Special Issue "Numerical and Evolutionary Optimization 2020"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (28 February 2021).

Special Issue Editors

Dr. Marcela Quiroz
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Guest Editor
Centro de Investigación en Inteligencia Artificial, University of Veracruz, 91000 Xalapa, Mexico
Interests: experimental algorithmics; metaheuristics; genetic algorithms; bin packing; machine learning; causal inference applications
Special Issues and Collections in MDPI journals
Prof. Juan Gabriel Ruiz
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Guest Editor
Departamento de Computacion, Universidad de la Sierra Juarez, Av. Universidad s/n, C.P. 68725, Ixtlan de Juarez, Oaxaca, Mexico
Interests: graphical user interface design; evolutionary computation
Dr. Luis Gerardo de la Fraga
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Guest Editor
Computer Science Department, Cinvestav, Av. IPN 2508, 07360 Mexico City, Mexico
Interests: computer vision; optimization; metaheuristics
Prof. Dr. Oliver Schütze
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Guest Editor
Depto de Computacion, CINVESTAV-IPN, 07360 Mexico City, Mexico
Interests: multi-objective optimization; evolutionary computation (genetic algorithms and evolution strategies); numerical analysis; engineering applications
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will consist of selected papers presented at the 8th International Workshop on Numerical and Evolutionary Optimization (NEO 2020), as well as other works related to NEO. High-quality papers considered to fit the scope of the journal will be evaluated by reviewers and those that are accepted will be published free of charge.

NEO 2020 focuses on optimization problems related to energy, however, all contributions related to numerical and evolutionary optimization are welcome. See http://neo.cinvestav.mx for more detailed information about the event.

The topics of interest include (but are not limited to) the following:

A) Optimization, machine learning and metaheuristics applied to:

  • Energy production and consumption;
  • Wind power;
  • Solar and PV energy;
  • Nuclear energy;
  • Bioenergy;
  • Ocean energy;
  • Hydro energy;

B) Search and optimization:

  • Single- and multi-objective optimization;
  • Advances in evolutionary algorithms and genetic programming;
  • Hybrid and memetic algorithms;
  • Set oriented numerics;
  • Stochastic optimization;
  • Robust optimization;

C) Real world problems:

  • Energy optimization and prediction;
  • Modeling and control of real-world energy systems;
  • Smart cities.

Dr. Marcela Quiroz
Dr. Juan Gabriel Ruiz
Dr. Luis Gerardo de la Fraga
Prof. Dr. Oliver Schütze
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (15 papers)

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Research

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Open AccessArticle
A Peptides Prediction Methodology for Tertiary Structure Based on Simulated Annealing
Math. Comput. Appl. 2021, 26(2), 39; https://doi.org/10.3390/mca26020039 - 29 Apr 2021
Viewed by 269
Abstract
The Protein Folding Problem (PFP) is a big challenge that has remained unsolved for more than fifty years. This problem consists of obtaining the tertiary structure or Native Structure (NS) of a protein knowing its amino acid sequence. The computational methodologies applied to [...] Read more.
The Protein Folding Problem (PFP) is a big challenge that has remained unsolved for more than fifty years. This problem consists of obtaining the tertiary structure or Native Structure (NS) of a protein knowing its amino acid sequence. The computational methodologies applied to this problem are classified into two groups, known as Template-Based Modeling (TBM) and ab initio models. In the latter methodology, only information from the primary structure of the target protein is used. In the literature, Hybrid Simulated Annealing (HSA) algorithms are among the best ab initio algorithms for PFP; Golden Ratio Simulated Annealing (GRSA) is a PFP family of these algorithms designed for peptides. Moreover, for the algorithms designed with TBM, they use information from a target protein’s primary structure and information from similar or analog proteins. This paper presents GRSA-SSP methodology that implements a secondary structure prediction to build an initial model and refine it with HSA algorithms. Additionally, we compare the performance of the GRSAX-SSP algorithms versus its corresponding GRSAX. Finally, our best algorithm GRSAX-SSP is compared with PEP-FOLD3, I-TASSER, QUARK, and Rosetta, showing that it competes in small peptides except when predicting the largest peptides. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters
Math. Comput. Appl. 2021, 26(2), 36; https://doi.org/10.3390/mca26020036 - 24 Apr 2021
Viewed by 217
Abstract
A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in [...] Read more.
A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
An Interactive Recommendation System for Decision Making Based on the Characterization of Cognitive Tasks
Math. Comput. Appl. 2021, 26(2), 35; https://doi.org/10.3390/mca26020035 - 21 Apr 2021
Viewed by 247
Abstract
The decision-making process can be complex and underestimated, where mismanagement could lead to poor results and excessive spending. This situation appears in highly complex multi-criteria problems such as the project portfolio selection (PPS) problem. Therefore, a recommender system becomes crucial to guide the [...] Read more.
The decision-making process can be complex and underestimated, where mismanagement could lead to poor results and excessive spending. This situation appears in highly complex multi-criteria problems such as the project portfolio selection (PPS) problem. Therefore, a recommender system becomes crucial to guide the solution search process. To our knowledge, most recommender systems that use argumentation theory are not proposed for multi-criteria optimization problems. Besides, most of the current recommender systems focused on PPS problems do not attempt to justify their recommendations. This work studies the characterization of cognitive tasks involved in the decision-aiding process to propose a framework for the Decision Aid Interactive Recommender System (DAIRS). The proposed system focuses on a user-system interaction that guides the search towards the best solution considering a decision-maker’s preferences. The developed framework uses argumentation theory supported by argumentation schemes, dialogue games, proof standards, and two state transition diagrams (STD) to generate and explain its recommendations to the user. This work presents a prototype of DAIRS to evaluate the user experience on multiple real-life case simulations through a usability measurement. The prototype and both STDs received a satisfying score and mostly overall acceptance by the test users. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessFeature PaperArticle
Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
Math. Comput. Appl. 2021, 26(2), 31; https://doi.org/10.3390/mca26020031 - 15 Apr 2021
Viewed by 263
Abstract
We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point [...] Read more.
We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
Convolutional Neural Network–Component Transformation (CNN–CT) for Confirmed COVID-19 Cases
Math. Comput. Appl. 2021, 26(2), 29; https://doi.org/10.3390/mca26020029 - 12 Apr 2021
Viewed by 322
Abstract
The COVID-19 disease constitutes a global health contingency. This disease has left millions people infected, and its spread has dramatically increased. This study proposes a new method based on a Convolutional Neural Network (CNN) and temporal Component Transformation (CT) called CNN–CT. This method [...] Read more.
The COVID-19 disease constitutes a global health contingency. This disease has left millions people infected, and its spread has dramatically increased. This study proposes a new method based on a Convolutional Neural Network (CNN) and temporal Component Transformation (CT) called CNN–CT. This method is applied to confirmed cases of COVID-19 in the United States, Mexico, Brazil, and Colombia. The CT changes daily predictions and observations to weekly components and vice versa. In addition, CNN–CT adjusts the predictions made by CNN using AutoRegressive Integrated Moving Average (ARIMA) and Exponential Smoothing (ES) methods. This combination of strategies provides better predictions than most of the individual methods by themselves. In this paper, we present the mathematical formulation for this strategy. Our experiments encompass the fine-tuning of the parameters of the algorithms. We compared the best hybrid methods obtained with CNN–CT versus the individual CNN, Long Short-Term Memory (LSTM), ARIMA, and ES methods. Our results show that our hybrid method surpasses the performance of LSTM, and that it consistently achieves competitive results in terms of the MAPE metric, as opposed to the individual CNN and ARIMA methods, whose performance varies largely for different scenarios. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
Effect of the Profile of the Decision Maker in the Search for Solutions in the Decision-Making Process
Math. Comput. Appl. 2021, 26(2), 28; https://doi.org/10.3390/mca26020028 - 31 Mar 2021
Viewed by 287
Abstract
Many real-world optimization problems involving several conflicting objective functions frequently appear in current scenarios and it is expected they will remain present in the future. However, approaches combining multi-objective optimization with the incorporation of the decision maker’s (DM’s) preferences through multi-criteria ordinal classification [...] Read more.
Many real-world optimization problems involving several conflicting objective functions frequently appear in current scenarios and it is expected they will remain present in the future. However, approaches combining multi-objective optimization with the incorporation of the decision maker’s (DM’s) preferences through multi-criteria ordinal classification are still scarce. In addition, preferences are rarely associated with a DM’s characteristics; the preference selection is arbitrary. This paper proposes a new hybrid multi-objective optimization algorithm called P-HMCSGA (preference hybrid multi-criteria sorting genetic algorithm) that allows the DM’s preferences to be incorporated in the optimization process’ early phases and updated into the search process. P-HMCSGA incorporates preferences using a multi-criteria ordinal classification to distinguish solutions as good and bad; its parameters are determined with a preference disaggregation method. The main feature of P-HMCSGA is the new method proposed to associate preferences with the characterization profile of a DM and its integration with ordinal classification. This increases the selective pressure towards the desired region of interest more in agreement with the DM’s preferences specified in realistic profiles. The method is illustrated by solving real-size multi-objective PPPs (project portfolio problem). The experimentation aims to answer three questions: (i) To what extent does allowing the DM to express their preferences through a characterization profile impact the quality of the solution obtained in the optimization? (ii) How sensible is the proposal to different profiles? (iii) How much does the level of robustness of a profile impact the quality of final solutions (this question is related with the knowledge level that a DM has about his/her preferences)? Concluding, the proposal fulfills several desirable characteristics of a preferences incorporation method concerning these questions. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification
Math. Comput. Appl. 2021, 26(2), 27; https://doi.org/10.3390/mca26020027 - 30 Mar 2021
Viewed by 316
Abstract
Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to [...] Read more.
Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
Differential Evolution under Fixed Point Arithmetic and FP16 Numbers
Math. Comput. Appl. 2021, 26(1), 13; https://doi.org/10.3390/mca26010013 - 04 Feb 2021
Viewed by 310
Abstract
In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating point (FP) numbers of 16 bits, and these last numbers are known as FP16. In this paper, it is considered that it is important [...] Read more.
In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating point (FP) numbers of 16 bits, and these last numbers are known as FP16. In this paper, it is considered that it is important to analyze differential evolution (DE) in these circumstances with the goal of reducing its consumption power, storage size of the variables, and improve its speed behavior. All these aspects become important if one needs to design a dedicated hardware, as an embedded DE within a circuit chip, that performs optimization. With these conditions DE is tested using three common multimodal benchmark functions: Rosenbrock, Rastrigin, and Ackley, in 10 dimensions. Results are obtained in software by simulating all numbers using C programming language. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
Open AccessArticle
Chaotic Multi-Objective Simulated Annealing and Threshold Accepting for Job Shop Scheduling Problem
Math. Comput. Appl. 2021, 26(1), 8; https://doi.org/10.3390/mca26010008 - 12 Jan 2021
Viewed by 525
Abstract
The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best [...] Read more.
The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessFeature PaperArticle
Prediction of Maximum Pressure at the Roofs of Rectangular Water Tanks Subjected to Harmonic Base Excitation Using the Multi-Gene Genetic Programming Method
Math. Comput. Appl. 2021, 26(1), 6; https://doi.org/10.3390/mca26010006 - 02 Jan 2021
Viewed by 446
Abstract
Liquid storage tanks subjected to base excitation can cause large impact forces on the tank roof, which can lead to structural damage as well as economic and environmental losses. The use of artificial intelligence in solving engineering problems is becoming popular in various [...] Read more.
Liquid storage tanks subjected to base excitation can cause large impact forces on the tank roof, which can lead to structural damage as well as economic and environmental losses. The use of artificial intelligence in solving engineering problems is becoming popular in various research fields, and the Genetic Programming (GP) method is receiving more attention in recent years as a regression tool and also as an approach for finding empirical expressions between the data. In this study, an OpenFOAM numerical model that was validated by the authors in a previous study is used to simulate various tank sizes with different liquid heights. The tanks are excited in three different orientations with harmonic sinusoidal loadings. The excitation frequencies are chosen as equal to the tanks’ natural frequencies so that they would be subject to a resonance condition. The maximum pressure in each case is recorded and made dimensionless; then, using Multi-Gene Genetic Programming (MGGP) methods, a relationship between the dimensionless maximum pressure and dimensionless liquid height is acquired. Finally, some error measurements are calculated, and the sensitivity and uncertainty of the proposed equation are analyzed. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessFeature PaperArticle
The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems
Math. Comput. Appl. 2020, 25(4), 80; https://doi.org/10.3390/mca25040080 - 20 Dec 2020
Viewed by 542
Abstract
Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect [...] Read more.
Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessArticle
Single-Objective Optimization of a CMOS VCO Considering PVT and Monte Carlo Simulations
Math. Comput. Appl. 2020, 25(4), 76; https://doi.org/10.3390/mca25040076 - 03 Dec 2020
Viewed by 420
Abstract
The optimization of analog integrated circuits requires to take into account a number of considerations and trade-offs that are specific to each circuit, meaning that each case of design may be subject to different constraints to accomplish target specifications. This paper shows the [...] Read more.
The optimization of analog integrated circuits requires to take into account a number of considerations and trade-offs that are specific to each circuit, meaning that each case of design may be subject to different constraints to accomplish target specifications. This paper shows the single-objective optimization of a complementary metal-oxide-semiconductor (CMOS) four-stage voltage-controlled oscillator (VCO) to maximize the oscillation frequency. The stages are designed by using CMOS current-mode logic or differential pairs and are connected in a ring structure. The optimization is performed by applying differential evolution (DE) algorithm, in which the design variables are the control voltage and the transistors’ widths and lengths. The objective is maximizing the oscillation frequency under the constraints so that the CMOS VCO be robust to Monte Carlo simulations and to process-voltage-temperature (PVT) variations. The optimization results show that DE provides feasible solutions oscillating at 5 GHz with a wide control voltage range and robust to both Monte Carlo and PVT analyses. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessFeature PaperArticle
An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation
Math. Comput. Appl. 2020, 25(4), 73; https://doi.org/10.3390/mca25040073 - 02 Nov 2020
Viewed by 717
Abstract
Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk [...] Read more.
Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Open AccessFeature PaperArticle
Differential Evolution in Robust Optimization Over Time Using a Survival Time Approach
Math. Comput. Appl. 2020, 25(4), 72; https://doi.org/10.3390/mca25040072 - 26 Oct 2020
Viewed by 669
Abstract
This study presents an empirical comparison of the standard differential evolution (DE) against three random sampling methods to solve robust optimization over time problems with a survival time approach to analyze its viability and performance capacity of solving problems in dynamic environments. A [...] Read more.
This study presents an empirical comparison of the standard differential evolution (DE) against three random sampling methods to solve robust optimization over time problems with a survival time approach to analyze its viability and performance capacity of solving problems in dynamic environments. A set of instances with four different dynamics, generated by two different configurations of two well-known benchmarks, are solved. This work also introduces a comparison criterion that allows the algorithm to discriminate among solutions with similar survival times to benefit the selection process. The results show that the standard DE holds a good performance to find ROOT solutions, improving the results reported by state-of-the-art approaches in the studied environments. Finally, it was found that the chaotic dynamic, disregarding the type of peak movement in the search space, is a source of difficulty for the proposed DE algorithm. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Review

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Open AccessFeature PaperReview
Surrogate Modeling Approaches for Multiobjective Optimization: Methods, Taxonomy, and Results
Math. Comput. Appl. 2021, 26(1), 5; https://doi.org/10.3390/mca26010005 - 31 Dec 2020
Cited by 1 | Viewed by 727
Abstract
Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain [...] Read more.
Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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