Final Pareto Front Research Articles

Optimization of high-speed angular contact ball bearing for aircraft gearbox utilizing an evolutionary multi-objective algorithm, NSGA-III

We develop a program for predicting bearing performance, including the maximum contact stress, bearing power loss, minimum lubricating film thickness, static safety factor, and dynamic life, and an optimal design for high-speed angular contact ball bearings in aircraft gearboxes using optimization algorithms. A program is developed to predict bearing performance by calculating the loads and displacements of individual balls based on the bearing’s kinematic and static equilibrium equations. Next, an optimization program is developed with non-dominated sorting genetic algorithm III (NSGA-III), wherein calculated bearing performance indicators serve as constraints or objective functions. The performance of individuals within the final Pareto front is evaluated using the inter-criteria correlation (CRITIC) and weighted product methods. The optimization performances of NSGA-III and NSGA-II are compared based on their hypervolume indicators. A solution of the kinematic and static equilibrium equations under the load cases and duty cycles of real aircraft gearboxes is obtained, enhancing the prediction accuracy. Furthermore, optimization, including bearing performance metrics rarely considered in previous studies, is performed. Optimal specifications superior to reference bearings employed in aircraft gearboxes are obtained, enhancing all three objective functions or specific objective functions. The optimization performance of NSGA-III is confirmed to surpass that of conventional NSGA-II.

Bio-inspired multi-objective algorithms applied on production scheduling problems

Production scheduling is a crucial task in the manufacturing process. In this way, the managers must decide the job's production schedule. However, this task is not simple, often requiring complex software tools and specialized algorithms to find the optimal solution. In this work, a multi-objective optimization model was developed to explore production scheduling performance measures to help managers in decision-making related to job attribution under three simulations of parallel machine scenarios. Five important production scheduling performance measures were considered (makespan, tardiness and earliness times, number of tardy and early jobs), and combined into three objective functions. To solve the scheduling problem, three multi-objective evolutionary algorithms are considered (Multi-objective Particle Swarm Optimization, Multi-objective Grey Wolf Algorithm, and Non-dominated Sorting Genetic Algorithm II), and the set of optimum solutions named Pareto Front, provided by each one is compared in terms of dominance, generating a new Pareto Front, denoted as Final Pareto Front. Furthermore, this Final Pareto Front is analyzed through an automatic bio-inspired clustering algorithm based on the Genetic Algorithm. The results demonstrated that the proposed approach efficiently solves the scheduling problem considered. In addition, the proposed methodology provided more robust solutions by combining different bio-inspired multi-objective techniques. Furthermore, the cluster analysis proved fundamental for a better understanding of the results and support for choosing the final optimum solution.

Multi-objective evolutionary approach based on K-means clustering for home health care routing and scheduling problem

This paper suggests a bi-objective mathematical model, called HHC-MOVRPTW for the home health care routing and scheduling problem. HHC-MOVRPTW aims to minimize the overall service time while minimizing the total tardiness compared to the visiting time preferences. The considered problem is a NP hard, combining the Personnel Scheduling Problem and the Vehicle Routing Problem with time windows. Three solution approaches are proposed to solve it. Firstly, the HHC-MOVRPTW is solved with a non-scalar method, called Lexicographical method, in order to obtain a first solution for the problem. It is subsequently solved by two well-known multi-objective evolutionary algorithms, namely the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2). Afterwards, a new hybridization approach, combined the evolutionary algorithm with K-means clustering technique is also suggested to improve the quality of the obtained Pareto sets. This is achieved by dividing the population of NSGA-II and SPEA-2 into sub-populations (clusters) and all sub-solutions have to be combined to find the final Pareto front. The computational experiments are performed using Solomon’s bench- mark instances. Thus, results prove the effectiveness of the proposed approaches and their suitability with the problem.

Towards time-effective optimization: Enviro-economic study of the C3MR LNG process

Liquefied natural gas (LNG) is an important energy carrier and one of the pillars of secure energy supply in many countries. However, energy requirements and the associated carbon footprint of its production are substantial. This, incombination with the rapidly growing production capacities, calls for efficient process design and operation. Arobustmulti-objective optimization study of a3.5 MTPA propane-precooled mixed-refrigerant (C3MR) LNG plant has been done employing the genetic algorithm (GA/NSGA-II), with 18 process parameters varying in a ±75% interval. The study has been performed in a novel Aspen Plus – Matlab interface for parallel flowsheet simulations which exploits the full computational capacity of a desktop computer. An over seven-fold increase in calculation speed has been achieved, allowing for a significant increase in the GA/NSGA-II population count (up to 1000 individuals) without the computations being excessively time-consuming. To choose the most suitable individual from the 1000 individuals in the final Pareto front, four decision making methods: Euclidean distance, fuzzy non-dimensionalized distance, and two statistical methods have been used and the results have been compared and discussed. As a result, amore than 12% reduction in LNG processing costs and a 14% cut in carbon dioxide emissions was achieved. This roughly translates into approx. 76 mil. USD/year decrease in the total annual processing costs and an over 76 KTPA decrease in the carbon dioxide emissions. In addition, the in-optimization behavior of process parameters was studied. Out of the 18 studied parameters, only six exhibited significant changes throughout theoptimization process while the others converged to a seeming overall optimum already in the first two runs. This implies a possibility of using similar parameter analyses in future optimization studies. Finally, results of the single- and dual-objective optimization were confronted with similar studies in the field and compared between each other. As the single-objective optimization yielded only marginal decrease in the respective objective function while significantly increasing the other one, the dual-objective optimization is favored.

Analysis of Bayesian Network Learning Techniques for a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm: a case study on MNK Landscape

This work investigates different Bayesian network structure learning techniques by thoroughly studying several variants of Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm (HMOBEDA), applied to the MNK Landscape combinatorial problem. In the experiments, we evaluate the performance considering three different aspects: optimization abilities, robustness and learning efficiency. Results for instances of multi- and many-objective MNK-landscape show that, score-based structure learning algorithms appear to be the best choice. In particular, HMOBEDA $$_{k2}$$ was capable of producing results comparable with the other variants in terms of the runtime of convergence and the coverage of the final Pareto front, with the additional advantage of providing solutions that are less sensible to noise while the variability of the corresponding Bayesian network models is reduced.

An integrated steam jet ejector power plant for drought adaptation considering water-exergy nexus in an optimal platform

Steam power plants contribute to anthropogenic climate change by emitting a considerable amount of carbon dioxide and losing significant freshwater. In the present study, a novel model-based steam jet ejector power plant is optimally designed to adapt to climate change by minimizing water losses and greenhouse emissions. An iterative thermo-mathematical program and a nonlinear mathematical model represent the system's energy and economic models. At the same time, an exergy analysis evaluates its performance according to the Second law of thermodynamics. A non-dominated sorting genetic algorithm generation III is interfaced with the developed empirical program to solve a multi-objective optimization model. Three decision-making scenarios including a maximum thermal efficiency (I), minimum cost of energy (II), and minimum heat losses (III) are considered to select appropriate configurations in the final Pareto front. Subsequently, a natural draft wet cooling tower and a once-through cooling system are coupled with the optimal configurations. The performance of the fully-integrated systems is evaluated using four new water-exergy nexus criteria including water withdrawal for exergy dissipation, lost exergy for exergy dissipation, water consumption for fuel and product exergies. Finally, a sensitivity analysis is performed to take the environmental fluctuations and model uncertainties into account. The comparative results showed that water consumption for product and fuel exergies improved by 63.65 and 64.08%, while water withdrawal for exergy dissipation of the system was approximately nine times smaller than available model-based steam power plants. Moreover, the energy efficiency of the proposed system was 1.42% greater than the previous systems at the cost of 0.018 $/MJ more cost of energy. Thus, the proposed system can tackle drought and mitigate climate change with more investment in the energy sector.

Incorporation of multimodal multiobjective optimization in designing a filter based feature selection technique

Current work reports about the development of a new feature selection technique fusing two concepts, multimodal multiobjective optimization and filter-based feature selection. Use of the concept of multimodality in multiobjective based feature selection helps in generating diverse set of feature subsets on final Pareto front. This approach evaluates the quality of the reduced feature set by utilizing different quality measures. This process of feature selection focuses on achieving two discrete objectives: (1) identification of a large number of Pareto-optimal solutions along with achieving a good distribution in both objective and decision spaces; (2) making a selection of feature subset with minimal redundancy and high correlation with classes. To achieve the second objective, a variety of objective functions based on information-theoretic measures like normalized mutual information and correlation with class attributes are utilized. A multiobjective ring-based Particle swarm Optimization (PSO) and non-dominated sorting with special crowding distance are employed to cover the aspects corresponding to the first objective. An evaluation is carried out on seven publicly available datasets concerning different classifiers. The results of these experiments illustrate that the multimodal PSO based feature selection approach finds more feature subsets than its simple PSO counterpart in multiobjective environment. And, the results are also compared with those of existing wrapper based multimodal multiobjective feature selection methods.

A sequential surrogate-based multiobjective optimization method: effect of initial data set

Process optimization based on high-fidelity computer simulations or real experimentation is commonly expensive. Therefore, surrogate models are frequently used to reduce the computational or experimental cost. However, surrogate models need to achieve a maximum accuracy with a limited number of sampled points. Sequential sampling is a procedure in which sequentially surrogates are fitted and each surrogate defines the points that need to be sampled and used to fit the next model. For optimization purposes, points are sampled on regions of high potential for the optimal solutions. In this work, we first compared the effect of using different initial sets of points (experimental designs) in a sequential surrogate-based multiobjective optimization method. The optimization method is tested on five benchmark problems and the performance is quantified based on the total number of function evaluations and the quality of the final Pareto Front. Then an industrial applications on titanium welding is presented to show the use of the method. The case study is based on real experimental data.

The development of a novel multi-objective optimization framework for non-vertical well placement based on a modified non-dominated sorting genetic algorithm-II

A single-objective well placement problem is one of the classical optimization problems in oilfield development and has been studied for many years, by researchers worldwide. However, the necessity to face practical applications and handle insufficient data in a single-objective optimization leads to the introduction of a multi-objective optimization framework, which consequently allows an engineer to manage more information. In this study, for the very first time, a multi-objective well placement optimization framework, based on a Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is utilized with a similarity-based mating scheme. To represent the power of this mating procedure, it is compared with two conventional mating selection methods (tournament and roulette wheel selection). In this novel framework, the net present value (NPV) and the recovery factor are considered to be the objective functions while the well coordinates, well types, horizontal section length, orientation, and water injection rate are all assumed as the problem variables. Compared to the tournament and roulette wheel selection methods, the convergence speed analysis of this method indicates a substantial reduction in time, with the number of iterations reduced by 26 and 20%, respectively. Among the mating technique, which is implemented in this work, the final Pareto front, presented in this similarity-based selection method, has more members in the same solution range. Having more individuals in the final Pareto front provides more scenarios for decision makers, which helps them in choosing an optimal scenario based on the limitations and interests of a company.

Interval Multiobjective Optimization With Memetic Algorithms.

One of the most important and widely faced optimization problems in real applications is the interval multiobjective optimization problems (IMOPs). The state-of-the-art evolutionary algorithms (EAs) for IMOPs (IMOEAs) need a great deal of objective function evaluations to find a final Pareto front with good convergence and even distribution. Further, the final Pareto front is of great uncertainty. In this paper, we incorporate several local searches into an existing IMOEA, and propose a memetic algorithm (MA) to tackle IMOPs. At the start, the existing IMOEA is utilized to explore the entire decision space; then, the increment of the hypervolume is employed to develop an activation strategy for every local search procedure; finally, the local search procedure is conducted by constituting its initial population, whose center is an individual with a small uncertainty and a big contribution to the hypervolume, taking the contribution of an individual to the hypervolume as its fitness function, and performing the conventional genetic operators. The proposed MA is empirically evaluated on ten benchmark IMOPs as well as an uncertain solar desalination optimization problem and compared with three state-of-the-art algorithms with no local search procedure. The experimental results demonstrate the applicability and effectiveness of the proposed MA.

Multi-objective optimization for parameter selection and characterization of optical flow methods

Optical flow methods are among the most accurate techniques for estimating displacement and velocity fields in a number of applications that range from neuroscience to robotics. The performance of any optical flow method will naturally depend on the configuration of its parameters, and for different applications there are different trade-offs between the corresponding evaluation criteria (e.g. the accuracy and the processing speed of the estimated optical flow). Beyond the standard practice of manual selection of parameters for a specific application, in this article we propose a framework for automatic parameter setting that allows searching for an approximated Pareto-optimal set of configurations in the whole parameter space. This final Pareto-front characterizes each specific method, enabling proper method comparison and proper parameter selection. Using the proposed methodology and two open benchmark databases, we study two recent variational optical flow methods. The obtained results clearly indicate that the method to be selected is application dependent, that in general method comparison and parameter selection should not be done using a single evaluation measure, and that the proposed approach allows to successfully perform the desired method comparison and parameter selection.

An adaptive strategy on the error of the objective functions for uncertainty-based derivative-free optimization

In this work, a strategy is developed to deal with the error affecting the objective functions in uncertainty-based optimization. We refer to the problems where the objective functions are the statistics of a quantity of interest computed by an uncertainty quantification technique that propagates some uncertainties of the input variables through the system under consideration. In real problems, the statistics are computed by a numerical method and therefore they are affected by a certain level of error, depending on the chosen accuracy. The errors on the objective function can be interpreted with the abstraction of a bounding box around the nominal estimation in the objective functions space. In addition, in some cases the uncertainty quantification methods providing the objective functions also supply the possibility of adaptive refinement to reduce the error bounding box. The novel method relies on the exchange of information between the outer loop based on the optimization algorithm and the inner uncertainty quantification loop. In particular, in the inner uncertainty quantification loop, a control is performed to decide whether a refinement of the bounding box for the current design is appropriate or not. In single-objective problems, the current bounding box is compared to the current optimal design. In multi-objective problems, the decision is based on the comparison of the error bounding box of the current design and the current Pareto front. With this strategy, fewer computations are made for clearly dominated solutions and an accurate estimate of the objective function is provided for the interesting, non-dominated solutions. The results presented in this work prove that the proposed method improves the efficiency of the global loop, while preserving the accuracy of the final Pareto front. The proposed method improves the efficiency of the uncertainty-based optimization by reducing the number of objective evaluations.The method relies on the presence of a derivative-free optimization method, and an adaptive uncertainty quantification method.The proposed method is conceived for multi-objective problems, but it applies to single-objective optimization as well.Results prove that the proposed method saves computations on the dominated solutions, and predicts with accuracy the Pareto front.

Multiobjective Antenna Design By Means of Sequential Domain Patching

A simple yet robust methodology for rapid multiobjective design optimization of antenna structures has been presented. The key component of our approach is sequential domain patching of the design space, which is a stencil-based search that aims at creating a path that connects the extreme Pareto-optimal designs, obtained by means of single-objective optimization runs. The patching process yields the initial approximation of the Pareto set representing the best possible tradeoffs between conflicting design objectives. It is realized-for the sake of computational efficiency-at the level of coarse-discretization electromagnetic (EM) simulation model. The final Pareto front is subsequently obtained using surrogate-assisted optimization where the EM simulation data acquired at the initial design stage is reused.

An object-oriented development environment to optimally design cyclic storage systems

Cyclic storage system (CSS) is defined as physically interconnected and operationally integrated surface water and groundwater subsystems with full direct interactions between the subsystems. Mathematical development and implementation of a CSS model is very complex and all previous works are fully case dependent with a minimum possibility of generalization. This article proposes an integrated development environment called CSSDev, which assists researchers to create and design object-oriented CSS models more easily. Using CSSDev, researchers may skip regeneration of repetitive simulation codes for common elements of a CSS. CSSDev employs NSGA-II to optimally select the design parameters of the models. Two objective functions of the optimization problem are system's total costs and total loss associated with the development alternatives. A real-world large-scale CSS has been modeled and optimized to illustrate the performance of CSSDev. The final Pareto-front is presented and two selected solutions from the set of optimal non-dominated ones are evaluated and discussed.

Simultaneous feature selection and symmetry based clustering using multiobjective framework

In this paper a new framework based on multiobjective optimization (MOO), namely FeaClusMOO, is proposed which is capable of identifying the correct partitioning as well as the most relevant set of features from a data set. A newly developed multiobjective simulated annealing based optimization technique namely archived multiobjective simulated annealing (AMOSA) is used as the background strategy for optimization. Here features and cluster centers are encoded in the form of a string. As the objective functions, two internal cluster validity indices measuring the goodness of the obtained partitioning using Euclidean distance and point symmetry based distance, respectively, and a count on the number of features are utilized. These three objectives are optimized simultaneously using AMOSA in order to detect the appropriate subset of features, appropriate number of clusters as well as the appropriate partitioning. Points are allocated to different clusters using a point symmetry based distance. Mutation changes the feature combination as well as the set of cluster centers. Since AMOSA, like any other MOO technique, provides a set of solutions on the final Pareto front, a technique based on the concept of semi-supervised classification is developed to select a solution from the given set. The effectiveness of the proposed FeaClustMOO in comparison with other clustering techniques like its Euclidean distance based version where Euclidean distance is used for cluster assignment, a genetic algorithm based automatic clustering technique (VGAPS-clustering) using point symmetry based distance with all the features, K-means clustering technique with all features is shown for seven higher dimensional data sets obtained from real-life.

SAR image segmentation based on quantum-inspired multiobjective evolutionary clustering algorithm

The segmentation task in the feature space of an image can be formulated as an optimization problem. Recent researches have demonstrated that the clustering techniques, using only one objective may not obtain suitable solution because the single objective function just can provide satisfactory result to one kind of corresponding data set. In this letter, a novel multiobjective clustering approach, named a quantum-inspired multiobjective evolutionary clustering algorithm (QMEC), is proposed to deal with the problem of image segmentation, where two objectives are simultaneously optimized. Based on the concepts and principles of quantum computing, the multi-state quantum bits are used to represent individuals and quantum rotation gate strategy is used to update the probabilistic individuals. The proposed algorithm can take advantage of the multiobjective optimization mechanism and the superposition of quantum states, and therefore it has a good population diversity and search capabilities. Due to a set of nondominated solutions in multiobjective clustering problems, a simple heuristic method is adopted to select a preferred solution from the final Pareto front and the results show that a good image segmentation result is selected. Experiments on one simulated synthetic aperture radar (SAR) image and two real SAR images have shown the superiority of the QMEC over three other known algorithms.

Optimal multi-objective distribution system reconfiguration with multi criteria decision making-based solution ranking and enhanced genetic operators

In electrical distribution system optimisation, the presence of multiple conflicting objectives is effectively addressed by using Pareto front analysis. This paper deals with optimal reconfiguration considering network losses and energy not supplied as multi-objectives. A set of original contributions are provided with reference to the construction and updating of the best-known Pareto front using a genetic algorithm-based solver. The crossover operator is extended to address multi-objective solutions. The mutation operator is extended to handle a broader number of cases. Multi-objective solution ranking is applied by resorting to multi criteria decision making methods during the creation of the offsprings in the crossover operator, as well as to provide an automatic support for the decision maker to identify the preferable solution in the final Pareto front. The proposed approach is applied on two reference test networks, for which the complete Pareto front is calculated from the entire set of multi-objective solutions. The resulting best-known Pareto front is compared with the complete Pareto front using a metric based on geometrical considerations. This comparison framework is helpful to assess the performance of the multi-objective optimisation solvers.

Development of a Robust Multiobjective Simulated Annealing Algorithm for Solving Multiobjective Optimization Problems

This paper describes the development of a robust algorithm for multiobjective optimization, known as robust multiobjective simulated annealing (rMOSA). rMOSA is a simulated annealing based multiobjective optimization algorithm, in which two new mechanisms are incorporated (1) to speed up the process of convergence to attain Pareto front (or a set of nondominating solutions) and (2) to get uniform nondominating solutions along the final Pareto front. A systematic procedure to call the process of choosing a random point in Archive for the perturbation step (in rMOSA) is chosen as the first mechanism to speed up the process of convergence to obtain/attain a final Pareto front, while the other is a systematic procedure to call the process of choosing a most uncrowded solution in Archive for the perturbation step to get a well-crowded uniform Pareto front. First, a Simple MOSA is developed by using the concepts of an archiving procedure, a simple probability function (which is used to set new-pt as current-pt), single parameter perturbation, and a simple annealing schedule. Then, the proposed two new mechanisms are implemented on top of Simple MOSA to develop a robust algorithm for multiobjective optimization (MOO), known as rMOSA. Seven steps involved in the development of rMOSA are thoroughly explained while presenting the algorithm. Four computationally intensive benchmark problems and one simulation-intensive two-objective problem for an industrial FCCU are solved using two newly developed algorithms (rMOSA and Simple MOSA) and two well-known currently existing MOO algorithms (NSGA-II-JG and NSGA-II). Performances of newly developed rMOSA and Simple MOSA (i.e., rMOSA without two new mechanisms) are compared with NSGA-II-JG and NSGA-II, using different metrics available in MOO literature. Newly developed rMOSA is proved to converge to Pareto sets in less number of simulations with well-crowded uniform nondominating solutions in them, for all the problems considered in this study. Hence, rMOSA can be considered as one of the best algorithm for solving computationally intensive and simulation-intensive MOO problems in chemical as well as other fields of engineering.

Insights on surface wave dispersion and HVSR: Joint analysis via Pareto optimality

Abstract Surface Wave (SW) dispersion and Horizontal-to-Vertical Spectral Ratio (HVSR) are known as tools able to provide possibly complementary information useful to depict the vertical shear-wave velocity profile. Their joint analysis might then be able to overcome the limits which inevitably affect such methodologies when they are singularly considered. When a problem involves the optimization (i.e. the inversion) of two or more objectives, the standard practice is represented by a normalized summation able to account for the typically different nature and magnitude of the considered phenomena (thus objective functions). This way, a single cost function is obtained and the optimization problem is performed through standard solvers. This approach is often problematic not only because of the mathematically and physically inelegant summation of quantities with different magnitudes and units of measurements. The critical point is indeed represented by the inaccurate performances necessarily obtained while dealing with problems characterized by several local minima and the impossibility of a rigorous assessment of the goodness and meaning of the final result. In the present paper joint analysis of both synthetic and field SW dispersion curves and HVSR datasets is performed via the Pareto front analysis. Results show the relevance of Pareto's criterion not only as ranking system to proceed in heuristic optimization (Evolutionary Algorithms) but also as a tool able to provide some insights about the characteristics of the analyzed signals and the overall congruency of data interpretation and inversion. Possible asymmetry of the final Pareto front models is discussed in the light of relative non-uniqueness of the two considered objective functions.