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6 pages, 449 KiB

Open AccessEditorial

Preface to the Special Issue “Mathematical Optimization and Evolutionary Algorithms with Applications”

by Antonin Ponsich, Bruno Domenech and Mariona Vilà

Mathematics 2023, 11(10), 2229; https://doi.org/10.3390/math11102229 - 10 May 2023

Viewed by 1162

Abstract

It is recognized that many real-world problems can be interpreted and formulated as optimization problems [...] Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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Research

Jump to: Editorial

16 pages, 3908 KiB

Open AccessArticle

Infeasibility Maps: Application to the Optimization of the Design of Pumping Stations in Water Distribution Networks

by Jimmy H. Gutiérrez-Bahamondes, Daniel Mora-Melia, Bastián Valdivia-Muñoz, Fabián Silva-Aravena and Pedro L. Iglesias-Rey

Mathematics 2023, 11(7), 1582; https://doi.org/10.3390/math11071582 - 24 Mar 2023

Cited by 4 | Viewed by 2200

Abstract

The design of pumping stations in a water distribution network determines the investment costs and affects a large part of the operating costs of the network. In recent years, it was shown that it is possible to use flow distribution to optimize both [...] Read more.

The design of pumping stations in a water distribution network determines the investment costs and affects a large part of the operating costs of the network. In recent years, it was shown that it is possible to use flow distribution to optimize both costs concurrently; however, the methodologies proposed in the literature are not applicable to real-sized networks. In these cases, the space of solutions is huge, a small number of feasible solutions exists, and each evaluation of the objective function implies significant computational effort. To avoid this gap, a new method was proposed to reduce the search space in the problem of pumping station design. This method was based on network preprocessing to determine in advance the maximum and minimum flow that each pump station could provide. According to this purpose, the area of infeasibility is limited by ranges of the decision variable where it is impossible to meet the hydraulic constraints of the model. This area of infeasibility is removed from the search space with which the algorithm works. To demonstrate the benefits of using the new technique, a new real-sized case study was presented, and a pseudo-genetic algorithm (PGA) was implemented to resolve the optimization model. Finally, the results show great improvement in PGA performance, both in terms of the speed of convergence and quality of the solution. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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13 pages, 295 KiB

Open AccessArticle

Optimization-Based Energy Disaggregation: A Constrained Multi-Objective Approach

by Jeewon Park, Oladayo S. Ajani and Rammohan Mallipeddi

Mathematics 2023, 11(3), 563; https://doi.org/10.3390/math11030563 - 20 Jan 2023

Cited by 7 | Viewed by 1292

Abstract

Recently, optimization-based energy disaggregation (ED) algorithms have been gaining significance due to their capability to perform disaggregation with minimal information compared to the pattern-based ED algorithms, which demand large amounts of data for training. However, the performances of optimization-based ED algorithms depend on [...] Read more.

Recently, optimization-based energy disaggregation (ED) algorithms have been gaining significance due to their capability to perform disaggregation with minimal information compared to the pattern-based ED algorithms, which demand large amounts of data for training. However, the performances of optimization-based ED algorithms depend on the problem formulation that includes an objective function(s) and/or constraints. In the literature, ED has been formulated as a constrained single-objective problem or an unconstrained multi-objective problem considering disaggregation error, sparsity of state switching, on/off switching, etc. In this work, the ED problem is formulated as a constrained multi-objective problem (CMOP), where the constraints related to the operational characteristics of the devices are included. In addition, the formulated CMOP is solved using a constrained multi-objective evolutionary algorithm (CMOEA). The performance of the proposed formulation is compared with those of three high-performing ED formulations in the literature based on the appliance-level and overall indicators. The results show that the proposed formulation improves both appliance-level and overall ED results. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

18 pages, 411 KiB

Open AccessArticle

Applying the Crow Search Algorithm for the Optimal Integration of PV Generation Units in DC Networks

by Luis Fernando Grisales-Noreña, Brandon Cortés-Caicedo, Gerardo Alcalá and Oscar Danilo Montoya

Mathematics 2023, 11(2), 387; https://doi.org/10.3390/math11020387 - 11 Jan 2023

Cited by 11 | Viewed by 1631

Abstract

This paper presents an efficient master–slave methodology to solve the problem of integrating photovoltaic (PV) generators into DC grids for a planning period of 20 years. The problem is mathematically formulated as Mixed-Integer Nonlinear Programming (MINLP) with the objective of minimizing the total [...] Read more.

This paper presents an efficient master–slave methodology to solve the problem of integrating photovoltaic (PV) generators into DC grids for a planning period of 20 years. The problem is mathematically formulated as Mixed-Integer Nonlinear Programming (MINLP) with the objective of minimizing the total annual operating cost. The main stage, consisting of a discrete-continuous version of the Crow search algorithm (DCCSA), is in charge of determining the installation positions of the PV generators and their corresponding power ratings. On the other hand, at the slave level, the successive approximation power flow method is used to determine the objective function value. Numerical results on 33- and 69-bus test systems demonstrate the applicability, efficiency and robustness of the developed approach with respect to different methodologies previously discussed in the scientific literature, such as the vortex search algorithm, the generalized normal distribution optimizer and the particle swarm optimization algorithm. Numerical tests are performed in the MATLAB programming environment using proprietary scripts. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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21 pages, 7639 KiB

Open AccessArticle

Multi-Objective Multi-Scale Optimization of Composite Structures, Application to an Aircraft Overhead Locker Made with Bio-Composites

by Xavier Martínez, Jordi Pons-Prats, Francesc Turon, Martí Coma, Lucía Gratiela Barbu and Gabriel Bugeda

Mathematics 2023, 11(1), 165; https://doi.org/10.3390/math11010165 - 28 Dec 2022

Cited by 4 | Viewed by 2602

Abstract

The use of composite materials has grown exponentially in transport structures due to their weight reduction advantages, added to their capability to adapt the material properties and internal micro-structure to the requirements of the application. This flexibility allows the design of highly efficient [...] Read more.

The use of composite materials has grown exponentially in transport structures due to their weight reduction advantages, added to their capability to adapt the material properties and internal micro-structure to the requirements of the application. This flexibility allows the design of highly efficient composite structures that can reduce the environmental impact of transport, especially if the used composites are bio-based. In order to design highly efficient structures, the numerical models and tools used to predict the structural and material performance are of great importance. In the present paper, the authors propose a multi-objective, multi-scale optimization procedure aimed to obtain the best possible structure and material design for a given application. The procedure developed is applied to an aircraft secondary structure, an overhead locker, made with a sandwich laminate in which both, the skins and the core, are bio-materials. The structural multi-scale numerical model has been coupled with a Genetic Algorithm to perform the optimization of the structure design. Two optimization cases are presented. The first one consists of a single-objective optimization problem of the fibre alignment to improve the structural stiffness of the structure. The second optimization shows the advantages of using a multi-objective and multi-scale optimization approach. In this last case, the first objective function corresponds to the shelf stiffness, and the second objective function consists of minimizing the number of fibres placed in one of the woven directions, looking for a reduction in the material cost and weight. The obtained results with both optimization cases have proved the capability of the software developed to obtain an optimal design of composite structures, and the need to consider both, the macro-structural and the micro-structural configuration of the composite, in order to obtain the best possible solution. The presented approach allows to perform the optimisation of both the macro-structural and the micro-structural configurations. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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20 pages, 2248 KiB

Open AccessArticle

Dynamic Optimization of the Multi-Skilled Resource-Constrained Project Scheduling Problem with Uncertainty in Resource Availability

by Min Wang, Guoshan Liu and Xinyu Lin

Mathematics 2022, 10(17), 3070; https://doi.org/10.3390/math10173070 - 25 Aug 2022

Cited by 6 | Viewed by 2555

Abstract

Multi-skilled resources have brought more flexibility to resource scheduling and have been a key factor in the research of resource-constrained project scheduling problems. However, existing studies are mainly limited to deterministic problems and neglect some uncertainties such as resource breakdowns, while resource availability [...] Read more.

Multi-skilled resources have brought more flexibility to resource scheduling and have been a key factor in the research of resource-constrained project scheduling problems. However, existing studies are mainly limited to deterministic problems and neglect some uncertainties such as resource breakdowns, while resource availability may change over time due to unexpected risks such as the COVID-19 pandemic. Therefore, this paper focuses on the multi-skilled project scheduling problem with uncertainty in resource availability. Different from previous assumptions, multi-skilled resources are allowed a switch in their skills, which we call dynamic skill assignment. For this complex problem, a nested dynamic scheduling algorithm called GA-PR is proposed, which includes three new priority rules to improve the solving efficiency. Moreover, the algorithm’s effectiveness is verified by an example, and the modified Project Scheduling Problem Library (PSPLIB) is used for numerical experimental analysis. Numerical experiments show that when the uncertainty in resource availability is considered, the more skills the resource has and the more resources are supplied, the better the dynamic scheduling method performs; on the other hand, the higher the probability of resource unavailability and the more skills are required, the worse the dynamic scheduling method performs.The results are helpful for improved decision making. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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19 pages, 1754 KiB

Open AccessArticle

Balancing Cost and Demand in Electricity Access Projects: Case Studies in Ecuador, Mexico and Peru

by Rosa Galleguillos-Pozo, Bruno Domenech, Laia Ferrer-Martí and Rafael Pastor

Mathematics 2022, 10(12), 1995; https://doi.org/10.3390/math10121995 - 9 Jun 2022

Cited by 2 | Viewed by 1451

Abstract

Rural areas in developing countries have the highest concentrations of unelectrified communities. There is a clear link between electricity consumption and the Human Development Index, as highlighted by the 7th Development Goal of the United Nations. Estimating the energy needs of the previously [...] Read more.

Rural areas in developing countries have the highest concentrations of unelectrified communities. There is a clear link between electricity consumption and the Human Development Index, as highlighted by the 7th Development Goal of the United Nations. Estimating the energy needs of the previously nonelectrified population is imprecise when designing rural electrification projects. Indeed, daily energy demand and peak power assessments are complex, since these values must be valid over the project’s lifetime, while tight budgets do not allow for the systems to be oversized. In order to assist project promoters, this study proposes a fuzzy mixed integer linear programming model (FMILP) for the design of wind–PV rural electrification systems including uncertainty in the demand requirements. Two different FMILP approaches were developed that maximized the minimum or the average satisfaction of the users. Next, the FMILP approaches were applied to six Latin American communities from three countries. Compared with the deterministic MILP (where the energy and peak power needs are considered as specific values), the FMILP results achieved a better balance between the project cost and the users’ satisfaction regarding the energy and peak power supplied. Regarding the two approaches, maximizing the users’ minimum satisfaction obtained globally better solutions. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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17 pages, 4152 KiB

Open AccessArticle

Joint Optimization of Ticket Pricing Strategy and Train Stop Plan for High-Speed Railway: A Case Study

by Jin Qin, Xiqiong Li, Kang Yang and Guangming Xu

Mathematics 2022, 10(10), 1679; https://doi.org/10.3390/math10101679 - 13 May 2022

Cited by 5 | Viewed by 2632

Abstract

In this study, we examined ticket pricing and train stop planning for the high-speed railway (HSR), which integrates two key aspects of railway operation and organization. We considered that passenger demand is sensitive to the generalized travel cost (depending on the ticket price [...] Read more.

In this study, we examined ticket pricing and train stop planning for the high-speed railway (HSR), which integrates two key aspects of railway operation and organization. We considered that passenger demand is sensitive to the generalized travel cost (depending on the ticket price and the travel time) and that the train stop plan can affect the travel time and passenger distribution. Then, a mixed-integer non-linear optimization model was proposed for the joint problem of ticket pricing and train stop planning to maximize HSR’s transport revenue and minimize passengers’ travel time. Based on the high similarity between combinatorial optimization problems and the solid annealing principle, we designed a combined simulated annealing (CSA) algorithm to solve practical problems. The results of a numerical example in the real HSR network showed that the proposed method can improve transport revenue by 5.1% and reduce passengers’ travel time loss by 11.15% without increasing transport capacity. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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24 pages, 4052 KiB

Open AccessArticle

Optimizing PV Microgrid Isolated Electrification Projects—A Case Study in Ecuador

by Bruno Domenech, Laia Ferrer-Martí, Facundo García, Georgina Hidalgo, Rafael Pastor and Antonin Ponsich

Mathematics 2022, 10(8), 1226; https://doi.org/10.3390/math10081226 - 8 Apr 2022

Cited by 8 | Viewed by 2461

Abstract

Access to electricity for the rural and indigenous population of Ecuador’s Amazon Region (RAE) is considered a critical issue by the national authorities. The RAE is an isolated zone with communities scattered throughout the rainforest, where the expansion of the national grid is [...] Read more.

Access to electricity for the rural and indigenous population of Ecuador’s Amazon Region (RAE) is considered a critical issue by the national authorities. The RAE is an isolated zone with communities scattered throughout the rainforest, where the expansion of the national grid is not a viable option. Therefore, autonomous electrification systems based on solar energy constitute an important solution, allowing the development of indigenous populations. This work proposes a tool for the design of stand-alone rural electrification systems based on photovoltaic technologies, including both microgrid or individual supply configurations. This tool is formulated as a Mixed Integer Linear Programming model including economic, technical and social aspects. This approach is used to design electrification systems (equipment location and sizing, microgrid configurations) in three real communities of the RAE. The results highlight the benefits of the developed tool and provide guidelines regarding RAE’s electrification. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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47 pages, 7402 KiB

Open AccessArticle

Enhanced Parallel Sine Cosine Algorithm for Constrained and Unconstrained Optimization

by Akram Belazi, Héctor Migallón, Daniel Gónzalez-Sánchez, Jorge Gónzalez-García, Antonio Jimeno-Morenilla and José-Luis Sánchez-Romero

Mathematics 2022, 10(7), 1166; https://doi.org/10.3390/math10071166 - 3 Apr 2022

Cited by 2 | Viewed by 2074

Abstract

The sine cosine algorithm’s main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm [...] Read more.

The sine cosine algorithm’s main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm over a set of state-of-the-art algorithms in terms of solution accuracy and convergence speed will be demonstrated by experimental tests. When these algorithms are transferred to the business sector, they must meet time requirements dependent on the industrial process. If these temporal requirements are not met, an efficient solution is to speed them up by designing parallel algorithms. The second major contribution of this work is the design of several parallel algorithms for efficiently exploiting current multicore processor architectures. First, one-level synchronous and asynchronous parallel ESCA algorithms are designed. They have two favors; retain the proposed algorithm’s behavior and provide excellent parallel performance by combining coarse-grained parallelism with fine-grained parallelism. Moreover, the parallel scalability of the proposed algorithms is further improved by employing a two-level parallel strategy. Indeed, the experimental results suggest that the one-level parallel ESCA algorithms reduce the computing time, on average, by 87.4% and 90.8%, respectively, using 12 physical processing cores. The two-level parallel algorithms provide extra reductions of the computing time by 91.4%, 93.1%, and 94.5% with 16, 20, and 24 processing cores, including physical and logical cores. Comparison analysis is carried out on 30 unconstrained benchmark functions and three challenging engineering design problems. The experimental outcomes show that the proposed ESCA algorithm behaves outstandingly well in terms of exploration and exploitation behaviors, local optima avoidance, and convergence speed toward the optimum. The overall performance of the proposed algorithm is statistically validated using three non-parametric statistical tests, namely Friedman, Friedman aligned, and Quade tests. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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17 pages, 3528 KiB

Open AccessFeature PaperArticle

Searching for a Unique Exciton Model of Photosynthetic Pigment–Protein Complexes: Photosystem II Reaction Center Study by Differential Evolution

by Denis D. Chesalin and Roman Y. Pishchalnikov

Mathematics 2022, 10(6), 959; https://doi.org/10.3390/math10060959 - 17 Mar 2022

Cited by 7 | Viewed by 1946

Abstract

Studying the optical properties of photosynthetic pigment–protein complexes (PPCs) in the visible light range, both experimentally and theoretically, is one of the ways of gaining knowledge about the function of the photosynthetic machinery of living species. To simulate the PPC optical response, it [...] Read more.

Studying the optical properties of photosynthetic pigment–protein complexes (PPCs) in the visible light range, both experimentally and theoretically, is one of the ways of gaining knowledge about the function of the photosynthetic machinery of living species. To simulate the PPC optical response, it is necessary to use semiclassical theories describing the effect of external fields–matter interaction, energy migration in molecular crystals, and electron–phonon coupling. In this paper, we report the results of photosystem II reaction center (PSIIRC) linear optical response simulations. Applying the multimode Brownian oscillator model and the theory of molecular excitons, we have demonstrated that the absorption, circular and linear dichroism, and steady-state fluorescence of PSIIRC can be accurately fitted with the help of differential evolution (DE), the multiparametric evolutionary optimization algorithm. To explore the effectiveness of DE, we used the simulated experimental data as the target functions instead of those actually measured. Only 2 of 10 DE strategies have shown the best performance of the optimization algorithm. With the best tuning parameters of DE/rand-to-best/1/exp strategy determined from the strategy tests, we found the exact solution for the PSIIRC exciton model and fitted the spectra with a reasonable convergence rate. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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13 pages, 551 KiB

Open AccessArticle

The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis

by Daniela Ambrosino and Carmine Cerrone

Mathematics 2022, 10(5), 804; https://doi.org/10.3390/math10050804 - 3 Mar 2022

Cited by 2 | Viewed by 1715

Abstract

This paper introduces a new variant of the Shortest Path Problem (

S P P

) called the Cost-Balanced Path Problem (

C B P P

). Various real problems can either be modeled as

B C P P

or include [...] Read more.

This paper introduces a new variant of the Shortest Path Problem (

S P P

) called the Cost-Balanced Path Problem (

C B P P

). Various real problems can either be modeled as

B C P P

or include

B C P P

as a sub-problem. We prove several properties related to the complexity of the

C B P P

problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the

C B P P

, as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirements are given. This paper validates the proposed model and its extensions with experimental tests based on random instances. The analysis of the results of the computational experiments shows that the proposed model and its extension can be used to model many real applications. Obviously, due to the problem complexity, the main limitation of the proposed approach is related to the size of the instances. A heuristic solution approach should be required for larger-sized and more complex instances. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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42 pages, 6908 KiB

Open AccessArticle

Multi-Objective Optimal Design of a Hydrogen Supply Chain Powered with Agro-Industrial Wastes from the Sugarcane Industry: A Mexican Case Study

by Luis Miguel Reyes-Barquet, José Octavio Rico-Contreras, Catherine Azzaro-Pantel, Constantino Gerardo Moras-Sánchez, Magno Angel González-Huerta, Daniel Villanueva-Vásquez and Alberto Alfonso Aguilar-Lasserre

Mathematics 2022, 10(3), 437; https://doi.org/10.3390/math10030437 - 29 Jan 2022

Cited by 15 | Viewed by 3586

Abstract

This paper presents an optimization modeling approach to support strategic planning for designing hydrogen supply chain (HSC) networks. The energy source for hydrogen production is proposed to be electricity generated at Mexican sugar factories. This study considers the utilization of existing infrastructure in [...] Read more.

This paper presents an optimization modeling approach to support strategic planning for designing hydrogen supply chain (HSC) networks. The energy source for hydrogen production is proposed to be electricity generated at Mexican sugar factories. This study considers the utilization of existing infrastructure in strategic areas of the country, which brings several advantages in terms of possible solutions. This study aims to evaluate the economic and environmental implications of using biomass wastes for energy generation, and its integration to the national energy grid, where the problem is addressed as a mixed-integer linear program (MILP), adopting maximization of annual profit, and minimization of greenhouse gas emissions as optimization criteria. Input data is provided by sugar companies and the national transport and energy information platform, and were represented by probability distributions to consider variability in key parameters. Independent solutions show similarities in terms of resource utilization, while also significant differences regarding economic and environmental indicators. Multi-objective optimization was performed by a genetic algorithm (GA). The optimal HSC network configuration is selected using a multi-criteria decision technique, i.e., TOPSIS. An uncertainty analysis is performed, and main economic indicators are estimated by investment assessment. Main results show the trade-off interactions between the HSC elements and optimization criteria. The average internal rate of return (IRR) is estimated to be 21.5% and average payback period is 5.02 years. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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22 pages, 5522 KiB

Open AccessArticle

An Adaptive Protection Scheme Based on a Modified Heap-Based Optimizer for Distance and Directional Overcurrent Relays Coordination in Distribution Systems

by Mohamed Abdelhamid, Salah Kamel, Emad M. Ahmed and Ephraim Bonah Agyekum

Mathematics 2022, 10(3), 419; https://doi.org/10.3390/math10030419 - 28 Jan 2022

Cited by 11 | Viewed by 1691

Abstract

This paper proposes an adaptive protection scheme (APS) based on the original heap-based optimization (HBO) and a modified HBO (MHBO). APS is used to solve protection relays coordination problems that include directional overcurrent relays (DOCRs) as well as the distance relay’s second zone [...] Read more.

This paper proposes an adaptive protection scheme (APS) based on the original heap-based optimization (HBO) and a modified HBO (MHBO). APS is used to solve protection relays coordination problems that include directional overcurrent relays (DOCRs) as well as the distance relay’s second zone times. The complexity of the coordination problem increases with the impact of distributed generators (DGs) switching (ON/OFF). Topological changes in grid configuration frequently occur in distributing networks, equipped with DGs, causing changes in the values and direction of short circuit currents. This issue becomes a challenge for protection systems to avoid relays miscoordination and save a network’s reliability. In the proposed MHBO, the Original HBO is modified by three points, population are divided into subgroups, then they are unified into one group gradually, those subgroups are exchanging some search agents between themselves, these search agents are called travelling agents, and the last one is about, upgrading an internal equation in the original algorithm. For validating the proposed relays coordination, the IEEE 8-bus test system, and the IEEE 14-bus distribution network are selected as case studies. The obtained simulated results of the proposed algorithm show better performance compared with those obtained by the previous algorithms. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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26 pages, 612 KiB

Open AccessArticle

A Novel Constraint Programming Decomposition Approach for the Total Flow Time Fixed Group Shop Scheduling Problem

by Francisco Yuraszeck, Gonzalo Mejía, Jordi Pereira and Mariona Vilà

Mathematics 2022, 10(3), 329; https://doi.org/10.3390/math10030329 - 21 Jan 2022

Cited by 11 | Viewed by 3222

Abstract

This work addresses a particular case of the group shop scheduling problem (GSSP) which will be denoted as the fixed group shop scheduling problem (FGSSP). In a FGSSP, job operations are divided into stages and each stage has a set of machines associated [...] Read more.

This work addresses a particular case of the group shop scheduling problem (GSSP) which will be denoted as the fixed group shop scheduling problem (FGSSP). In a FGSSP, job operations are divided into stages and each stage has a set of machines associated to it which are not shared with the other stages. All jobs go through all the stages in a specific order, where the operations of the job at each stage need to be finished before the job advances to the following stage, but operations within a stage can be performed in any order. This setting is common in companies such as leaf spring manufacturers and other automotive companies. To solve the problem, we propose a novel heuristic procedure that combines a decomposition approach with a constraint programming (CP) solver and a restart mechanism both to avoid local optima and to diversify the search. The performance of our approach was tested on instances derived from other scheduling problems that the FGSSP subsumes, considering both the cases with and without anticipatory sequence-dependent setup times. The results of the proposed algorithm are compared with off-the-shelf CP and mixed integer linear programming (MILP) methods as well as with the lower bounds derived from the study of the problem. The experiments show that the proposed heuristic algorithm outperforms the other methods, specially on large-size instances with improvements of over 10% on average. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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20 pages, 16700 KiB

Open AccessArticle

ReRec: A Divide-and-Conquer Approach to Recommendation Based on Repeat Purchase Behaviors of Users in Community E-Commerce

by Jun Wu, Yuanyuan Li, Li Shi, Liping Yang, Xiaxia Niu and Wen Zhang

Mathematics 2022, 10(2), 208; https://doi.org/10.3390/math10020208 - 10 Jan 2022

Cited by 19 | Viewed by 2487

Abstract

Existing studies have made a great endeavor in predicting users’ potential interests in items by modeling user preferences and item characteristics. As an important indicator of users’ satisfaction and loyalty, repeat purchase behavior is a promising perspective to extract insightful information for community [...] Read more.

Existing studies have made a great endeavor in predicting users’ potential interests in items by modeling user preferences and item characteristics. As an important indicator of users’ satisfaction and loyalty, repeat purchase behavior is a promising perspective to extract insightful information for community e-commerce. However, the repeated purchase behaviors of users have not yet been thoroughly studied. To fill in this research gap from the perspective of repeated purchase behavior and improve the process of generation of candidate recommended items this research proposed a novel approach called ReRec (Repeat purchase Recommender) for real-life applications. Specifically, the proposed ReRec approach comprises two components: the first is to model the repeat purchase behaviors of different types of users and the second is to recommend items to users based on their repeat purchase behaviors of different types. The extensive experiments are conducted on a real dataset collected from a community e-commerce platform, and the performance of our model has improved at least about 13.6% compared with the state-of-the-art techniques in recommending online items (measured by F-measure). Specifically, for active users, with

w = 1

and

N_{(U_{A})} \in [5, 25]

, the results of ReRec show a significant improvement (at least 50%) in recommendation. With

α

and

σ

as 0.75 and 0.2284, respectively, the proposed ReRec for unactive users is also superior to (at least 13.6%) the evaluation indicators of traditional Item CF when

N_{(U_{B})} \in [6, 25]

. To the best of our knowledge, this paper is the first to study recommendations in community e-commerce. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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25 pages, 10486 KiB

Open AccessArticle

Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

by Saúl Zapotecas-Martínez, Abel García-Nájera and Adriana Menchaca-Méndez

Mathematics 2022, 10(1), 19; https://doi.org/10.3390/math10010019 - 21 Dec 2021

Cited by 6 | Viewed by 3471

Abstract

One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the [...] Read more.

One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the most investigated indicators in the design of indicator-based evolutionary algorithms (IBEAs). The main deficiency of IBEAs that use the Lebesgue measure is their computational cost which increases with the number of objectives of the problem. On this matter, the investigation presented in this paper introduces an evolutionary algorithm based on the Lebesgue measure to deal with box-constrained continuous multi-objective optimization problems. The proposed algorithm implicitly uses the regularity property of continuous multi-objective optimization problems that has suggested effectiveness when solving continuous problems with rough Pareto sets. On the other hand, the survival selection mechanism considers the local property of the Lebesgue measure, thus reducing the computational time in our algorithmic approach. The emerging indicator-based evolutionary algorithm is examined and compared versus three state-of-the-art multi-objective evolutionary algorithms based on the Lebesgue measure. In addition, we validate its performance on a set of artificial test problems with various characteristics, including multimodality, separability, and various Pareto front forms, incorporating concavity, convexity, and discontinuity. For a more exhaustive study, the proposed algorithm is evaluated in three real-world applications having four, five, and seven objective functions whose properties are unknown. We show the high competitiveness of our proposed approach, which, in many cases, improved the state-of-the-art indicator-based evolutionary algorithms on the multi-objective problems adopted in our investigation. Full article

(This article belongs to the Special Issue Mathematical Optimization and Evolutionary Algorithms with Applications)

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