Multi-objective Problem Research Articles

Hybrid response dynamic multi-objective optimization algorithm based on multi-arm bandit model

Dynamic multi-objective optimization is a relatively challenging problem within the field of multi-objective optimization. Nevertheless, these problems have significant real-world applications. The key to addressing dynamic multi-objective problems effectively is promptly tracking changes in the Pareto set (PS) and Pareto front (PF). Dynamic multi-objective optimization encompasses various types of problems, and a single-type response strategy proves effective for some specific scenarios. However, as problem complexity and diversity increase, a single-type response strategy often falls short in solving dynamic multi-objective optimization problems. To address this issue, this paper proposes a hybrid response dynamic multi-objective optimization algorithm. The suggested algorithm utilizes the multi-arm bandit model to adaptively adjust the proportion of different response strategies for each type of multi-objective optimization problem. Furthermore, it achieves rapid convergence through an enhanced two-stage MOEA/D. Experiments demonstrate the effectiveness of the strategies employed in the proposed algorithm and its competitiveness compared to other state-of-the-art algorithms.

Multi-layer adaptive spatial-temporal feature fusion network for efficient food image recognition

Numerous deep learning methods have been developed to tackle the challenges of recognizing food images, including convolutional neural networks, deep feature extraction, and deep feature fusion methods. This research proposes a new architecture called ASTFF-Net that uses deep feature fusion to tackle various challenges in food recognition, including similarity patterns between two categories, multi-object problems, light conditions, camera position, noise objects, and blurred images. ASTFF-Net is a robust and adaptive spatial–temporal fusion network designed to address these challenges effectively. The ASTFF-Net architecture consisted of three networks. In the spatial feature extraction network, the ResNet50 architecture was used to extract robust spatial features, and the reduction operation was utilized to minimize parameter size. Subsequently, the spatial features were passed through a 1D convolution (Conv1D) to fit the features into the recurrent neural networks. In the temporal feature extraction network, the spatial features were given to the long short-term memory, allowing the network to learn from various long sequence patterns. In the adaptive feature fusion network, the robust spatial and temporal features were fused and assigned to the Conv1D, followed by the softmax function. The ASTFF-Net architecture is also intended to decrease the number of network parameters and prevent overfitting problems. Experimental results on four benchmark food image datasets: Food11, UEC Food-100, UEC Food-256, and ETH Food-101, demonstrate that the proposed ASTFF-Nets, particularly ASTFF-NetB3, were more competitive compared with other existing methods.

Multi-objective optimization of virtual machine migration among cloud data centers

AbstractWorkload migration among cloud data centers is currently an evolving task that requires substantial advancements. The incorporation of fuzzy systems holds potential for enhancing performance and efficiency within cloud computing. This study addresses a multi-objective problem wherein the goal is to maximize the interpretability and the percentage of renewable energy consumed by a fuzzy meta-scheduler system in cloud scenarios. To accomplish this objective, the present research proposes a novel approach utilizing a multi-objective Knowledge Acquisition with a Swarm Intelligence Approach algorithm. Additionally, it takes advantage of a framework built on CloudSim, which includes virtual machine migration capabilities based on an expert system. Furthermore, a hierarchical fuzzy system is employed to assess rule base interpretability, along with another multi-objective algorithm, named Non-dominated Sorting Genetic Algorithm II. The framework and hierarchical system are employed to perform various simulation results concerning renewable energy and interpretability, while the algorithms aim to enhance the system’s performance and interpretability. Empirical results demonstrate that it is possible to improve the performance of cloud data centers while improving the interpretability of the corresponding fuzzy rule-based system. The proposed multi-objective algorithm shows comparable or superior performance to the genetic algorithm across diverse scenarios. The simulation results indicate that improvements in cloud data center performance can be achieved while enhancing system interpretability. The average improvement in the interpretability index ranges from 0.6 to 6%, with a corresponding increase in renewable energy utilization ranging from 5 to 6%.

Optimization of Distributed Energy Resources Operation in Green Buildings Environment.

Without a well-defined energy management plan, achieving meaningful improvements in human lifestyle becomes challenging. Adequate energy resources are essential for development, but they are both limited and costly. In the literature, several solutions have been proposed for energy management but they either minimize energy consumption or improve the occupant's comfort index. The energy management problem is a multi-objective problem where the user wants to reduce energy consumption while keeping the occupant's comfort index intact. To address the multi-objective problem this paper proposed an energy control system for a green environment called PMC (Power Management and Control). The system is based on hybrid energy optimization, energy prediction, and multi-preprocessing. The combination of GA (Genetic Algorithm) and PSO (Particle Swarm Optimization) is performed to make a fusion methodology to improve the occupant comfort index (OCI) and decrease energy utilization. The proposed framework gives a better OCI when compared with its counterparts, the Ant Bee Colony Knowledge Base framework (ABCKB), GA-based prediction framework (GAP), Hybrid Prediction with Single Optimization framework (SOHP), and PSO-based power consumption framework. Compared with the existing AEO framework, the PMC gives practically the same OCI but consumes less energy. The PMC framework additionally accomplished the ideal OCI (i-e 1) when compared with the existing model, FA-GA (i-e 0.98). The PMC model consumed less energy as compared to existing models such as the ABCKB, GAP, PSO, and AEO. The PMC model consumed a little bit more energy than the SOHP but provided a better OCI. The comparative outcomes show the capability of the PMC framework to reduce energy utilization and improve the OCI. Unlike other existing methodologies except for the AEO framework, the PMC technique is additionally confirmed through a simulation by controlling the indoor environment using actuators, such as fan, light, AC, and boiler.

Cellular gradient algorithm for solving complex mechanical optimization design problems

In mechanical optimization design problems, there are often some non-continuous or non-differentiable objective functions. For these non-continuous and non-differentiable optimization objectives, it is often difficult for existing optimal design algorithms to find the desired optimal solutions. In this paper, we incorporate the idea of gradient descent into cellular automata and propose a Cellular Gradient (CG) method. First, we have given the basic rules and algorithmic framework of CG and designed three kinds of growth and extinction rules respectively. Then, the three evolutionary rules for cellular within a single cycle are analyzed separately for form and ordering. The best expressions for the cellular jealous neighbor rule and the solitary regeneration rule are given, and the most appropriate order in which the rules are run is selected. Finally, the solution results of the cellular gradient algorithm and other classical optimization design algorithms are compared with a multi-objective multi-parameter mechanical optimization design problem as an example. The computational results show that the cellular gradient algorithm has an advantage over other algorithms in solving global and dynamic mechanical optimal design problems. The novelty of CG is to provide a new way of thinking for solving optimization problems with global discontinuities.

Research on the traction characteristic evaluation of urban rail vehicles based on entropy weight TOPSIS

This paper aims to investigate the influence of different speed at the end of the constant power section of the traction characteristic curve (TCC) on the vehicle dynamic performance and evaluate the TCC. A dynamics co-simulation model is developed in SIMPACK and MATLAB for dynamic analysis of the urban rail vehicle (URV) under different traction characteristics. Then it is used to investigate how acceleration distance and vehicle dynamic performance varies with the speed at the end of the constant power section of the TCC under different starting torques. Moreover, the entropy weight TOPSIS method which is widely used to solve the multi-objective decision-making problem is chosen to evaluate the traction characteristics based on various dynamic performance indexes over 25 test sections and acceleration distance. The results show that under traction conditions, the starting torque has effects on the lateral and vertical accelerations of car body, lateral and vertical wheel-rail contact forces, derailment coefficient and wheel unloading factor. The higher the torque, the greater the value of each index, that means the poorer the vehicle ride characteristics and running safety. For a given starting torque, the dynamic performance indexes increase with the increase of the speed at the end of the constant power section from 50 km/h to 80 km/h during the vehicle speed-up process. The maximum growth rate of the lateral and vertical accelerations of car body, lateral and vertical wheel-rail contact forces are 17%, 8%, 8% and 2%, respectively, when the speed at the end of the constant power section increases from 50 km/h to 80 km/h. Last, the comprehensive evaluation of traction characteristics using entropy-weight TOPSIS method reveals when the starting torque is 800 [Formula: see text], 1000 [Formula: see text], 1200 [Formula: see text] and 1400 [Formula: see text], the corresponding optimal speed at the end of the constant power section is 80 km/h, 80 km/h, 70 km/h and 50 km/h, respectively. The result of the study can provide theoretical support for traction characteristic design and traction control for URVs.

Distribution Expansion Planning of Electrical Networks Considering Electrical Losses and Financial Losses Due to Voltage Sags and Interruptions

Currently, distribution system planning is crucial to meet both the present and future electricity needs of customers with minimal investments. This paper introduces a novel methodology to solve the distribution expansion planning problem by employing a heuristic based on genetic algorithms (GA). The proposed GA aims to minimize investment costs, electrical losses, and financial losses due to voltage sags and power interruptions. This GA is applied in the 18-busbar network with three planning stages. The results show that the GA deals with efficiency with the multi-objective problem obtaining solutions with reduced iterations and with minimum investments considering electrical losses, and financial losses.

Revolutionizing optimization: An innovative nutcracker optimizer for single and multi-objective problems

Nutcracker Optimization Algorithm (NOA) is a recently proposed meta-heuristic algorithm inspired by foraging and storing behavior of nutcracker birds. NOA demonstrates strong performance across various test sets and optimization problems. However, it faces challenges in effectively balancing exploration and exploitation, particularly in high-dimensional and complex applications. In this paper, an improved variant of NOA based on Bernoulli map strategy and seasonal behavior strategy, called INOA, is proposed. Firstly, the Bernoulli map strategy enhances the quality of the initial population during the initialization process. Secondly, the seasonal behavior strategy is employed to balance the exploration and exploitation of NOA, enabling it to effectively handle high-dimensional problems by improving convergence and exploration capabilities. Additionally, this paper extends INOA to a multi-objective version called MONOA, enabling the algorithm to solve multi-objective problems. The proposed algorithm, INOA, undergoes evaluation using 30 classical benchmark problems, CEC-2014, CEC-2017, CEC-2019 test suites, and two real-world engineering design problems. INOA’s performance is compared with three categories of optimization methods: (1) recently-developed algorithms, i.e., NOA, BWO, DBO, RIME, MGO, HBA, and SO, (2) highly-cited algorithms, i.e., SMA, MPA, GWO, and (3) high-performing optimizers and winners of CEC competition, i.e., CJADE, L-SHADE-RSP, L-SHADE, and EBOwithCMAR. The proposed algorithm, MONOA, undergoes evaluation using well-known ZDT and DTLZ suites, as well as six constrained and engineering design problems. MONOA’s performance is compared with some state-of-the-art approaches such as MOPSO, NSSO, MOGOA, MOSMA, and MOMGA. Five performance indicators are employed for comparison purposes. Experimental results and comparisons affirm the efficacy of INOA in solving complex and higher-dimensional optimization problems. Similarly, the findings underscore the effectiveness of MONOA in solving diverse multi-objective problems with distinct characteristics.

Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators

Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators

Optimal active and reactive energy management for a smart microgrid system under the Moroccan grid pricing code

This article presents an innovative active and reactive energy management system (AR-EMS) specifically designed for residential buildings in Morocco, seamlessly integrated with a Smart Microgrid (SMG) and the Electrical Power Grid (EPG) supplier. The considered SMG incorporates a Photovoltaic system (PV) and an Energy Storage System (ESS). In Morocco, the EPG utilizes a Range Tariff System (RTS), where the tariff structure depends on the total energy consumed at the end of each month. Hence, the proposed AR-EMS is designed to computes optimal active and reactive power setpoints of each source at 15-minute intervals for the next 30 days, based on forecasts of energy consumption and PV power production. The AR-EMS consists of two distinct layers: the Long-Term Optimization Layer (LTOL) and the Short-Term Optimization Layer (STOL). The LTOL focuses on optimizing active and reactive power flow over an extended time horizon of 30 days, relying on forecasted data. In contrast, the STOL involves short-term forecasting and energy optimization over the next 24-hour horizon, addressing the LTOL forecasting uncertainties. The proposed strategy emphasizes a multi-objective problem aiming at minimizing both active and reactive energy bill, ESS degradation cost, Peak-to-Average Ratio (PAR) and carbon emissions. The considered problem is solved using a metaheuristic algorithm, specifically the Lexicographic approach within the Particle Swarm Optimization (PSO) method. To validate the effectiveness of the proposed approach, two comparative analyses are conducted. The first involves the impact of time horizons on the energy cost and the management performances within the Moroccan context. The second comparison, highlights the benefits and shortfalls of using simultaneous active and reactive power management, comparing it with a system exclusively managing active power (A-EMS). Both compared strategies are evaluated using the Moroccan tariff RTS and real world data. The comparative analysis highlights the advantages of the proposed AR-EMS, demonstrating benefits in terms of active and reactive energy bill reduction by 58.9% and 83.2%, respectively, and showcases a 49.3% reduction in carbon emissions while improving the EPG power factor by 6% compared to A-EMS, In conclusion, the optimization results are encouraging the Moroccan government to further develop the installation of SMGs.

Two-stage differential evolution with dynamic population assignment for constrained multi-objective optimization

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction.

Generalized Performance of LSTM in Time-Series Forecasting

ABSTRACT Optimizing the time-series forecasting performance is a multi-objective problem which enables the comparison of general applicability of methods across multiple use cases such as finance and demographics. Libra, a time-series forecasting framework which shifts the problem of optimization from minimizing single to multiple evaluation measures and use cases, is used as a benchmark to evaluate the performance of the Long Short-Term Memory (LSTM) neural network. LSTMs with parameter tuning have been shown to perform well with time-series forecasting. This paper applies LSTMs (mostly with standard parameters and variations of some of them) to the Libra framework and concludes that due to data characteristic variance and without increased hardware and time constraints LSTMs do not outperform the median measures of Libra.

Automatic grouping of wind turbine types via multi-objective formulation for nonuniform wind farm layout optimization using an analytical wake model

This study introduces a novel methodology that aims to minimize the number of different wind turbine types used in nonuniform wind farms. This approach involves a trade-off to tackle the logistical challenges associated with installing, operating, and maintaining such wind farms. To accomplish this, a Gaussian analytical wake model is used in conjunction with evolutionary algorithms (NSGA-II and SMS-EMOA) for multi-objective optimization. A multi-objective problem is formulated, regarding wind farm capacity factor (CF) and levelized cost of energy (LCOE), and addressed using two distinct approaches. In the first approach, proposed here, the number of different wind turbine types is limited and treated as an additional objective. In contrast, the second approach allows for flexibility in choosing any number of different turbine types. Comparing the results obtained, it was observed that the methodology presented here yielded a reduced number of different turbine types without compromising CF and LCOE objectives. A multi-criteria decision maker was applied to extract the final non-dominated solutions from the obtained Pareto set. Finally, economic indicators show the profitability of these solutions.

Multi-objective optimization of bias current coefficient based on NSGA- III for active magnetic bearing with redundant electromagnetic actuators

PurposeThe multi-objective optimization configuration strategy is proposed due to the configuration of EMAs in fault-tolerant control of active magnetic bearing with redundant electromagnetic actuators involving high-dimensional, nonlinear, conflicting goals.Design/methodology/approachA multi-objective optimization model for bias current coefficients is established based on the nonlinear model of active magnetic bearings with redundant electromagnetic actuators. Based on the non-dominated sorting genetic algorithm III, a numerical method is used to obtain feasible and non-inferior sets for the bias current coefficient.Findings(1) The conflicting relationship among the three optimization objectives was analyzed for various failure modes of EAMs. (2) For different EMAs' failure modes, the multi-objective optimization configuration strategy can simultaneously achieve the optimal or sub-optimal effective EMF, flux margins, and stability of EMF. Moreover, the characteristics of the optimal Pareto front are consistent with the physical properties of the AMB. (3) Compared with the feasible configuration of C0, the non-inferior configurations can significantly improve the performance of AMB, and the advantages of the multi-objective optimization configuration strategy become more prominent as the asymmetry of the residual supporting structure intensifies.Originality/valuei) Considering the variation of the rotor displacement during the support reconstruction, a decision-making model that can accurately characterize the dynamic performance of AMB is presented. (ii) The interaction law between AMB and rotor under different failure modes of EMAs is analyzed, and the configuration principles for redundant EMAs are proposed. (iii) Based on the dynamic characteristics of AMB during the support reconstruction, effective EMF, energy consumption, and the Pearson correlation coefficient between the desired EMFs and the decoupled control currents are used as objective functions. iv. The NSGA-III is combined with the decision-making model to address the multi-objective optimization configuration problem of C0.

Multi-objective models for crop rotation planning problems

CONTEXTAgriculture is a vital component of the global economy and modern societies. It has undergone significant consolidation and transformation in response to the food supply crisis, highlighting the important relationship between humans and the environment. However, concerns remain about food security, particularly with the projected population growth of over 9.5 billion by 2050. The computerization of agri-food supply chains has emerged as a significant response to these challenges. OBJECTIVE(1) Develop a multi-objective model that explores both net return and crop diversity. (2) Solve the problem using techniques that guarantee optimality. (3) Evaluate the gain in crop diversity versus the net return of the optimized configuration. METHODSThe study presents four Multi-objective Mixed-Integer Linear Programming models with integer and binary decision variables for Crop Rotation Planning Problems. The objectives are to maximize net income and increase crop diversity and land utilization. RESULTS AND CONCLUSIONSThe study exclusively employs linear programming techniques to solve the models resulting in an optimal solution. A comparative analysis with existing models in the literature, which primarily focused on maximizing net income, yielded a noteworthy result. The proposed models demonstrate an average increase of 60% in crop diversity, with net return losses of less than 5%. SIGNIFICANCEIn conclusion, this research provides valuable information for crop rotation planning and highlights the importance of agricultural farm management and precision agriculture in addressing current challenges. The innovative nature of this research is exemplified by the use of mixed-integer linear programming techniques to solve a multi-objective problem with integer and binary variables. The obtained results demonstrate increased crop diversity and minimal economic losses, which have significant implications for several areas of agricultural science, policy, and practice.

A novel memory-based artificial gorilla troops optimizer for installing biomass distributed generators in unbalanced radial networks

Optimizing unbalanced distribution networks through the strategic integration of distributed generators (DGs) has long been recognized as a significant challenge. Selecting the optimal sizes and locations for these generators is crucial for minimizing network power loss and enhancing voltage profiles. The previously published methods have been plagued by issues such as slow convergence rates, entrapment in local optima, complexity, and extensive computational requirements. Addressing these limitations, this paper introduces an efficient methodology: the Memory-based Artificial Gorilla Troops Optimizer (MGTO). This approach leverages memory-based mechanisms to enhance exploration and decision-making, facilitating the seamless integration of various biomass DGs (BDGs) into unbalanced IEEE 37-bus radial networks. The immigration of gorillas during the exploration phase is enriched through the utilization of stored memories of candidate trajectories within the search space, enabling the silverback to make informed decisions. Furthermore, a multi-objective variant of MGTO is developed in collaboration with Fuzzy Decision-Making (FDM), allowing for the simultaneous optimization of multiple targets. To demonstrate the MGTO effectiveness, it is rigorously compared against a comprehensive set of established optimization algorithms, including the Honey Badger Algorithm (HBA), Runge Kutta Optimizer (RUN), and others. The results proved the dominance of the proposed MGTO by getting minimum power loss and voltage fluctuation of 0.364 % and 15.4 %, respectively, while in the multi-objective problem, the best results are 0.513 % loss and 17.9% voltage fluctuation. The results proved the consistency of the proposed MGTO in installing different BDGs into an unbalanced distribution network.

Multi-objective energy management in a renewable and EV-integrated microgrid using an iterative map-based self-adaptive crystal structure algorithm

The use of plug-in hybrid electric vehicles (PHEVs) provides a way to address energy and environmental issues. Integrating a large number of PHEVs with advanced control and storage capabilities can enhance the flexibility of the distribution grid. This study proposes an innovative energy management strategy (EMS) using an Iterative map-based self-adaptive crystal structure algorithm (SaCryStAl) specifically designed for microgrids with renewable energy sources (RESs) and PHEVs. The goal is to optimize multi-objective scheduling for a microgrid with wind turbines, micro-turbines, fuel cells, solar photovoltaic systems, and batteries to balance power and store excess energy. The aim is to minimize microgrid operating costs while considering environmental impacts. The optimization problem is framed as a multi-objective problem with nonlinear constraints, using fuzzy logic to aid decision-making. In the first scenario, the microgrid is optimized with all RESs installed within predetermined boundaries, in addition to grid connection. In the second scenario, the microgrid operates with a wind turbine at rated power. The third case study involves integrating plug-in hybrid electric vehicles (PHEVs) into the microgrid in three charging modes: coordinated, smart, and uncoordinated, utilizing standard and rated RES power. The SaCryStAl algorithm showed superior performance in operation cost, emissions, and execution time compared to traditional CryStAl and other recent optimization methods. The proposed SaCryStAl algorithm achieved optimal solutions in the first scenario for cost and emissions at 177.29 €ct and 469.92 kg, respectively, within a reasonable time frame. In the second scenario, it yielded optimal cost and emissions values of 112.02 €ct and 196.15 kg, respectively. Lastly, in the third scenario, the SaCryStAl algorithm achieves optimal cost values of 319.9301 €ct, 160.9827 €ct and 128.2815 €ct for uncoordinated charging, coordinated charging and smart charging modes respectively. Optimization results reveal that the proposed SaCryStAl outperformed other evolutionary optimization algorithms, such as differential evolution, CryStAl, Grey Wolf Optimizer, particle swarm optimization, and genetic algorithm, as confirmed through test cases.

A coevolutionary algorithm using Self-organizing map approach for multimodal multi-objective optimization

Multimodal Multi-Objective Problems (MMOPs) are frequently encountered in the real world. Traditional Multimodal Multi-Objective Evolutionary Algorithms (MMEAs) often find multiple Pareto optimal solutions with the same objective values. However, in real-world problems, there often exist multiple global optimal solutions and local optimal solutions at the same time. Ensuring that these solution sets are obtained simultaneously is the concern of most current researchers. To address this issue, this paper proposes a novel multimodal multi-objective evolutionary algorithm named CoSOMEA. In the CoSOMEA, a Self-organizing map (SOM) neural network is used to extract the information of decision space to ensure better exploration of the global optima and exploitation of the local optima. Meanwhile, coevolutionary mechanism are used to ensure a balance between the exploration and exploitation in order to avoid the algorithm falling into local areas. The three test suites named IDMP, IDMP_ee and MMF are adopted to verify the effectiveness of proposed algorithm. Experimental results demonstrate that the CoSOMEA exhibits competitive performance in solving MMOPs compared to other state-of-the-art MMEAs.

A Pareto-optimality based black widow spider algorithm for energy efficient flexible job shop scheduling problem considering new job insertion

The utilization of flexible job shops is on the rise, driven by the decreasing life cycle of consumer products. In dynamic flexible job shops, the occurrence of disruptive events like machine breakdown, tool wear, and new job arrivals is common, emphasizing the critical need for efficient scheduling to achieve productivity and cost-effectiveness. Additionally with the growing concerns about energy consumption and global warming, the imperative to contemplate workshops with lower energy usage is becoming increasingly significant. Therefore, in this study a multi-objective dynamic flexible job shop scheduling problem (MODFJSP) with insertion of new jobs for optimization objectives: makespan, total energy consumption and schedule instability is addressed. A novel multi-objective black widow spider algorithm (MOBWSA), inspired by the mating behavior of black widow spiders, is proposed. The MOBWSA ensures an optimal balance between minimizing makespan and energy consumption through its superior evolutionary processes of procreation, mutation and cannibalism. Furthermore, a strategic on/off strategy is implemented to enhance energy efficiency. The disruptions in schedule at rescheduling stage are addressed through the proposed sigmoidal weighted instability function. To handle the multi-objective nature of the problem this work incorporates Pareto-optimality approach in combination with novel hybrid crowding distance metric. The optimization is further aided by exploitation of search space through an ensemble of local search operators. Testing and evaluation of the MOBWSA with 30 benchmark problems is conducted, and its performance for multiple metrics is compared with recently published state-of-the-art algorithms. The results establish the effectiveness and efficiency of the proposed algorithm.

Adaptive projection plane and reference point strategy for multi-objective particle swarm optimization

Achieving a balance between convergence and diversity and their mutual enhancement is a complex task in the process of algorithm improvement. This is crucial because it is directly related to the effectiveness of the algorithm in obtaining accurate and uniformly distributed Pareto frontiers. Although significant progress has been made in particle swarm algorithms, exploring new approaches is necessary. In this paper, we construct a projection plane (projection line in 2D) based on the extreme values of the non-dominated solutions, select a set of uniform reference points on the projection plane, and then project the non-dominated solutions onto the constructed projection plane to form projection points. The reference points and projection points on the projection plane are thus utilized to guide the updating of the population as well as the maintenance of the external archive, a strategy that enhances the algorithm's global exploration and local exploitation capabilities. Secondly, we aggregate the target values of particles into a single scalar value and combine the idea of particle fusion to design a scheme for the particle selection of individual optimal particles. This paper further improves the algorithm's overall performance by using the information between populations to select individual optimal particles. Lastly, it is evaluated against a number of multi-objective algorithms that are currently in use and perform well on 22 test problems. The findings demonstrate that the algorithm this paper proposes performs better when solving multi-objective problems.