Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

Expedited constrained multi-objective aerodynamic shape optimization by means of physics-based surrogates

Despite the success of Evolutionary Algorithms in solving complex problems, they may require many function evaluations. This becomes an issue when dealing with costly problems. Surrogate models may overcome this difficulty, though their use in problems with medium to large dimensionality is underexplored in the literature. Problems with multiple conflicting objectives can be formulated as Multi-objective Optimization Problems (MOPs). MOPs have received a great attention lately, mainly with Multi-objective Evolutionary Algorithms (MOEAs). This paper proposes ELMOEA/D-DE, a surrogate-assisted MOEA, for solving expensive MOPs in small evaluation budgets. ELMOEA/D-DE encompasses a state-of-the-art MOEA based on decomposition, Differential Evolution (DE) operators and Extreme Learning Machines. This paper tests three variants of ELMOEA/D-DE, using different DE operators, for solving five known benchmark MOPs with 10 to 60 decision variables. All variants achieve good results in terms of hyper volume metric and the best variant with operator DE/rand/1/bin is compared with two state-of-the-art approaches (MOEA/D-RBF and a non-surrogate-based MOEA), achieving the best results in all but one problems instances.

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

In data center companies, cloud computing can host multiple types of heterogeneous virtual machines (VMs) and provide many features, including flexibility, security, support, and even better maintenance than traditional centers. However, some issues need to be considered, such as the optimization of energy usage, utilization of resources, reduction of time consumption, and optimization of virtual machine placement. Therefore, this paper proposes an alternative multiobjective optimization (MOP) approach that combines the salp swarm and sine-cosine algorithms (MOSSASCA) to determine a suitable solution for virtual machine placement (VMP). The objectives of the proposed MOSSASCA are to maximize mean time before a host shutdown (MTBHS), to reduce power consumption, and to minimize service level agreement violations (SLAVs). The proposed method improves the salp swarm and the sine-cosine algorithms using an MOP technique. The SCA works by using a local search approach to improve the performance of traditional SSA by avoiding trapping in a local optimal solution and by increasing convergence speed. To evaluate the quality of MOSSASCA, we perform a series of experiments using different numbers of VMs and physical machines. The results of MOSSASCA are compared with well-known methods, including the nondominated sorting genetic algorithm (NSGA-II), multiobjective particle swarm optimization (MOPSO), a multiobjective evolutionary algorithm with decomposition (MOEAD), and a multiobjective sine-cosine algorithm (MOSCA). The results reveal that MOSSASCA outperforms the compared methods in terms of solving MOP problems and achieving the three objectives. Compared with the other methods, MOSSASCA exhibits a better ability to reduce power consumption and SLAVs while increasing MTBHS. The main differences in terms of power consumption between the MOSCA, MOPSO, MOEAD, and NSGA-II and the MOSSASCA are 0.53, 1.31, 1.36, and 1.44, respectively. Additionally, the MOSSASCA has higher MTBHS value than MOSCA, MOPSO, MOEAD, and NSGA-II by 362.49, 274.70, 585.73 and 672.94, respectively, and the proposed method has lower SLAV values than MOPSO, MOEAD, and NSGA-II by 0.41, 0.28, and 1.27, respectively.

A hyperparameter-optimized Kriging surrogate model was developed for the structural collapse behavior framework presented in this paper. The assessment is conducted on a stiffened panel subject to axial load and lateral pressure, typical of the deck structure of a bulk carrier ship. This behavior is characterized using nonlinear finite element analysis to determine the collapse response. The surrogate model’s hyperparameters were optimized using a Genetic Algorithm to achieve the best performance, and the trained framework can predict ultimate strength. By following this approach, the problem can be reformulated as a multi-objective optimization task. This framework involves associating the Kriging surrogate model with a multi-objective evolutionary optimization algorithm based on Genetic Algorithms to balance the trade-off between the weight and ultimate strength of the stiffened panel. The results confirm the applicability of the Kriging surrogate framework to predict the ultimate strength and assess the collapse analysis of the stiffened panels, ensuring accuracy through GA-based hyperparameter optimization.

Constraints handling in Nash/Adjoint optimization methods for multi-objective aerodynamic design

Distribution system (DS) service restoration is a very complex multi-objective and multi-constraint optimization problem, which requires high-quality Pareto fronts for helping the DS operators' work. This paper proposes a multi-objective evolutionary algorithm (MOEA) that combines the advantages of MOEAs in Tables with the properties of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to recover Pareto fronts of the service problem. Its main differentials are its ability of recovering high-quality Pareto fronts, even in large-scale DSs, and of prioritizing switching operations in Remotely Controlled Switches (RCSs), independently of amount of RCSs. In opposite of Manually Controlled Switches (MCSs), RCS can be faster and cheapest operated from operating center. Several tests were carried out to validate and to compare the proposed MOEA to three MOEAs published in literature. Four metrics were used for assessing the quality of Pareto fronts generated and a Welch's t hypothesis test enabled the comparison of MOEAs' performance. Test results indicate the proposed MOEA outperforms those three MOEAs published in literature.

In this paper we propose a methodology based on an evolutionary multiobjective optimization algorithm for the problem of up-grading (expansion) the physical topology of transparent optical networks. The aim is to define the new topology layout and the specification of the new optical devices that should be deployed in an existing network in order to improve its performance, considering simultaneously the total installation cost (capital cost) and the total network blocking probability (performance criteria). To accomplish that, we propose a capital cost model for the network. We considered the following physical layer impairments: losses in optical devices, amplified spontaneous emission in optical amplifier and homodyne crosstalk in optical cross connect. The multiobjective optimization evolutionary algorithm used in the optimization process is the NSGA-II. Our proposed methodology can solve the expand physical topology design problem taking into account the physical layer impairments and the capital costs simultaneously. We also present a case study to show the effectiveness of our methodology.

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

An improved multi-objective population-based extremal optimization algorithm with polynomial mutation

Existing multi-objective (MO) evolutionary algorithms apply a fixed search space in the parameter domain. This approach needs a good guess or a-prior knowledge of a promising search area since a wrongly specified range of search space often leads to poor solutions. To address the issue, this paper proposes a novel approach of adaptive search space for MO optimization. Through the method of shrinking and expanding, the technique is capable of directing the evolution to reach more promising search regions even if it is not covered in the initial search space. The role of the inductive learning process is also introduced, which is performed by an exploratory multi-objective evolutionary algorithm to enhance the search from being trapped in local optima as well as to promote the population diversity along the discovered Pareto-optimal front. Features of the proposed approach are experimented and investigated upon benchmark MO optimization problems.

In order to obtain maximally innovative and successful product designs, the utilization of optimization strategies at the product design planning stage is of prime importance, and the methods proposed in this paper enable multiobjective optimization technologies to be effectively applied. The necessity and effectiveness of utilizing optimization techniques at the product design planning stage are first explained, and the features that this requires are then clarified. Optimization solutions provided at the product design planning stage, while far from final, can nevertheless be used to obtain guidelines for more preferable product designs. For this purpose, even if characteristics evaluated at the product design planning stages are simplified and/or idealized, the interrelationships among all related characteristics should be simultaneously and thoroughly explored. The successful application of optimization techniques at the product design planning stage requires the rapid presentation and evaluation of a variety of alternative designs, a deeper understanding of the reasons for the optimized designs that are developed, and breakthrough of the initial optimized design solutions, so that the most effective design can ultimately be implemented in a manufactured product. This paper proposes multiobjective design optimization methodologies and procedures, utilized at the product design planning stage, to achieve these goals.

Many real-world optimization problems are characterized by multiple conflicting objectives, which are known as multi-objective optimization problems (MOPs). In the last two decades, evolutionary algorithms have shown promising performance in solving various MOPs, and a large number of multi-objective evolutionary algorithms (MOEAs) have been proposed. In order to determine the most suitable MOEA for a specific MOP, it is usually necessary to perform experiments to compare the performance of multiple candidate MOEAs. In 2017, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which provides the source codes of many state-of-the-art MOEAs and helps researchers perform batch experiments on these MOEAs. In this work, we illustrate the method of using the newest version of PlatEMO to solve MOPs in applications, by means of a case study on the feature selection problem, which is an important and difficult task in machine learning and data mining. This paper details the method of adding the feature selection problem to PlatEMO, and presents the experimental results of eight MOEAs on nine datasets in feature selection.