Real-world Engineering Design Problems Research Articles

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Differential evolution with the adaptive penalty method for structural multi-objective optimization

Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance.

A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems

Particle swarm optimization (PSO) has attracted the attention of many researchers because of its simple concept and easy implementation. However, it suffers from premature convergence due to quick loss of population diversity. Meanwhile, real-world engineering design problems are generally nonlinear or large-scale or constrained optimization problems. To enhance the performance of PSO for solving large-scale numerical optimizations and engineering design problems, an adaptive disruption strategy which originates from the disruption phenomenon of astrophysics, is proposed to shift the abilities between global exploration and local exploitation. Meanwhile, a Cauchy mutation is utilized to a certain dimension of the best particle to help particle jump out the local optima. Nine well-known large-scale unconstrained problems, ten complicated shifted and/or rotated functions and four famous constrained engineering problems are utilized to validate the performance of the proposed algorithm compared against those of state-of-the-art algorithms. Experimental results and statistic analysis confirm effectiveness and promising performance of the proposed algorithm.

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

ABSTRACTReference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.

Pareto frontier exploration in multiobjective topology optimization using adaptive weighting and point selection schemes

Topology optimization has been used in many industries and applied to a variety of design problems. In real-world engineering design problems, topology optimization problems often include a number of conflicting objective functions, such to achieve maximum stiffness and minimum mass of a design target. The existence of conflicting objective functions causes the results of the topology optimization problem to appear as a set of non-dominated solutions, called a Pareto-optimal solution set. Within such a solution set, a design engineer can easily choose the particular solution that best meets the needs of the design problem at hand. Pareto-optimal solution sets can provide useful insights that enable the structural features corresponding to a certain objective function to be isolated and explored. This paper proposes a new Pareto frontier exploration methodology for multiobjective topology optimization problems. In our methodology, a level set-based topology optimization method for a single-objective function is extended for use in multiobjective problems, using a population-based approach in which multiple points in the objective space are updated and moved to the Pareto frontier. The following two schemes are introduced so that Pareto-optimal solution sets can be efficiently obtained. First, weighting coefficients are adaptively determined considering the relative position of each point. Second, points in sparsely populated areas are selected and their neighborhoods are explored. Several numerical examples are provided to illustrate the effectiveness of the proposed method.

Multi-objective structural design problem optimization using parameterized t-norm based fuzzy optimization programming technique

Real world engineering design problems are usually characterized by the presence of many conflicting objectives. In this paper, we will make an approach to solve multi-objective structural model using parameterized t-norms based on fuzzy optimization programming technique. Here, binary t-norms are expressed in extended n-ary t-norms and their basic properties and some special cases have been discussed. In this structural model formulation, the objective functions are the weight of the truss and the deflection of loaded joint; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here to demonstrate the efficiency of our proposed optimization approach. The test problem includes a three-bar planar truss subjected to a single load condition. This approximation approach is used to solve this multi-objective structural optimization model. The model is illustrated with numerical examples.

Engineering design optimization using an improved local search based epsilon differential evolution algorithm

Many engineering problems can be categorized into constrained optimization problems (COPs). The engineering design optimization problem is very important in engineering industries. Because of the complexities of mathematical models, it is difficult to find a perfect method to solve all the COPs very well. \(\varepsilon \) constrained differential evolution (\(\varepsilon \)DE) algorithm is an effective method in dealing with the COPs. However, \(\varepsilon \)DE still cannot obtain more precise solutions. The interaction between feasible and infeasible individuals can be enhanced, and the feasible individuals can lead the population finding optimum around it. Hence, in this paper we propose a new algorithm based on \(\varepsilon \) feasible individuals driven local search called as \(\varepsilon \) constrained differential evolution algorithm with a novel local search operator (\(\varepsilon \)DE-LS). The effectiveness of the proposed \(\varepsilon \)DE-LS algorithm is tested. Furthermore, four real-world engineering design problems and a case study have been studied. Experimental results show that the proposed algorithm is a very effective method for the presented engineering design optimization problems.

距離制約を考慮した局所探索に基づく二目的最適化法

Conflicting interrelationships among objective functions are often encountered in real-world engineering design problems. If such exist in a multiobjective optimization problem, no unique solution can simultaneously minimize all of the objective functions. Instead, the solutions of a multiobjective optimization problem are obtained as non-dominated solutions called a Pareto optimal solution set. Since a comprehensive Pareto optimal solution set enables the analysis of the trade-off relationships between conflicting objective functions, obtaining such a solution set can be highly beneficial because it increases flexibility when making engineering design decisions. Therefore, this paper proposes an aggregative gradient-based multiobjective optimization method for bi-objective optimization problems, which can ensure the diversity of the Pareto optimal solution set. The proposed method utilizes an aggregative optimization approach where multiple points are concurrently updated during the optimization process. First, an appropriate searching direction for each point is calculated by solving a linear programming problem considering point distribution. Next, design sensitivities are calculated at each point for use as gradient information in the objective functions and constraints. Then, the design variables of all points are updated using a local optimization technique that considers the previously calculated searching direction. During this update process, the proposed method introduces distance constraints among all the points in the objective function space in order to maintain their diversity, which ensures the diversity of the obtained Pareto optimal solution set. These steps are iteratively conducted until the optimization process is converged. Several numerical examples, including a topology optimization problem, are provided to confirm the usefulness of the proposed bi-objective optimization method.

An integrated approach to automated innovization for discovering useful design principles: Case studies from engineering

Computational optimization methods are most often used to find a single or multiple optimal or near-optimal solutions to the underlying optimization problem describing the problem at hand. In this paper, we elevate the use of optimization to a higher level in arriving at useful problem knowledge associated with the optimal or near-optimal solutions to a problem. In the proposed innovization process, first a set of trade-off optimal or near-optimal solutions are found using an evolutionary algorithm. Thereafter, the trade-off solutions are analyzed to decipher useful relationships among problem entities automatically so as to provide a better understanding of the problem to a designer or a practitioner. We provide an integrated algorithm for the innovization process and demonstrate the usefulness of the procedure to three real-world engineering design problems. New and innovative design principles obtained in each case should clearly motivate engineers and practitioners for its further application to more complex problems and its further development as a more efficient data analysis procedure.

The GA-ACO Method Applied to Engineering Design

The purpose of this paper is to describe refinements to the recently developed GA-ACO method and to show its application to a real world engineering design problem. The GA-ACO method is a genetic algorithm with a new operator, called an ACO operator. ACO stands for Ant Colony Optimization. The ACO operator uses pheromone trails, a method from Ant Colony Optimization to influence the genetic algorithm. The GA-ACO method is used to optimize an engineering design. Engineers produce a preliminary design for a system using a CAD tool. The output of the CAD tool is then translated into a design graph. Many additional characteristics of the design can be represented by labels on the design graph. The GA-ACO method is then used to optimize these labels. This technique can be applied widely to many design optimization problems. The application considered in this paper concerns optimization of designs for efficient assembly. It uses problems in engineering design encountered at Newport News Shipbuilding, the largest shipyard in the United States. We present a comparison of variations of the GA-ACO method with a standard genetic algorithm for this type of problem.

MOMS-GA: A Multi-Objective Multi-State Genetic Algorithm for System Reliability Optimization Design Problems

A custom genetic algorithm was developed and implemented to solve multiple objective multi-state reliability optimization design problems. Many real-world engineering design problems are multi-objective in nature, and among those, several of them have various levels of system performance ranging from perfectly functioning to completely failed. This multi-objective genetic algorithm uses the universal moment generating function approach to evaluate the different reliability or availability indices of the system. The components are characterized by having different performance levels, cost, weight, and reliability. The solution to the multi-objective multi-state problem is a set of solutions, known as the Pareto-front, from which the analyst may choose one solution for system implementation. Two illustrative examples are presented to show the performance of the algorithm; and the multi-objective formulation considered for both of them is the maximization of system availability, and the minimization of both system cost, and weight.

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.

Max-min surrogate-assisted evolutionary algorithm for robust design

Solving design optimization problems using evolutionary algorithms has always been perceived as finding the optimal solution over the entire search space. However, the global optima may not always be the most desirable solution in many real-world engineering design problems. In practice, if the global optimal solution is very sensitive to uncertainties, for example, small changes in design variables or operating conditions, then it may not be appropriate to use this highly sensitive solution. In this paper, we focus on combining evolutionary algorithms with function approximation techniques for robust design. In particular, we investigate the application of robust genetic algorithms to problems with high dimensions. Subsequently, we present a novel evolutionary algorithm based on the combination of a max-min optimization strategy with a Baldwinian trust-region framework employing local surrogate models for reducing the computational cost associated with robust design problems. Empirical results are presented for synthetic test functions and aerodynamic shape design problems to demonstrate that the proposed algorithm converges to robust optimum designs on a limited computational budget.

Robustness considerations in multi-objective optimal design

In real-world engineering design problems we have to search for solutions that simultaneously optimize a wide range of different criteria. Furthermore, the optimal solutions also have to be robust. Therefore, this paper presents a method where a multi-objective genetic algorithm is combined with response surface methods in order to assess the robustness of the identified optimal solutions. The design example is two different concepts of hydraulic actuation systems, which have been modelled in a simulation environment to which an optimization algorithm has been coupled. The outcome from the optimization is a set of Pareto optimal solutions that elucidate the trade-off between energy consumption and control error for each system. Based on these Pareto fronts, promising regions could be identified for each concept. In these regions, sensitivity analyses are performed and thus it can be determined how different design parameters affect the system at different optimal solutions.

Pareto optimization using the struggle genetic crowding algorithm

Many real-world engineering design problems involve the simultaneous optimization of several conflicting objectives. In this paper, a method combining the struggle genetic crowding algorithm with Pareto-based population ranking is proposed to elicit trade-off frontiers. The new method has been tested on a variety of published problems, reliably locating both discontinuous Pareto frontiers as well as multiple Pareto frontiers in multi-modal search spaces. Other published multi-objective genetic algorithms are less robust in locating both global and local Pareto frontiers in a single optimization. For example, in a multi-modal test problem a previously published non-dominated sorting GA (NSGA) located the global Pareto frontier in 41% of the optimizations, while the proposed method located both global and local frontiers in all test runs. Additionally, the algorithm requires little problem specific tuning of parameters.