Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

Optimal Power Flow Using Flower Pollination Algorithm: A Case Study of 500 kV Java-Bali Power System

Flower Pollination Algorithm (FPA) is one of metaheuristic methods that is widely used in optimization problems. This method was inspired by the nature of flower pollination. In this research, FPA is applied to solve Optimal Power Flow (OPF) problems with case study of 500 kV Java-Bali power system in Indonesia. The system consists of 25 bus with 30 lines and 8 generating units. Control variables are generation of active power and voltage magnitude at PV bus and swing bus under several power system constraints. The results show that FPA method is capable of solving OPF problem. This method decreased the generator fuel cost of PT. PLN (Persero), the state-owned company in charge of providing electricity in Indonesia, up to 13.15%

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

A Pareto-Based Sensitivity Analysis and Multiobjective Calibration Approach for Integrating Streamflow and Evaporation Data

Evaporation is gaining increasing attention as a calibration and evaluation variable in hydrologic studies that seek to improve the physical realism of hydrologic models and go beyond the long-established streamflow-only calibration. However, this trend is not yet reflected in sensitivity analyses aimed at determining the relevant parameters to calibrate, where streamflow has traditionally played a leading role. On the basis of a Pareto optimization approach, we propose a framework to integrate the temporal dynamics of streamflow and evaporation into the sensitivity analysis and calibration stages of the hydrologic modeling exercise, here referred to as “Pareto-based sensitivity analysis” and “multiobjective calibration.” The framework is successfully applied to a case study using the Variable Infiltration Capacity (VIC) model in three catchments located in Spain as representative of the different hydroclimatic conditions within the Iberian Peninsula. Several VIC vegetation parameters were identified as important to the performance estimates for evaporation during sensitivity analysis, and therefore were suitable candidates to improve the model representation of evaporative fluxes. Sensitivities for the streamflow performance, in turn, were mostly driven by the soil and routing parameters, with little contribution from the vegetation parameters. The multiobjective calibration experiments were carried out for the most parsimonious parameterization after a comparative analysis of the performance gains and losses for streamflow and evaporation, and yielded optimal adjustments for both hydrologic variables simultaneously. Results from this study will help to develop a better understanding of the trade-offs resulting from the joint integration of streamflow and evaporation data into modeling frameworks.ALHAMBRA cluster (http://alhambra. ugr.es) of the University of GranadaProject P20_00035, funded by the FEDER/ Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades, the project CGL2017-89836-RThe Spanish Ministry of Economy and CompetitivenessEuropean Community Funds (FEDER)The project PID2021- 126401OB-I00MCIN/ AEI/10.13039/501100011033/FEDER Una manera de hacer Europa and the project LifeWatch-2019-10-UGR-01 funded by FEDER/Ministerio de Ciencia e InnovaciónThe Ministry of Education, Culture and Sport of Spain through an FPU Grant (reference FPU17/02098)Aid for Research Stays in the Hydrology and Quantitative Water Management Group of Wageningen University (reference EST19/00169)Universidad de Granada/CBU

A New Fusion of Salp Swarm with Sine Cosine for Optimization of Non-linear Functions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The foremost objective of this article is to develop a novel hybrid powerful meta-heuristic that integrates the Salp Swarm Algorithm with Sine Cosine Algorithm (called HSSASCA) for improving the convergence performance with the exploration and exploitation being superior to other comparative standard algorithms. In this method, the position of salp swarm in the search space is updated by using the position equations of sine cosine; hence the best and possible optimal solutions are obtained based on the sine or cosine function. During this process, each salp adopts the information sharing strategy of sine and cosine functions to improve their exploration and exploitation ability. The inspiration behind incorporating changes in Salp Swarm Optimizer Algorithm is to assist the basic approach to avoid premature convergence and to rapidly guide the search towards the probable search space. The algorithm is validated on twenty-two standard mathematical optimization functions and three applications namely the three-bar truss, tension/compression spring and cantilever beam design problems. The aim is to examine and confirm the valuable behaviors of HSSASCA in searching the best solutions for optimization functions. The experimental results reveal that HSSASCA algorithm achieves the highest accuracies with least runtime in comparison with the others

Bio-inspired computation for big data fusion, storage, processing, learning and visualization: state of the art and future directions

This overview gravitates on research achievements that have recently emerged from the confluence between Big Data technologies and bio-inspired computation. A manifold of reasons can be identified for the profitable synergy between these two paradigms, all rooted on the adaptability, intelligence and robustness that biologically inspired principles can provide to technologies aimed to manage, retrieve, fuse and process Big Data efficiently. We delve into this research field by first analyzing in depth the existing literature, with a focus on advances reported in the last few years. This prior literature analysis is complemented by an identification of the new trends and open challenges in Big Data that remain unsolved to date, and that can be effectively addressed by bio-inspired algorithms. As a second contribution, this work elaborates on how bio-inspired algorithms need to be adapted for their use in a Big Data context, in which data fusion becomes crucial as a previous step to allow processing and mining several and potentially heterogeneous data sources. This analysis allows exploring and comparing the scope and efficiency of existing approaches across different problems and domains, with the purpose of identifying new potential applications and research niches. Finally, this survey highlights open issues that remain unsolved to date in this research avenue, alongside a prescription of recommendations for future research.This work has received funding support from the Basque Government (Eusko Jaurlaritza) through the Consolidated Research Group MATHMODE (IT1294-19), EMAITEK and ELK ARTEK programs. D. Camacho also acknowledges support from the Spanish Ministry of Science and Education under PID2020-117263GB-100 grant (FightDIS), the Comunidad Autonoma de Madrid under S2018/TCS-4566 grant (CYNAMON), and the CHIST ERA 2017 BDSI PACMEL Project (PCI2019-103623, Spain)

A New K means Grey Wolf Algorithm for Engineering Problems

Purpose: The development of metaheuristic algorithms has increased by researchers to use them extensively in the field of business, science, and engineering. One of the common metaheuristic optimization algorithms is called Grey Wolf Optimization (GWO). The algorithm works based on imitation of the wolves' searching and the process of attacking grey wolves. The main purpose of this paper to overcome the GWO problem which is trapping into local optima. Design or Methodology or Approach: In this paper, the K-means clustering algorithm is used to enhance the performance of the original Grey Wolf Optimization by dividing the population into different parts. The proposed algorithm is called K-means clustering Grey Wolf Optimization (KMGWO). Findings: Results illustrate the efficiency of KMGWO is superior to GWO. To evaluate the performance of the KMGWO, KMGWO applied to solve 10 CEC2019 benchmark test functions. Results prove that KMGWO is better compared to GWO. KMGWO is also compared to Cat Swarm Optimization (CSO), Whale Optimization Algorithm-Bat Algorithm (WOA-BAT), and WOA, so, KMGWO achieves the first rank in terms of performance. Statistical results proved that KMGWO achieved a higher significant value compared to the compared algorithms. Also, the KMGWO is used to solve a pressure vessel design problem and it has outperformed results. Originality/value: Results prove that KMGWO is superior to GWO. KMGWO is also compared to cat swarm optimization (CSO), whale optimization algorithm-bat algorithm (WOA-BAT), WOA, and GWO so KMGWO achieved the first rank in terms of performance. Also, the KMGWO is used to solve a classical engineering problem and it is superiorComment: 15 pages. World Journal of Engineering, 202

Spatial energetics:a thermodynamically-consistent methodology for modelling resource acquisition, distribution, and end-use networks in nature and society

Resource acquisition, distribution, and end-use (RADE) networks are ubiquitous in natural and human-engineered systems, connecting spatially-distributed points of supply and demand, to provide energy and material resources required by these systems for growth and maintenance. A clear understanding of the dynamics of these networks is crucial to protect those supported and impacted by them, but past modelling efforts are limited in their explicit consideration of spatial size and topology, which are necessary to the thermodynamically-realistic representation of the energetics of these networks. This thesis attempts to address these limitations by developing a spatially-explicit modelling framework for generalised energetic resource flows, as occurring in ecological and coupled socio-ecological systems. The methodology utilises equations from electrical engineering to operationalise the first and second laws of thermodynamics in flow calculations, and places these within an optimisation algorithm to replicate the selective pressure to maximise resource transfer and consumption and minimise energetic transport costs. The framework is applied to the nectar collection networks of A. mellifera as a proof-of-concept. The promising performance of the methodology in calculating the energetics of these networks in a flow-conserving manner, replicating attributes of foraging networks, and generating network structures consistent with those of known RADE networks, demonstrate the validity of the methodology, and suggests several potential avenues for future refinement and application

Mapping and assessing ecosystem services in an agricultural landscape following a tiered approach

Agricultural ecosystems are anthropogenically highly transformed ecosystems, mainly designed to maximise the delivery of provisioning ecosystem services (ES) such as food, material and fuel, often at the expense of other ES. Especially, conventional agriculture and agricultural landscape simplification have become major causes of climate change, ecosystem degradation and biodiversity loss. At the same time, the production of provisioning services depends on other, mainly regulating, ES. In the long-term, the viability of agricultural ecosystems and the delivery of provisioning ES rely on more sustainable farming practices and the conservation of ES and biodiversity. This calls for a shift in the agricultural production paradigm, towards more multifunctional and sustainable agricultural landscapes. Spatially explicit assessments of ES are key components in supporting the shift towards sustainable land use management: they inform on how and where land use decisions can affect ecosystems, on potential trade-offs between the delivery of different ES and help to design targeted ES conservation measures. Understanding the distribution patterns and the main drivers influencing the delivery of ES is needed to determine where land use management measures can be improved to maximise the delivery of (specific) ES. Specifically, spatial information on ES can assist economical decisions underlying agricultural practices: for instance, higher pollination and natural pest control ES potentials can increase crop yields and save resources. The central question of this thesis is to assess how different ES assessment methods influence the predictions of ES supply potential, aiming to find the adapted level of information needed for an ES assessment at the local scale, in an agricultural landscape. To address this research question, several ES mapping and assessment methods, using simple (tier 1) to more complex (tiers 2 and 3) approaches, were developed and applied to a case study area in northern Germany. Additionally, this work aims at informing land use planners and decision-makers on the capacity of the landscape to deliver multiple ES. First, the ES matrix approach (tier 1) was used to assess the importance of spatial resolution and of accounting for ecosystem condition (tier 2). The two following studies developed and implemented more complex methods (tier 3) based on species distribution models (SDMs). SDMs were used to model the relationships between ES providers (ESP) (here wild bees and natural enemies of pests) and a combination of abiotic and biotic factors at different scales. The results of this thesis show that designing multifunctional landscapes ideally requires a rather comprehensive assessment. For most regulation and cultural ES, simple proxies are not suitable for a local quantitative assessment of ES, as they cannot sufficiently cover the spatial heterogeneity of ES capacities and functions that arise from different ecosystem properties and conditions. This is particularly the case of ES delivered by living and mobile organisms such as pollination and natural pest control, whose potentials are determined by multi-scale variables and processes. A comprehensive assessment of every ES is, however, often not feasible. This thesis shows how the use of different modelling methods and the tiered approach can assist in the assessment of multiple ES. Proxy indicators and models should be used whenever empirical data and knowledge of ecological processes are limited. Indicators and models are, however, only simplified representations of complex processes. ES mapping and assessment outputs should therefore be interpreted considering the assumptions behind the models and knowing the associated uncertainties.Landwirtschaftliche Ökosysteme (ÖS) sind anthropogen stark veränderte ÖS, die hauptsächlich darauf ausgelegt sind, die Bereitstellung von Ökosystemleistungen (ÖSL) wie Nahrung, Material und Brennstoff zu maximieren - oft auf Kosten anderer ÖSL. Insbesondere die konventionelle Landwirtschaft und die Vereinfachung der Agrarlandschaft sind wesentlich mitverantwortlich für den Klimawandel, die Verschlechterung von ÖS und den Verlust der biologischen Vielfalt. Gleichzeitig hängt die Fähigkeit eines ÖS Nahrung und andere Rohstoffe zur Verfügung zu stellen von anderen, hauptsächlich regulierenden, ÖSL ab. Langfristig hängen die Lebensfähigkeit landwirtschaftlicher ÖS und die Bereitstellung von ÖSL von nachhaltigeren landwirtschaftlichen Praktiken und der Erhaltung von Ökosystemen in gutem Zustand und der Biodiversität ab. Räumlich explizite Bewertungen von ÖSL sind ein Schlüssel zur Unterstützung eines nachhaltigen Landnutzungsmanagements: Sie informieren, wie und wo Ökosysteme beeinflussen werden können, über potenzielle Kompromisse zwischen der Bereitstellung verschiedener ÖSL und helfen bei der Entwicklung gezielter Maßnahmen zur Erhaltung von ÖSL. Insbesondere räumliche Informationen zu ÖSL können wirtschaftliche Entscheidungen unterstützen: Höhere Bestäubungs- und natürliche Schädlingsbekämpfungspotentiale von ÖSL können beispielsweise die Ernteerträge steigern und Ressourcen sparen. Die zentrale Frage dieser Arbeit ist es zu bewerten wie verschiedene ÖSL-Bewertungsmethoden die Vorhersagen des ÖSL-Versorgungspotentials auf lokaler Ebene beeinflussen. Dafür wurden mehrere ÖSL-Kartierungs- und Bewertungsmethoden unter Verwendung einfacher (Stufe 1) bis hin zu komplexeren (Stufen 2 und 3) Ansätzen entwickelt und auf ein Fallstudiengebiet in Norddeutschland angewendet. Darüber hinaus sollen Landnutzungsplaner und Entscheidungsträger über die Fähigkeit der Landschaft informiert werden mehrere ÖS bereitzustellen. Zunächst wurde der ÖSL-Matrix-Ansatz (Stufe 1) verwendet, um die Bedeutung der räumlichen Auflösung und der Berücksichtigung des Ökosystemzustands (Stufe 2) zu bewerten. Die beiden nachfolgenden Studien entwickelten und implementierten komplexere Methoden (Stufe 3) auf der Grundlage von Artenverteilungsmodellen („species distribution models“ - SDMs). SDMs wurden verwendet, um die Beziehungen zwischen ÖSL-Anbietern (hier Wildbienen und natürlichen Feinden) und mit abiotischen und biotischen Faktoren auf verschiedenen Skalen zu modellieren. Die Ergebnisse dieser Arbeit zeigen, dass die Gestaltung multifunktionaler Landschaften eine umfassende Bewertung erfordert. Für die meisten regulatorischen und kulturellen ÖSLs sind einfache Proxys nicht für eine lokale quantitative Bewertung von ÖSL geeignet, da sie die räumliche Heterogenität von ÖSL-Kapazitäten und -Funktionen, die sich aus unterschiedlichen Ökosystemeigenschaften und -bedingungen ergeben, nicht ausreichend abdecken können. Dies gilt insbesondere für ÖSL, die von lebenden und mobilen Organismen wie Bestäubung und Schädlingsbekämpfung geliefert werden, deren Potenziale durch mehrskalige Variablen und Prozesse bestimmt werden. Eine umfassende Bewertung aller ÖSL ist jedoch oft nicht praktikabel. Diese Arbeit zeigt, wie die Verwendung verschiedener Modellierungsmethoden und der gestufte Ansatz bei der Bewertung mehrerer ÖSL helfen können. Proxy-Indikatoren und -Modelle sollten verwendet werden, wenn empirische Daten und Kenntnisse über ökologische Prozesse begrenzt sind