Multi-objective Gravitational Search Algorithm Research Articles

Star-Quake: A New Operator in Multi-Objective Gravitational Search Algorithm for Task Scheduling in IoT-Based Cloud–Fog Computing System

Star-Quake: A New Operator in Multi-Objective Gravitational Search Algorithm for Task Scheduling in IoT-Based Cloud–Fog Computing System

Addressing a Collaborative Maintenance Planning Using Multiple Operators by a Multi-Objective Metaheuristic Algorithm

Selective maintenance has a significant impact on the sustainable management of maintenance operations. The collaboration of multiple maintenance teams/operators is helpful to achieve sustainability for selective maintenance sequence planning. For products with a large number of components, a single maintenance team/operator is inefficient due to a long completion time which is not acceptable for emergency planning. Providing specific and efficient maintenance sequence planning is critical to effectively handle different types of emergencies (e.g., wartime) while avoiding vague task assignments to multiple maintenance teams/operators. For scheduling many maintenance jobs while improving the efficiency and quality of maintenance operations, this study proposes a collaborative maintenance planning based on the concept of imperfect maintenance. In this regard, this study develops a multi-objective optimization model to optimize parallel maintenance sequences considering maintenance profit, maintenance cost, maintenance team, and resource limitations. We show the feasibility of the proposed multi-objective optimization model through a real case of maintenance practice for the components of an assistor device. For analyzing the complexity of the proposed maintenance sequence planning problem, this study introduces a new multi-objective metaheuristic algorithm which is an enhanced multi-objective gravitational search algorithm (EMOGSA) to find high-quality Pareto solutions for the proposed problem. Different multi-objective evaluation metrics are used to study the performance of the proposed algorithm. From the results, the proposed model and developed solution algorithm can help maintenance decision-makers to determine complex maintenance planning. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper deals product with a maintenance and proposes gravitational search algorithm based on only maintenance task, which maintenance task. The goal of this paper is to analyze the maintenance problem from the perspective of collaboration of multiple maintenance teams/operators.

Improved gravitational search algorithm and novel power flow prediction network for multi-objective optimal active dispatching problems

Multi-objective optimal active dispatching (MO-OAD) is a high-profile topic in power grid optimizations. Traditional methods are insufficient for the MO-OAD problem due to its nonconvexity and strict constraints. Therefore, an improved multi-objective gravitational search algorithm (IMGSA) with better population diversity and search capability is put forward in this paper. Five MO-OAD experiments considering various user requirements demonstrate that the IMGSA achieves preferable Pareto-front (PF) over the non-dominated sorting genetic algorithm-II (NSGA-II) and other recently published algorithms. More importantly, to further explore potential elite schemes after obtaining the best compromise scheme (BCS) of IMGSA, an efficient power flow prediction model based on the radial basis function (RBF) network is proposed for the first time. By accurately mapping the nonlinear relationship between the control variables of MO-OAD and optimization objectives, more than five elite dispatching schemes are determined by the suggested RBF prediction model. These elite schemes greatly reduce the fuel cost, power loss and exhaust emission of different IEEE power systems. Quantitative evaluations such as generational distance (GD) and hyper-volume (HV) indicators prove that the proposed IMGSA with RBF prediction model (IMGSA-RBF) is more competitive than many existing algorithms. Detailed MO-OAD experiments show that IMGSA-RBF method has significant advantages in PF-uniformity, PF-diversity, and the quality of optimal dispatching schemes. In general, the innovative IMGSA-RBF method provides a valuable technology to realize desirable power grid operation with less carbon emission and better economy.

A community detection approach for the resource leveling problem in a multi-project scheduling environment

This paper develops an integrated mathematical formulation that embraces the Resource Leveling Problem (RLP) and the Multi-Project Scheduling Problem (MPSP). To incorporate both aspects into one formulation, the proposed model is bi-objective that seeks to minimize projects’ durations and resource usage, simultaneously. Resources are not available in all time periods because of sickness, failure, maintenance, holidays, training, laying off, etc. This assumption complicates the scheduling process for multiple concurrent projects that share a limited number of resources with finite capacities. To tackle this intricacy, a coherent approach is required that not only schedules activities of multiple projects, but also levels resource consumptions as efficient as possible. Therefore, this study offers an approach based on the Community Detection problem to identify homogeneous communities of activities that have common resource requirements. These communities are obtained by the Vibration Damping Optimization (VDO) method through modularity maximization. The identified communities help the projects’ planner to avoid simultaneous scheduling of the activities within a community; hence, resource consumptions are minimized. A Multi-Objective Gravitational Search Algorithm (MOGSA) is developed to solve the proposed bi-objective problem. The MOGSA uses the communities detected by the VDO and schedules the projects. The MOGSA has been invigorated by using two Cellular Automata (CA), namely “Seeds” and “Wolfram’s elementary cellular automaton” in its procedures. A set of test problems have been examined to compare the efficacy of the MOGSA with some of the best existing algorithms. The results demonstrate that the MOGSA is highly competitive and yields proper solutions comparing to the outputs of well-known optimizers. Besides, a real construction case study has been presented to demonstrate that the proposed model and algorithm can deliver practical solutions.

Design optimization of the complementary voltage controlled oscillator using a multi-objective gravitational search algorithm

Design optimization of the complementary voltage controlled oscillator using a multi-objective gravitational search algorithm

A Comparison Study of Multi-Objective Bonobo Optimizers for Optimal Integration of Distributed Generation in Distribution Systems

In this paper, the three newly published Multi-Objective Bonobo Optimizer (MOBO) variants are assessed and evaluated using statistical analysis for solving the multi-objective optimization of Distributed Generation (DG) into distribution systems. The main objectives of the study are to minimize system loss and enhance voltage profile. While the first variant, MOBO1, depends on the sort and grid-index approach, the second variant, MOBO2, relies on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithm technique. The last variant, MOBO3, is inspired by the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The three MOBO algorithms are compared to themselves and to other algorithms solving the same optimization problem. These algorithms include the MOJAYA, Multi-Objective Artificial Ecosystem-Based Algorithm (MOAEO), Multi-Objective Gravitational Search Algorithm (MOGSA), and Multi-Objective Particle Swarm Optimization (MOPSO). The 33-bus and 85-bus radial distribution systems are used test systems for solving the optimal allocation of single- and three-DG units operating at unity power factor. In order to find the best compromise solution, the Pareto Optimal front method is adopted with the help of a fuzzy-based function. The obtained results show the effectiveness of the MOBO variants compared with other algorithms in terms of different statistical parameters and multi-objective performance metrics such as diversity, hypervolume, spacing, and set coverage. While the MOBO algorithm reduces power loss and TVD by 39.59 and 68.31% for a single DG, they are reduced to 58.13 and 88.44% for three DG units allocated to the 33-bus distribution system, respectively. On the other hand, the MOBO algorithm reduces power loss and TVD by 37.28 and 66.84% for a single DG, respectively, they are decreased to 46.35 and 82.53% for three DG units assigned to the 85-bus distribution system. Among the three MOBO variants, it is found that the MOBO1 is superior for a single-DG allocation, while the MOBO3 is the best for the allocation of three-DG units.

An Intelligent BMS With Probabilistic MO-GSA Based CDMAS Integrating Edge Controller Analytics

One of the most challenging facets of any Battery Management System is scheduling the charging and discharging cycles of each battery without compromising the uninterruptible power supplies to meet demand. A battery-powered system may include several batteries of varying sorts, models, makes, sizes, and lifespans, etc which employs a diversity of charging techniques. Subsequently, each battery would have its own charging-discharging path. Even when a battery of the same capacity and make is used with the same load profile, the charging curves differ. This is because batteries have differential electrochemical characteristics and deteriorate to some extent with each use. Accordingly, the Battery Management System should schedule the batteries so that degradation and usage are kept to a minimum. This paper developed an adaptive Intelligent Battery Management System that can schedule batteries with minimal power loss, increased battery life, and higher financial benefit, even when batteries of various sizes, capacities, production types, lifespans, charge cycle models etc are incorporated. Multi-zonal approaches are used, combining the benefits of edge analytics and Centralized Data Management and Analytics System. Every millisecond, the battery parameters will be monitored using an energy monitoring circuit integrated with an edge controller. However, the edge controller alone will not be able to process such a vast volume of data on its own, the data will be divided into two categories and analyzed in two phases. All of the big data is delivered to a Centralized Data Management and Analytics System using Low-power wide-area network, and this data is labeled as primary data. A second set of data is extracted from big data within the edge controller via metadata processing before it is transmitted to Centralized Data Management and Analytics System. This secondary data is processed against safety standards stored in read only memory and rapid judgments are performed using edge analytics if necessary. The Centralized Data Management and Analytics System employs a number of analytics techniques. An Auto-Regressive Integrated Moving Average method will be used to forecast the State of Charge of batteries. With the help of this forecasted data, the Multi-Objective Gravitational Search Algorithm is then used to schedule the best battery allocation based on a number of objectives such as battery temperature runaway, unit cost of consumption including span of service, last used time period, State of Charge (%), State of Charge (WH), and so on. Between Auto-Regressive Integrated Moving Average and Gravitational Search Algorithm, a Naive Bayes probabilistic estimator is encased to identify the best general population for Gravitational Search Algorithm, avoiding repeated battery swapping and improving power efficiency. The whole device is evaluated in Hardware in a Loop model. When comparing the performance of the developed model to that of other optimization models, it is evident that Gravitational Search Algorithm outperforms other methods when population is constrained.

An improved multi-objective gravitational search algorithm

Multi-objective search algorithm is a common optimization tool to deal with complex multi-objective problems, such as Multiple Objectives Particle Swarm Optimization (MOPSO) and Non dominated Sorting Genetic Algorithm-II (NSGA-II). Gravitational Search Algorithm (GSA) is a new heuristic evolutionary algorithm, which is based on the Newtonian gravity and the laws of motion to search optimal solutions. Some of agents have bigger mass, so other smaller mass agents are affected easily to fall into local optimization. In order to improve the search ability of the algorithm, this paper proposes an Improved Multi-Objective Gravitational Search Algorithm (IMOGSA). The proposed method uses the fast non-dominated sorting strategy and crowding distance of NSGA-II, and uses Sine Cosine Algorithm (SCA). Using strategy of NSGA-II is to reduce the complexity of the algorithm, in addition, using SCA is to improve the convergence and distribution of IMOGSA by improving the weight of acceleration. Finally, the proposed method has been compared with other well-known heuristic search methods by using some benchmark functions.

Procurement of electrical energy and operating reserve ancillary services in wind incorporated deregulated system considering demand response

This study presents the procurement of electrical energy and operating reserve ancillary services (ORASs) by the simultaneous clearing of the wind integrated power market under the pool-based deregulated environment. This investigation is important due to the intermittent output of wind generators, which is a serious concern for medium and high wind penetration and requirement of high operating reserves for maintaining the security of such systems. The market model is presented for the clearing of energy and ORAS market, where both thermal generators and demand response offers supply the reserves. This model is analysed for energy and spinning reserve (ESR) cost minimisation, emission minimisation, and co-optimisation of ESR cost and emission. The non-dominated sorting multi-objective gravitational search algorithm is employed to obtain Pareto optimal solutions. The efficacy of the presented method is investigated on IEEE 30-bus, IEEE 118-bus, and IEEE 300-bus test systems for different levels of wind uncertainty. The results are compared with multi-objective particle swarm optimisation.

Characteristics Analysis and Fuzzy Fractional-Order PID Parameter Optimization for Primary Frequency Modulation of a Pumped Storage Unit Based on a Multi-Objective Gravitational Search Algorithm

Compared with conventional hydropower units, the pumped storage unit has the characteristics of diverse working conditions and frequent switching. Therefore, the stability and regulation quality of the primary frequency modulation transition process of the regulating system is very important. Due to the “S” characteristics of the pumped storage unit (PSU), the pumped storage unit regulating system has a strong nonlinearity, and the conventional proportional-integral-derivative (PID) controller cannot provide high-quality control under low water head conditions. In this paper, the nonlinear PSU model with an elastic water hammer effect is studied, and the fuzzy fractional-order PID (FFOPID) controller is designed to improve the stability of the system. The membership function and the control parameters of the fractional-order PID are optimized based on the multi-objective gravitational search algorithm (MOGSA). The experimental results show that the optimized design of the FFOPID controller has better control quality than the traditional PID controller, the fractional-order PID (FOPID) controller, and the fuzzy PID controller (FPID) when the system is disturbed by the rotating speed under low water head.

Toward a Robust Multi-Objective Metaheuristic for Solving the Relay Node Placement Problem in Wireless Sensor Networks.

During the last decade, Wireless sensor networks (WSNs) have attracted interest due to the excellent monitoring capabilities offered. However, WSNs present shortcomings, such as energy cost and reliability, which hinder real-world applications. As a solution, Relay Node (RN) deployment strategies could help to improve WSNs. This fact is known as the Relay Node Placement Problem (RNPP), which is an NP-hard optimization problem. This paper proposes to address two Multi-Objective (MO) formulations of the RNPP. The first one optimizes average energy cost and average sensitivity area. The second one optimizes the two previous objectives and network reliability. The authors propose to solve the two problems through a wide range of MO metaheuristics from the three main groups in the field: evolutionary algorithms, swarm intelligence algorithms, and trajectory algorithms. These algorithms are the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), Multi-Objective Artificial Bee Colony (MO-ABC), Multi-Objective Firefly Algorithm (MO-FA), Multi-Objective Gravitational Search Algorithm (MO-GSA), and Multi-Objective Variable Neighbourhood Search Algorithm (MO-VNS). The results obtained are statistically analysed to determine if there is a robust metaheuristic to be recommended for solving the RNPP independently of the number of objectives.

An effective design of parity check matrix for LDPC codes using multi-objective gravitational search algorithm

The low-density parity-check (LDPC) code is an efficient contender for capacity approaching error correction over many important channels. In this paper, we design a parity check matrix for error correction using multi-objective gravitational search algorithm. The overall steps of the proposed technique are explained with three steps: 1) new objective function generation; 2) optimised parity check matrix generation using MGSA; 3) an LDPC encoding-decoding system design. At first, a multi-objective function is derived based on four efficient objectives like low density, maximum hamming minimum distance, maximum marginal entropy, and maximum cyclic lifting degree. Our GSA-based approach is developed with efficient agent representation, fitness computation along with usual GSA operators. Once the parity check matrix is computed, this matrix is utilised for LDPC encoding. The proposed approach is evaluated through bit error rate (BER) measure. From the results, we ensure that the proposed technique outperformed the existing technique by achieving the BER of 0.0513, 0.0348, and 0.0270 in fourth iteration.

An effective design of parity check matrix for LDPC codes using multi-objective gravitational search algorithm

An effective design of parity check matrix for LDPC codes using multi-objective gravitational search algorithm

Coordinated Multi-Objective Optimization for Multiple Trade-Offs in Pumped Outage Condition of Pumped Storage System

The transient process of pumped storage system (PSS) experienced pump mode, turbine mode and switching mode in pumped outage condition, spanning hump zone and S-shaped region. The conflicting dynamic indicators make it difficult to meet the requirements of the transient process. How to specify optimal operating strategies and improve the reliability of PSS in the pumped outage condition has become a key issue. This problem is addressed in this work based on coordinated multi-objective optimization, and three stages are included: nonlinear modeling, strategy optimization and decision making. A trade-off is embodied in each stage. Firstly, the real-time accurate equivalent circuit model is applied for PSS. The spatiotemporal discrete analysis is presented to enable the trade-off between computing efficiency and model accuracy in stage 1. Then, the neighborhood-search chaotic mutation multi-objective gravitational search algorithm, integrating multiple constraints, is performed to solve the Pareto front. It achieves the trade-off between algorithm convergence and searching diversity in stage 2. Further, fuzzy analytic hierarchy process is innovatively introduced to select the most compatible solution, which comprehensively considers the quantitative and qualitative factors. It accomplishes the trade-off in conflicting objectives and indicators in stage 3. Compared with the on-site operation in pumped outage condition, the maximum reversing speed decreased from 545 rpm to 161.45 rpm, the maximum water pressure of volute can be reduced by 4.55%, and the minimum draft tube pressure can be improved by 6.94%. The coordinated multi-objective optimization provides a novel technical guidance for the safe and stable operation of PSS.

MOGSABAT: a metaheuristic hybrid algorithm for solving multi-objective optimisation problems

This study proposes a novel strength of multi-objective gravitational search algorithm and bat algorithm MOGSABAT to solve multi-objective optimisation problem. The proposed MOGSABAT algorithm is divided into three stages. In the first stage (moving space), a switch in a solution from single function to multiple functions that contain more than one objective to use the gravitational search algorithm GSA is determined. We established a new equation to calculate the masses of individuals in the population using the theoretical work found in the strength Pareto evolutionary algorithm. In the second stage (moving in space), how to handle the bat algorithm BAT to solve multiple functions is established. We applied the theoretical work of multi-objective particle swarm optimisation into the BAT algorithm to solve multiple functions. In the third stage, multi-objective GSA and multi-objective BAT are integrated to obtain the hybrid MOGSABAT algorithm. MOGSABAT is tested by adopting a three-part evaluation methodology that (1) describes the benchmarking of the optimisation problem (bi-objective and tri-objective) to evaluate the performance of the algorithm; (2) compares the performance of the algorithm with that of other intelligent computation techniques and parameter settings; and (3) evaluates the algorithm based on mean, standard deviation and Wilcoxon signed-rank test statistic of the function values. The optimisation results and discussion confirm that the MOGSABAT algorithm competes well with advanced metaheuristic algorithms and conventional methods.

Clustering of Remote Sensing Imagery Using a Social Recognition-Based Multi-objective Gravitational Search Algorithm

Cognitively inspired swarm intelligence algorithms (SIAs) have attracted much attention in the research area of clustering since it can give machine the ability of self-learning to achieve better classification results. Recently, the SIA-based multi-objective optimization (MOO) methods have shown their superiorities in data clustering. However, their performances are limited when applying to the clustering of remote sensing imagery (RSI). To construct an excellent MOO-based clustering method, this paper presents a social recognition-based multi-objective gravitational search algorithm (SMGSA) to achieve simultaneous optimization of two conflicting cluster validity indices, i.e., the Xie-Beni (XB) index and the Jm index. In the SMGSA, searching particles not only are guided by those elite particles stored in an external archive by the gravitational force but also learn from the social recognition of the whole population through the position difference. SMGSA thereby formed with outstanding exploitation ability. Comparison experiments on two public RSI data sets, including a moderate aerial image and a hyperspectral, validated that the MOO-based clustering methods could obtain more accurate results than the single validity index-based method. Moreover, the SMGSA-based method can achieve superior results than that of the multi-objective gravitational search algorithm without social recognition ability. The proposed SMGSA performs favorable balance between the two conflicting cluster validity indices and achieves preferable classification for the RSI. In addition, this study indicates that the swarm intelligence-based cognitive computing is potential for the intelligent interpretation and understanding of complicated remote sensing scene.

Comparison of stability service cost in power grids considering different types of WTs

This study presents a comparative study on dynamic behaviour of two different types of wind turbines (WTs) that are widely used in power systems. Mathematical modelling of two types of WTs in the multi-machine power system is presented, and a suitable framework for the study is provided. To compare the cost of provision of stability service by each of two different WTs, a technical–economical two-objective optimisation problem considering damping indices and generation cost will be formulated and solved by multi-objective gravitational search algorithm method. The presented strategy is carried out for each WT and Pareto-optimal curves are extracted. It is shown that in a system with poor dynamic situation, expensive production units are used that this phenomenon will increase generation cost. Generation costs are analysed by considering two WTs, doubly fed asynchronous generator and permanent magnet synchronous generator and dynamic condition for each type are evaluated. Two scenarios are assumed for evaluation; the first one without retuning of stabilisers and the second one with stabilisers retuned due to system generation situation. The proposed scheme is tested on modified 16-machine 5-area network and simulation results are compared.

A comprehensive survey on gravitational search algorithm

Abstract Gravitational Search Algorithm (GSA) is an optimization method inspired by the theory of Newtonian gravity in physics. Till now, many variants of GSA have been introduced, most of them are motivated by gravity-related theories such as relativity and astronomy. On the one hand, to solve different kinds of optimization problems, modified versions of GSA have been presented such as continuous (real), binary, discrete, multimodal, constraint, single-objective, and multi-objective GSA. On the other hand, to tackle the difficulties in real-world problems, the efficiency of GSA has been improved using specialized operators, hybridization, local search, and designing the self-adaptive algorithms. Researchers have utilized GSA to solve various engineering optimization problems in diverse fields of applications ranging from electrical engineering to bioinformatics. Here, we discussed a comprehensive investigation of GSA and a brief review of GSA developments in solving different engineering problems to build up a global picture and to open the mind to explore possible applications. We also made a number of suggestions that can be undertaken to help move the area forward.

Optimization of Guide Vane Closing Schemes of Pumped Storage Hydro Unit Using an Enhanced Multi-Objective Gravitational Search Algorithm

The optimization of guide vane closing schemes (OGVCS) of pumped storage hydro units (PSHUs) is a cooperative control and optimal operation research field in renewable energy power generation technology. This paper presents an OGVCS model of PSHUs considering the rise rate of the unit rotational speed, the specific node pressure of each hydraulic unit, as well as various complicated hydraulic and mechanical constraints. The OGVCS model is formulated as a multi-objective optimization problem to optimize conflicting objectives, i.e., unit rotational speed and water hammer pressure criteria. In order to realize an efficient solution of the OGVCS model, an enhanced multi-objective bacterial-foraging chemotaxis gravitational search algorithm (EMOBCGSA) is proposed to solve this problem, which adopts population reconstruction, adaptive selection chemotaxis operator of local searching strategy and elite archive set to efficiently solve the multi-objective problem. In particular a novel constraints-handling strategy with elimination and local search based on violation ranking is used to balance the various hydraulic and mechanical constraints. Finally, simulation cases of complex extreme operating conditions (i.e., load rejection and pump outage) of a ‘single tube-double units’ type PSHU system are conducted to verify the feasibility and effectiveness of the proposed EMOBCGSA in solving OGVCS problems. The simulation results indicate that the proposed EMOBCGSA can provide a lower rise rate of the unit rotational speed and smaller water hammer pressure than other methods established recently while considering various complex constraints in OGVCS problems.

Integrated optimization of cutting parameters and scheduling for reducing carbon emissions

In order to reduce carbon emissions in manufacturing processes and overcome the limitations of previous researches which optimized cutting parameters and scheduling independently and ignored their comprehensive effects on carbon emissions, an integrated optimization model of cutting parameters and scheduling is proposed to minimize completion time and carbon emissions in manufacturing processes. The proposed integrated model is based on the facts that machining time, cutting-tool wear and energy consumption of machine tools depend on cutting parameters, and further affect scheduling aiming at minimizing completion time and carbon emissions in manufacturing processes. Since cutting parameter optimization is a continuous optimization problem but scheduling optimization is a discrete optimization problem, it is very difficult to optimize both simultaneously. Therefore, an improved multi-objective gravitational search algorithm with a strong global search capability which combines crossover and mutation operators is designed to solve the proposed model. Any solution in the search space consists of two parts, Cutting parameters and job sequence. They are optimized simultaneously in each iteration in the proposed algorithm. Finally, three workpieces to be processed in two machines including turning and milling are taken as an example. It shows that the proposed integrated optimization can further reduce 2.9 percent of carbon emission and the 2.56 percent of completion time comparing to the traditional separated optimization. The validity of the proposed model and algorithm is verified by computational results.