optimization problems
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2022 ◽  
Vol 18 (2) ◽  
pp. 1-25
Jing Li ◽  
Weifa Liang ◽  
Zichuan Xu ◽  
Xiaohua Jia ◽  
Wanlei Zhou

We are embracing an era of Internet of Things (IoT). The latency brought by unstable wireless networks caused by limited resources of IoT devices seriously impacts the quality of services of users, particularly the service delay they experienced. Mobile Edge Computing (MEC) technology provides promising solutions to delay-sensitive IoT applications, where cloudlets (edge servers) are co-located with wireless access points in the proximity of IoT devices. The service response latency for IoT applications can be significantly shortened due to that their data processing can be performed in a local MEC network. Meanwhile, most IoT applications usually impose Service Function Chain (SFC) enforcement on their data transmission, where each data packet from its source gateway of an IoT device to the destination (a cloudlet) of the IoT application must pass through each Virtual Network Function (VNF) in the SFC in an MEC network. However, little attention has been paid on such a service provisioning of multi-source IoT applications in an MEC network with SFC enforcement. In this article, we study service provisioning in an MEC network for multi-source IoT applications with SFC requirements and aiming at minimizing the cost of such service provisioning, where each IoT application has multiple data streams from different sources to be uploaded to a location (cloudlet) in the MEC network for aggregation, processing, and storage purposes. To this end, we first formulate two novel optimization problems: the cost minimization problem of service provisioning for a single multi-source IoT application, and the service provisioning problem for a set of multi-source IoT applications, respectively, and show that both problems are NP-hard. Second, we propose a service provisioning framework in the MEC network for multi-source IoT applications that consists of uploading stream data from multiple sources of the IoT application to the MEC network, data stream aggregation and routing through the VNF instance placement and sharing, and workload balancing among cloudlets. Third, we devise an efficient algorithm for the cost minimization problem built upon the proposed service provisioning framework, and further extend the solution for the service provisioning problem of a set of multi-source IoT applications. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are promising.

2022 ◽  
Vol 41 (1) ◽  
pp. 1-10
Jonas Zehnder ◽  
Stelian Coros ◽  
Bernhard Thomaszewski

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse problems, but the cost of assembling and factorizing the associated matrices has so far been a major stumbling block. In this work, we show how the dense Gauss-Newton Hessian can be transformed into an equivalent sparse matrix that can be assembled and factorized much more efficiently. This leads to drastically reduced computation times for many inverse problems, which we demonstrate on a diverse set of examples. We furthermore show links between sensitivity analysis and nonlinear programming approaches based on Lagrange multipliers and prove equivalence under specific assumptions that apply for our problem setting.

Mahmoud Abbas El-Dabah ◽  
Ragab Abdelaziz El-Sehiemy ◽  
Mohamed Ahmed Ebrahim ◽  
Zuhair Alaas ◽  
Mohamed Mostafa Ramadan

This paper proposes the application of a novel metaphor-free population optimization based on the mathematics of the Runge Kutta method (RUN) for parameter extraction of a double-diode model of the unknown solar cell and photovoltaic (PV) module parameters. The RUN optimizer is employed to determine the seven unknown parameters of the two-diode model. Fitting the experimental data is the main objective of the extracted unknown parameters to develop a generic PV model. Consequently, the root means squared error (RMSE) between the measured and estimated data is considered as the primary objective function. The suggested objective function achieves the closeness degree between the estimated and experimental data. For getting the generic model, applications of the proposed RUN are carried out on two different commercial PV cells. To assess the proposed algorithm, a comprehensive comparison study is employed and compared with several well-matured optimization algorithms reported in the literature. Numerical simulations prove the high precision and fast response of the proposed RUN algorithm for solving multiple PV models. Added to that, the RUN can be considered as a good alternative optimization method for solving power systems optimization problems.

2022 ◽  
Vol 54 (8) ◽  
pp. 1-35
Akbar Telikani ◽  
Amirhessam Tahmassebi ◽  
Wolfgang Banzhaf ◽  
Amir H. Gandomi

Evolutionary Computation (EC) approaches are inspired by nature and solve optimization problems in a stochastic manner. They can offer a reliable and effective approach to address complex problems in real-world applications. EC algorithms have recently been used to improve the performance of Machine Learning (ML) models and the quality of their results. Evolutionary approaches can be used in all three parts of ML: preprocessing (e.g., feature selection and resampling), learning (e.g., parameter setting, membership functions, and neural network topology), and postprocessing (e.g., rule optimization, decision tree/support vectors pruning, and ensemble learning). This article investigates the role of EC algorithms in solving different ML challenges. We do not provide a comprehensive review of evolutionary ML approaches here; instead, we discuss how EC algorithms can contribute to ML by addressing conventional challenges of the artificial intelligence and ML communities. We look at the contributions of EC to ML in nine sub-fields: feature selection, resampling, classifiers, neural networks, reinforcement learning, clustering, association rule mining, and ensemble methods. For each category, we discuss evolutionary machine learning in terms of three aspects: problem formulation, search mechanisms, and fitness value computation. We also consider open issues and challenges that should be addressed in future work.

2022 ◽  
Vol 54 (8) ◽  
pp. 1-34
Ye Tian ◽  
Langchun Si ◽  
Xingyi Zhang ◽  
Ran Cheng ◽  
Cheng He ◽  

Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 274
Álvaro Gómez-Rubio ◽  
Ricardo Soto ◽  
Broderick Crawford ◽  
Adrián Jaramillo ◽  
David Mancilla ◽  

In the world of optimization, especially concerning metaheuristics, solving complex problems represented by applying big data and constraint instances can be difficult. This is mainly due to the difficulty of implementing efficient solutions that can solve complex optimization problems in adequate time, which do exist in different industries. Big data has demonstrated its efficiency in solving different concerns in information management. In this paper, an approach based on multiprocessing is proposed wherein clusterization and parallelism are used together to improve the search process of metaheuristics when solving large instances of complex optimization problems, incorporating collaborative elements that enhance the quality of the solution. The proposal deals with machine learning algorithms to improve the segmentation of the search space. Particularly, two different clustering methods belonging to automatic learning techniques, are implemented on bio-inspired algorithms to smartly initialize their solution population, and then organize the resolution from the beginning of the search. The results show that this approach is competitive with other techniques in solving a large set of cases of a well-known NP-hard problem without incorporating too much additional complexity into the metaheuristic algorithms.

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 276
Helong Yu ◽  
Shimeng Qiao ◽  
Ali Asghar Heidari ◽  
Chunguang Bi ◽  
Huiling Chen

The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, this paper proposed a new variant SOA based on individual disturbance (ID) and attraction-repulsion (AR) strategy, called IDARSOA, which employed ID to enhance the ability to jump out of local optimum and adopted AR to increase the diversity of population and make the exploration of solution space more efficient. The effectiveness of the IDARSOA has been verified using representative comprehensive benchmark functions and six practical engineering optimization problems. The experimental results show that the proposed IDARSOA has the advantages of better convergence accuracy and a strong optimization ability than the original SOA.

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