Special Issue "Numerical and Evolutionary Optimization"

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

Deadline for manuscript submissions: closed (31 July 2019).

Special Issue Editors

Dr. Adriana Lara
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Guest Editor
Instituto Politécnico Nacional ESFM-IPN, 07730 Mexico City, Mexico
Interests: multi-objective optimization; optimization; evolutionary computation; mathematical programming; memetic algorithms
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
Dr. Efrén Mezura-Montes
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Guest Editor
Centro de Investigación en Inteligencia Artificial, University of Veracruz, 91000 Xalapa, Mexico
Interests: evolutionary computing; swarm intelligence; complex optimization problem solving; machine learning
Special Issues and Collections in MDPI journals
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,

The development of powerful search and optimization techniques is of great importance in science and engineering, particularly in today's world, which requires researchers and practitioners to tackle a variety of challenging real-world problems as technology becomes an ever-more-important aspect of everyday life. There are two well-established and widely-known fields that are addressing these issues: (i) traditional numerical optimization techniques and (ii) comparatively recent bio-inspired heuristics, such as evolutionary algorithms and genetic programming. Both of these fields have developed approaches with their unique strengths and weaknesses, allowing them to solve some challenging problems while sometimes failing in others.

Recent studies have shown that the consideration of elements coming from both fields can lead to great synergies, e.g., in understanding of certain algorithms or in the design of new search techniques.

The aim of this Special Issue is to collect papers on the intersection of numerical and evolutionary optimization. We strongly encourage the development of fast and reliable hybrid methods, that maximize the strengths and minimize the weaknesses of each underlying paradigm, while also being applicable to a broader class of problems. Moreover, this Special Issue fosters the understanding and adequate treatment of real-world problems, particularly in emerging fields that affect us all, such as health care, smart cities, and big data, among many others.

Topics of interest include (but are not limited to):


(A) 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

(B) Real World Problems:

  • Health systems
  • Computer vision and pattern recognition
  • Energy conservation and prediction
  • Modeling and control of real-world systems
  • Smart cities

Dr. Adriana Lara
Dr. Marcela Quiroz
Dr. Efrén Mezura-Montes
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 1000 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 (11 papers)

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Research

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Open AccessFeature PaperArticle
Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms
Math. Comput. Appl. 2019, 24(3), 82; https://doi.org/10.3390/mca24030082 - 13 Sep 2019
Abstract
The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in [...] Read more.
The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
Improved Differential Evolution Algorithm for Flexible Job Shop Scheduling Problems
Math. Comput. Appl. 2019, 24(3), 80; https://doi.org/10.3390/mca24030080 - 06 Sep 2019
Abstract
This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to [...] Read more.
This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to the meta-heuristics from the literature review. For FJSP, by comparing the problem group with the makespan and the mean relative errors (MREs), it was found that for small-sized Kacem problems, value adjusting with “DE/rand/1” and exponential crossover at position 2. Moreover, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 3.25. For medium-sized Brandimarte problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave a mean relative error of 7.11. For large-sized Dauzere-Peres and Paulli problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 4.20. From the comparison of the DE results with other methods, it was found that the MRE was lower than that found by Girish and Jawahar with the particle swarm optimization (PSO) method (7.75), which the improved DE was 7.11. For large-sized problems, it was found that the MRE was lower than that found by Warisa (1ST-DE) method (5.08), for which the improved DE was 4.20. The results further showed that basic DE and improved DE with jump search are effective methods compared to the other meta-heuristic methods. Hence, they can be used to solve the FJSP. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessFeature PaperArticle
Pool-Based Genetic Programming Using Evospace, Local Search and Bloat Control
Math. Comput. Appl. 2019, 24(3), 78; https://doi.org/10.3390/mca24030078 - 29 Aug 2019
Abstract
This work presents a unique genetic programming (GP) approach that integrates a numerical local search method and a bloat-control mechanism within a distributed model for evolutionary algorithms known as EvoSpace. The first two elements provide a directed search operator and a way to [...] Read more.
This work presents a unique genetic programming (GP) approach that integrates a numerical local search method and a bloat-control mechanism within a distributed model for evolutionary algorithms known as EvoSpace. The first two elements provide a directed search operator and a way to control the growth of evolved models, while the latter is meant to exploit distributed and cloud-based computing architectures. EvoSpace is a Pool-based Evolutionary Algorithm, and this work is the first time that such a computing model has been used to perform a GP-based search. The proposal was extensively evaluated using real-world problems from diverse domains, and the behavior of the search was analyzed from several different perspectives. The results show that the proposed approach compares favorably with a standard approach, identifying promising aspects and limitations of this initial hybrid system. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm
Math. Comput. Appl. 2018, 23(4), 79; https://doi.org/10.3390/mca23040079 - 12 Dec 2018
Cited by 1
Abstract
The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within [...] Read more.
The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within a fixed given cycle time), where the aim is to minimize the number of workstations. After establishing the method, the results from previous research studies were compared with the results from this study. For the UALBP, two groups of benchmark problems were used for the experiments: (1) For the medium-sized UALBP (21–45 tasks), it was found that the DE algorithm DE/best/2 to Exponential Crossover 1 produced better solutions when compared to the other metaheuristic methods: it could generate 25 optimal solutions from a total of 25 instances, and the average time used for the calculation was 0.10 seconds/instance; (2) for the large-scale UALBP (75–297 tasks), it was found that the basic DE algorithm and improved differential evolution algorithm generated better solutions, and DE/best/2 to Exponential Crossover 1 generated the optimal solutions and achieved the minimum solution search time when compared to the other metaheuristic methods: it could generate 36 optimal solutions from a total of 62 instances, and the average time used for the calculation was 4.88 seconds/instance. From the comparison of the DE algorithms, it was found that the improved differential evolution algorithm generated optimal solutions with a better solution search time than the search time of the basic differential evolution algorithm. The basic and improved DE algorithm are the effective methods for balancing UALBP-1 when compared to the other metaheuristic methods. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
Surrogate-Based Optimization Using an Open-Source Framework: The Bulbous Bow Shape Optimization Case
Math. Comput. Appl. 2018, 23(4), 60; https://doi.org/10.3390/mca23040060 - 13 Oct 2018
Cited by 1
Abstract
Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. These kinds of problems typically involve the interaction of three main [...] Read more.
Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. These kinds of problems typically involve the interaction of three main applications: a solid modeler, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization work-flow entirely based on open-source tools; it is fault tolerant and software agnostic, allows for asynchronous simulations, and has a high degree of automation. To demonstrate the usability and flexibility of the proposed methodology, we tested it in a practical case related to the naval industry, where we aimed at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. As design variables, we considered the protrusion and immersion of the bulbous bow, and we used surrogate-based optimization. From the results presented, a non-negligible resistance reduction is obtainable using the proposed work-flow and optimization strategy. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessFeature PaperArticle
A (p,q)-Averaged Hausdorff Distance for Arbitrary Measurable Sets
Math. Comput. Appl. 2018, 23(3), 51; https://doi.org/10.3390/mca23030051 - 18 Sep 2018
Cited by 3
Abstract
The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. As a remedy in the context [...] Read more.
The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. As a remedy in the context of evolutionary multi-objective optimization (EMO), the averaged Hausdorff distance Δ p has been proposed that is better suited as an indicator for the performance assessment of EMO algorithms since such methods tend to generate outliers. Later on, the two-parameter indicator Δ p , q has been proposed for finite sets as an extension to Δ p which also averages distances, but which yields some desired metric properties. In this paper, we extend Δ p , q to a continuous function between general bounded subsets of finite measure inside a metric measure space. In particular, this extension applies to bounded subsets of R k endowed with the Euclidean metric, which is the natural context for EMO applications. We show that our extension preserves the nice metric properties of the finite case, and finally provide some useful numerical examples that arise in EMO. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
An Improved Differential Evolution Algorithm for Crop Planning in the Northeastern Region of Thailand
Math. Comput. Appl. 2018, 23(3), 40; https://doi.org/10.3390/mca23030040 - 10 Aug 2018
Cited by 1
Abstract
This research aimed to solve the economic crop planning problem, considering transportation logistics to maximize the profit from cultivated activities. Income is derived from the selling price and production rate of the plants; costs are due to operating and transportation expenses. Two solving [...] Read more.
This research aimed to solve the economic crop planning problem, considering transportation logistics to maximize the profit from cultivated activities. Income is derived from the selling price and production rate of the plants; costs are due to operating and transportation expenses. Two solving methods are presented: (1) developing a mathematical model and solving it using Lingo v.11, and (2) using three improved Differential Evolution (DE) Algorithms—I-DE-SW, I-DE-CY, and I-DE-KV—which are DE with swap, cyclic moves (CY), and K-variables moves (KV) respectively. The algorithms were tested by 16 test instances, including this case study. The computational results showed that Lingo v.11 and all DE algorithms can find the optimal solution eight out of 16 times. Regarding the remaining test instances, Lingo v.11 was unable to find the optimal solution within 400 h. The results for the DE algorithms were compared with the best solution generated within that time. The DE solutions were 1.196–1.488% better than the best solution generated by Lingo v.11 and used 200 times less computational time. Comparing the three DE algorithms, MDE-KV was the DE that was the most flexible, with the biggest neighborhood structure, and outperformed the other DE algorithms. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem
Math. Comput. Appl. 2018, 23(3), 34; https://doi.org/10.3390/mca23030034 - 03 Jul 2018
Cited by 6
Abstract
This research article aims to solve the special case of the location routing problem (SLRP) when the objective function is the fuel consumption. The fuel consumption depends on the distance of travel and the condition of the road. The condition of the road [...] Read more.
This research article aims to solve the special case of the location routing problem (SLRP) when the objective function is the fuel consumption. The fuel consumption depends on the distance of travel and the condition of the road. The condition of the road causes the vehicle to use a different speed, which affects fuel usage. This turns the original LRP into a more difficult problem. Moreover, the volume of the goods that are produced in each node could be more or less than the capacity of the vehicle, and as the case study requires the transportation of latex, which is a sensitive good and needs to be carried within a reasonable time so that it does not form solid before being used in the latex process, the maximum time that the latex can be in the truck is limited. All of these attributes are added into the LRP and make it a special case of LRP: a so-called SLRP (a special case of location routing problem). The differential evolution algorithms (DE) are proposed to solve the SLRP. We modified two points in the original DE, which are that (1) the mutation formula is introduced and (2) the new rule of a local search is presented. We call this the modified differential evolution algorithm (MDE). From the computational result, we can see that MDE generates a 13.82% better solution than that of the original version of DE in solving the test instances. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessArticle
The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm
Math. Comput. Appl. 2018, 23(2), 25; https://doi.org/10.3390/mca23020025 - 17 May 2018
Abstract
Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of [...] Read more.
Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of “reduced” models is also proposed if the original model is misspecified via over-parameterization. In this research, weighted IV-optimality is applied to mixture experiments with a set of prior weights assigned to the potential mixture models of interest. To address the issue of implementation, a genetic algorithm was developed to generate weighted IV-optimal mixture designs that are robust across multiple models. In our examples, we assign models with p parameters to have equal weights, but weights will vary based on varying p. Fraction-of-design-space (FDS) plots are used to compare the performance of an experimental design in terms of the prediction variance properties. An illustrating example is presented. The result shows that the GA-generated designs studied are robust across a set of potential mixture models. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Open AccessFeature PaperArticle
How Am I Driving? Using Genetic Programming to Generate Scoring Functions for Urban Driving Behavior
Math. Comput. Appl. 2018, 23(2), 19; https://doi.org/10.3390/mca23020019 - 03 Apr 2018
Cited by 2
Abstract
Road traffic injuries are a serious concern in emerging economies. Their death toll and economic impact are shocking, with 9 out of 10 deaths occurring in low or middle-income countries; and road traffic crashes representing 3% of their gross domestic product. One way [...] Read more.
Road traffic injuries are a serious concern in emerging economies. Their death toll and economic impact are shocking, with 9 out of 10 deaths occurring in low or middle-income countries; and road traffic crashes representing 3% of their gross domestic product. One way to mitigate these issues is to develop technology to effectively assist the driver, perhaps making him more aware about how her (his) decisions influence safety. Following this idea, in this paper we evaluate computational models that can score the behavior of a driver based on a risky-safety scale. Potential applications of these models include car rental agencies, insurance companies or transportation service providers. In a previous work, we showed that Genetic Programming (GP) was a successful methodology to evolve mathematical functions with the ability to learn how people subjectively score a road trip. The input to this model was a vector of frequencies of risky maneuvers, which were supposed to be detected in a sensor layer. Moreover, GP was shown, even with statistical significance, to be better than six other Machine Learning strategies, including Neural Networks, Support Vector Regression and a Fuzzy Inference system, among others. A pending task, since then, was to evaluate if a more detailed comparison of different strategies based on GP could improve upon the best GP model. In this work, we evaluate, side by side, scoring functions evolved by three different variants of GP. In the end, the results suggest that two of these strategies are very competitive in terms of accuracy and simplicity, both generating models that could be implemented in current technology that seeks to assist the driver in real-world scenarios. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Review

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Open AccessFeature PaperReview
A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction
Math. Comput. Appl. 2018, 23(2), 30; https://doi.org/10.3390/mca23020030 - 01 Jun 2018
Cited by 3
Abstract
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. [...] Read more.
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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