S-metric Selection Evolutionary Multi-objective Algorithm Research Articles

Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems

A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.

Continuous Cartesian Genetic Programming based representation for multi-objective neural architecture search

We propose a novel neural architecture search (NAS) approach for the challenge of designing convolutional neural networks (CNNs) that achieve a good tradeoff between complexity and accuracy. We rely on Cartesian genetic programming (CGP) and integrated real-based and block-chained CNN representation, for optimization using multi-objective evolutionary algorithms (MOEAs) in the continuous domain. We introduce two variants, CGP-NASV1 and CGP-NASV2, which differ in the granularity of their respective search spaces. To evaluate the proposed algorithms, we utilized the non-dominated sorting genetic algorithm II (NSGA-II) on the CIFAR-10, CIFAR-100,and SVHN datasets. Additionally, we extended the empirical analysis while maintaining the same solution representation to assess other searching techniques such as differential evolution (DE), the multi-objective evolutionary algorithm based on decomposition (MOEA/D), and the S metric selection evolutionary multi-objective algorithm (SMS-EMOA). The experimental results demonstrate that our approach exhibits competitive classification performance and model complexity compared to state-of-the-art methods.

Adaptive Controller Tuning Method Based on Online Multiobjective Optimization: A Case Study of the Four-Bar Mechanism.

The efficient speed regulation of four-bar mechanisms is required for many industrial processes. These mechanisms are hard to control due to the highly nonlinear behavior and the presence of uncertainties or disturbances. In this paper, different Pareto-front approximation search approaches in the adaptive controller tuning based on online multiobjective metaheuristic optimization are studied through their application in the four-bar mechanism speed regulation problem. Dominance-based, decomposition-based, metric-driven, and hybrid search approaches included in the algorithms, such as nondominated sorting genetic algorithm II, multiobjective evolutionary algorithm based on decomposition and differential evolution, S-metric selection evolutionary multiobjective algorithm, and nondominated sorting genetic algorithm III, respectively, are considered in this paper. Also, a proposed metric-driven algorithm based on the differential evolution and the hypervolume indicator (HV-MODE) is incorporated into the analysis. The comparative descriptive and nonparametric statistical evidence presented in this paper shows the effectiveness of the adaptive controller tuning based on online multiobjective metaheuristic optimization and reveals the advantages of the metric-driven search approach.

Static and incremental dynamic approaches for multi-objective bitmap join indexes selection in data warehouses

Data warehouses are very large databases and play key role in intelligent decision making in enterprises. The bitmap join indexes selection problem is crucial in the data warehouse physical design and known to be NP-hard. All the existing methods that solve this problem use single objective function and static query workload during the optimization. In the present work, we propose a multi-objective formulation of the problem using I) a static query workload and II) an incremental dynamic query workload. Three best well-known multi-objective evolutionary algorithms, Non-dominated sorting-based genetic algorithm II, S-Metric Selection Evolutionary Multi-Objective Algorithm and Strength Pareto Evolutionary Algorithm 2, are used to solve the multi-objective bitmap join indexes selection problem using both static and incremental dynamic query workloads. A set of experiments are performed to demonstrate the effectiveness of the proposed approaches. The incremental dynamic approach demonstrates a new perspective on bitmap join indexes optimization in a changing environment of an operational data warehouse.

A reliable build orientation optimization method in additive manufacturing: the application to FDM technology

Additive manufacturing (AM) is a group of processes which manufacture a part by adding sequential layers of material on each other. In the last decade, these processes have been extensively applied in industry for constructing small volumes of complex, customized parts. Since parts are built layer-by-layer, the build orientation affects the surface quality and the total cost of the part. The search for optimal build orientation is not trivial since these factors are, typically, in conflict with each other. The major limitation of the methods described in the literature to choose the optimal build direction is in the insufficient accuracy of the estimates of the manufacturing cost and of the surface quality. These factors are very complex to be estimated, and accuracy in their evaluation requires methods that are very time-consuming. On the contrary, in practical use, a multi-objective optimization process requires an objective function that is reliable and easy to be evaluated. In order to overcome these problems, in this paper, original methods to estimate the manufacturing cost and surface quality as a function of build orientation are presented. They are implemented, for the fused deposition modeling (FDM) technology, in a multi-objective optimization problem that is solved by an S-metric selection evolutionary multi-objective algorithm (SMS-EMOA), obtaining an approximation of the Pareto front. The final selection of the recommended orientation is performed by the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. Properly designed case studies are used to evaluate the reliability of the proposed method, and the results are compared with the state-of-the-art method to find optimal build orientation.

Synergy Effects in Electric and Hybrid Electric Aircraft

The interest in electric and hybrid electric power system has been increasing, in recent times, due to the benefits of this technology, such as high power-to-weight ratio, reliability, compactness, quietness, and, above all, elimination of local pollutant emissions. One of the key factors of these technologies is the possibility to exploit the synergy between powertrain, structure, and mission. This investigation addresses this topic by applying multi-objective optimization to two test cases — a fixed-wing, tail-sitter, Vertical Take-off and Landing Unmanned Aerial Vehicle (VTOL-UAV), and a Medium-Altitude Long-Endurance Unmanned Aerial Vehicle (MALE-UAV). Cruise time and payload weight were selected as goals for the first optimization problem, while fuel consumption and electric endurance were selected for the second one. The optimizations were performed with Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), by taking several constraints into account. The VTOL-UAV optimization was performed, at different levels (structure only, power system only, structure and power system together). To better underline the synergic effect of electrification, the potential benefit of structural integration and multi-functionalization was also addressed. The optimization of the MALE-UAV was performed at two different levels (power system only, power system, and mission profile together), to explore the synergic effect of hybridization. Results showed that large improvements could be obtained, either in the first test case when, both, the powertrain design and the aircraft structure were considered, and in the optimization of the hybrid electric UAV, where the optimization of the aircraft flight path gave a strong contribution to the overall performances.

Efficient algorithms for solving nonlinear fractional programming problems

In this paper, an efficient algorithm based on the Pascoletti-Serafini scalarization (PS) approach is proposed to obtain almost uniform approximations of the entire Pareto front of bi-objective optimization problems. Five test problems with convex, non-convex, connected, and disconnected Pareto fronts are applied to evaluate the quality of approximations obtained by the proposed algorithm. Results are compared with results of some algorithms including the normal constraint (NC), weighted constraint (WC), Benson type, differential evolution (DE) with binomial crossover, non-dominated sorting genetic algorithm-II (NSGA-II), and S metric selection evolutionary multiobjective algorithm (SMS-EMOA). The results confirm the effectiveness of the presented bi-objective algorithm in terms of the quality of approximations of the Pareto front and CPU time. In addition, two algorithms are presented for approximately solving fractional programming (FP) problems. The first algorithm is based on an objective space cut and bound method for solving convex FP problems and the second algorithm is based on the proposed bi-objective algorithm for solving nonlinear FP problems. In addition, several examples are provided to demonstrate the performance of these suggested fractional algorithms.

Two efficient algorithms for constructing almost even approximations of the Pareto front in multi-objective optimization problems

ABSTRACTIn this article, two algorithms are proposed for constructing almost even approximations of the Pareto front of multi-objective optimization problems. The first algorithm is a hybrid of the ε-constraint and Pascoletti–Serafini scalarization methods for solving bi-objective problems. The second is a modification of the successive Pareto optimization (SPO) algorithm for solving three-objective problems. In these algorithms, the MATLAB fmincon solver is used to solve single-objective optimization problems, which returns a local optimal solution. Some metrics are considered to evaluate the quality of approximations obtained by the suggested algorithms on six test problems, and their results are compared with other algorithms (normal constraint, weighted constraint, SPO, differential evolution, multi-objective evolutionary algorithm/decomposition–differential evolution, non-dominated sorting genetic algorithm-II and S-metric selection evolutionary multi-objective algorithm). Experimental results show that the proposed algorithms provide almost even approximations of the whole Pareto front, and better quality of approximation and CPU time compared with established algorithms.

An Improved S-Metric Selection Evolutionary Multi-Objective Algorithm With Adaptive Resource Allocation

One of the main disadvantages of evolutionary multi-objective algorithms (EMOAs) based on hypervolume is the computational cost of the hypervolume computation. This deficiency gets worse either when an EMOA calculates the hypervolume several times or when it is dealing with problems having more than three objectives. In this sense, some researchers have designed strategies to reduce the number of hypervolume calculations. Among them, the use of the locality property of the hypervolume has emerged as an alternative to deal with this problem. This property states that if a solution is moving in its neighborhood, only its contribution is affected and the contributions of the rest of the solutions remain the same. In this paper, we present a novel evolutionary approach that exploits the locality property of the hypervolume. The proposed approach adopts a probability to use two or three individuals in its environmental selection procedure. In this way, it only needs to compute two or three hypervolume contributions per iteration. The proposed algorithm is evaluated by solving the standard benchmark test problems and two real-world applications where the features of the problems are unknown. According to the results, the proposed approach is a promising alternative for solving problems with a high number of objectives because of three main reasons: 1) it is competitive with respect to the state-of-the-art EMOAs based on hypervolume; 2) it does not need extra information about the problem (which is particularly essential when solving real-world applications); and 3) its computational cost is much lower than the other hypervolume-based EMOAs.

Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach.

An alternative hypervolume-based selection mechanism for multi-objective evolutionary algorithms

In this paper, we are interested in selection mechanisms based on the hypervolume indicator with a particular emphasis on the mechanism used in an improved version of the S metric selection evolutionary multi-objective algorithm (SMS-EMOA) called iSMS-EMOA, which exploits the locality property of the hypervolume. Here, we propose a new selection scheme which approximates the contribution of solutions to the hypervolume and it is designed to preserve the locality property exploited by iSMS-EMOA. This approach is proposed as an alternative to the use of exact hypervolume calculations and is aimed for solving many-objective optimization problems. The proposed approach is called "approximate version of the improved SMS-EMOA (aviSMS-EMOA)" and is validated using standard test problems (with three or more objectives) and performance indicators taken from the specialized literature. Our preliminary results indicate that our proposed approach is a good alternative to solve many-objective optimization problems, if we consider both quality in the solutions and running time required to obtain them because it outperforms two versions of the original SMS-EMOA that approximate the contributions to the hypervolume, it outperforms MOEA/D using penalty boundary intersection and it is competitive with respect to the original SMS-EMOA in several of the test problems adopted. Also, its computational cost is reasonable (it is slower than MOEA/D, but faster than SMS-EMOA).

Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary Algorithms by Means of Desirability Functions

In this paper, a concept for efficiently approximating the practically relevant regions of the Pareto front (PF) is introduced. Instead of the original objectives, desirability functions (DFs) of the objectives are optimized, which express the preferences of the decision maker. The original problem formulation and the optimization algorithm do not have to be modified. DFs map an objective to the domain [0, 1] and nonlinearly increase with better objective quality. By means of this mapping, values of different objectives and units become comparable. A biased distribution of the solutions in the PF approximation based on different scalings of the objectives is prevented. Thus, we propose the integration of DFs into the S-metric selection evolutionary multiobjective algorithm. The transformation ensures the meaning of the hypervolumes internally computed. Furthermore, it is shown that the reference point for the hypervolume calculation can be set intuitively. The approach is analyzed using standard test problems. Moreover, a practical validation by means of the optimization of a turning process is performed.