAs). However, the large number of simulation evaluations needed for MOGAs has been preventing their applications to realistic engineering design problems. In this paper, details of a substantially more efficient MOGA are formulated and demonstrated through a thermal analysis simulation model of a data center cabinet. First, a reduced-order model of the cabinet problem is constructed using the Proper Orthogonal Decomposition (POD). The POD model is then used to form the objective and constraint functions of an optimization model. Next, this optimization model is integrated with the new MOGA. The new MOGA uses a “kriging” guided operation in addition to conventional genetic algorithm operations to search the design space for global optimal design solutions. This approach for optimal design is essential to handle complex multi-objective situations, where the optimal solutions may be non-obvious from simple analyses or intuition. It is shown that in optimizing the data center cabinet problem, the new MOGA outperforms a conventional MOGA by estimating the Pareto front using 50% fewer simulation calls, which makes its use very promising for complex thermal design problems. Recommended by: Monem Beitelmal     

Reliability-based design optimization using probabilistic sufficiency factor

A probabilistic sufficiency factor approach is proposed that combines safety factor and probability of failure. The probabilistic sufficiency factor approach represents a factor of safety relative to a target probability of failure. It provides a measure of safety that can be used more readily than the probability of failure or the safety index by designers to estimate the required weight increase to reach a target safety level. The probabilistic sufficiency factor can be calculated from the results of Monte Carlo simulation with little extra computation. The paper presents the use of probabilistic sufficiency factor with a design response surface approximation, which fits it as a function of design variables. It is shown that the design response surface approximation for the probabilistic sufficiency factor is more accurate than that for the probability of failure or for the safety index. Unlike the probability of failure or the safety index, the probabilistic sufficiency factor does not suffer from accuracy problems in regions of low probability of failure when calculated by Monte Carlo simulation. The use of the probabilistic sufficiency factor accelerates the convergence of reliability-based design optimization.     

Probability of failure for uncertain control systems using neural networks and multi-objective uniform-diversity genetic algorithms (MUGA)

There are much research effort in the literature using Monte Carlo simulation (MCS) which is a direct and simple numerical method, however, it can be computationally very expensive as the governing dynamic equations of the system to be simulated for each random sample using the MCS. In this paper, polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are obtained to simply calculate the probability of failure in the MCS, instead of direct solution of dynamic equation of system. In this way, some input–output data consisting of uncertain parameters of system and controller parameters as inputs and probability of failure of some cost functions as output are used for training such GMDH-type neural networks which replace the very time consuming direct solution of dynamical systems during the MCS. A multi-objective genetic algorithm is also used for Pareto optimal design of PI and PID controllers for both first and second order uncertain system with time delays using methodology of this paper. The objective functions that are considered for such Pareto multi-objective optimization are namely, probability of failure of settling time (P_TS) and probability of failure of overshoot (P_OS). The comparisons of the obtained results using the method of this paper with those obtained using direct method shows a significant reduction in computational time, whilst the accuracy is maintained.     

Stacking sequence design of a composite wing under a random gust using a genetic algorithm

The layup optimization by genetic algorithm (GA) for the composite wing subject to random gust is presented. The aim of optimization is to maximize the strength of wing and the failure index of Tsai-Hill criterion is used as the objective function. The failure index is calculated by Monte Carlo simulation because the external loading and the material properties have random characteristics. The optimization results are validated by comparing the failure probability of the initial and optimal designs. In addition, the optimum by maximum stiffness criterion is also obtained to show that current objective function is appropriate for the design of composite wing.     

A genetic algorithm approach for multi-objective optimization of supply chain networks

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management. It is an important and strategic operations management problem in supply chain management, and usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective SCN design problem. To deal with multi-objective and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. An experimental study using actual data from a company, which is a producer of plastic products in Turkey, is carried out into two stages. While the effects of weight approaches on the performance of proposed solution procedure are investigated in the first stage, the proposed solution procedure and simulated annealing are compared according to quality of Pareto-optimal solutions in the second stage.     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach.     

Multi-objective optimization of sensor array using genetic algorithm

A multi-objective optimization method using genetic algorithm was proposed for sensor array optimization. Based on information theory, selectivity and diversity were used as the criteria for constructing two objective functions. A statistic measurement of resolving power, general resolution factor, and visual inspection were used to evaluate the optimization results with the aid of principal component analysis. In each Pareto set, most nondominated solutions had better statistics than the combination using all potential sensors. Also the principal component plots showed that different vapor classes were generally better separated after optimization. The experiment results indicated that the proposed method could successfully identify a set of Pareto optimal solutions of small size; and most optimized sensor arrays provided input with improved quality, i.e. better separation of target analytes. The running time for implementing the multi-objective optimization was satisfactory.     

Convergence analysis of a self-adaptive multi-objective evolutionary algorithm based on grids

Evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms, especially with self-adaption, are relatively scarce. This paper analyzes the convergence properties of a self-adaptive (μ+1)-algorithm. The convergence of the algorithm is defined, and general convergence conditions are studied. Under these conditions, it is proven that the proposed self-adaptive (μ+1)-algorithm converges in probability or almost surely to the Pareto-optimal front.     

A hybrid multi-objective approach based on the genetic algorithm and neural network to design an incremental cellular manufacturing system

One important issue related to the implementation of cellular manufacturing systems (CMSs) is to decide whether to convert an existing job shop into a CMS comprehensively in a single run, or in stages incrementally by forming cells one after the other, taking the advantage of the experiences of implementation. This paper presents a new multi-objective nonlinear programming model in a dynamic environment. Furthermore, a novel hybrid multi-objective approach based on the genetic algorithm and artificial neural network is proposed to solve the presented model. From the computational analyses, the proposed algorithm is found much more efficient than the fast non-dominated sorting genetic algorithm (NSGA-II) in generating Pareto optimal fronts.     

Testing control software using a genetic algorithm

Complex software is difficult to test. When that software has been developed by a third party in response to a requirements specification and is to be used in an electronic control unit in the automotive, aerospace or marine industries, this testing process can be even more difficult, but is an essential task. However, testing all possible combinations of inputs to software can be time-consuming, tedious and may be intractable. This paper presents a genetic algorithm (GA) designed to search for significant input and output combinations to a software control system. By “significant” is meant those which produce an output (or result) which is not in line with the original specification. It is intended that such a tool should be used to support the human tester by focusing their attention on areas of concern which they can investigate further.     

Genetic algorithm design of neural network and fuzzy logic controllers

This paper discusses the design of neural network and fuzzy logic controllers using genetic algorithms, for real-time control of flows in sewerage networks. The soft controllers operate in a critical control range, with a simple set-point strategy governing “easy” cases. The genetic algorithm designs controllers and set-points by repeated application of a simulator. A comparison between neural network, fuzzy logic and benchmark controller performance is presented. Global and local control strategies are compared. Methods to reduce execution time of the genetic algorithm, including the use of a Tabu algorithm for training data selection, are also discussed. The results indicate that local control is superior to global control, and that the genetic algorithm design of soft controllers is feasible even for complex flow systems of a realistic scale. Neural network and fuzzy logic controllers have comparable performance, although neural networks can be successfully optimised more consistently.