Non-dominated Solutions Research Articles

Multi-objective comprehensive container scheduling and resource allocation for container cloud using tuna swarm optimization algorithm

The paper addresses the optimization challenges in cloud resource task execution within the container paradigm, introducing the Multi-Objective Comprehensive Container Scheduling and Resource Allocation (MOCCSRA) scheme. It aims to enhance cost-effectiveness and efficiency by utilizing the Tuna Swarm Optimization (TSO) technique to optimize task planning and resource allocation. This novel approach considers various objectives for task scheduling optimization, including energy efficiency, compliance with service level agreements (SLAs), and quality of service (QoS) metrics like CPU utilization, memory usage, data transmission time, container-VM correlation, and container grouping. Resource allocation decisions are guided by the VM cost and task completion period factors. MOCCSRA distinguishes itself by tackling the multi-objective optimization challenge for task scheduling and resource allocation, producing non-dominated Pareto-optimal solutions. It effectively identifies optimal tasks and matches them with the most suitable VMs for deploying containers, thereby streamlining the overall task execution process. Through comprehensive simulations, the results demonstrate MOCCSRA’s superiority over traditional container scheduling methods, showcasing reductions in resource imbalance and notable enhancements in response times. This research introduces an innovative and practical solution that notably advances the optimization field for cloud-based container systems, meeting the increasing demand for efficient resource utilization and enhanced performance in cloud computing environments.

Multi-Objective Particle Swarm Optimization Algorithm based on Position Vector Offset

In response to the issue that particle swarm optimization algorithms tend to fall into local optima when dealing with multi-objective optimization tasks, a multi-objective optimization algorithm based on particle swarm is proposed. This algorithm is based on the relationship between the position vectors of particles, changing the selection and movement strategies of particles to find the true Pareto front. Firstly, two additional position vectors are added around the iterating particles to enhance their search capability; then, a non-dominated vector archive is established to record the non-dominated solutions of the iterating particles and the additional position vectors, increasing particle diversity. Finally, additional position vectors with high fitness are selected to produce a shift in the iterating particle's position, accelerating particle convergence. Comparing this algorithm with dMOPSO, SMPSO, NMPSO, and MOPSOCD algorithms, simulation experiments show that the proposed PVSPSO algorithm has stronger optimization ability.

Supporting tactical harvest planning decisions of major fruits through a multi-objective modeling approach by using exact methods

An important stage of the agri-food supply chain is production (agricultural practices and harvesting), where relevant decisions are made in a short period of intensive activity. Regarding the major fruit supply chain, the complexity of these decisions increases because most fruit export companies manage several orchards with different fruit species and varieties. Moreover, the amount of labor and resources must be estimated at least two months in advance of the harvest so that they can be relied upon during the harvest season. In this study, a multi-objective modeling approach for supporting tactical harvest planning decisions of major fruits is developed, aiming to evidence its adequacy and to identify different harvest plans according to the prioritized objectives. Therefore, a multi-objective linear programming (MOLP) model, which considers three conflicting objectives, is proposed. The three objectives correspond to minimizing harvest costs, fruit loss and harvest days. For solving the MOLP model, five a posteriori multi-objective exact methods are compared using a synthetic instance based on a real case. The Pareto frontiers obtained by these methods are analyzed using three metrics related to accuracy, cardinality, and diversity criteria, so that the most suitable method can be selected. Thus, the selected method is applied to an actual case study of a Chilean fruit export company. In addition, the ε-constraint method is used in this case study to compare the obtention of non-dominated solutions in the convex and non-convex regions of the Pareto frontier. The results show that harvest plans vary significantly according to the prioritization of the objective functions. Thus, the percentage difference between each objective function’s worst and best values is around 497% when the harvest costs are minimized, around 1,448% when the fruit loss is minimized, and around 18% when the number of harvest days is minimized. In addition, the adequacy of the multi-objective approach rather than the mono-objective approach to support tactical harvest planning decisions is demonstrated. Furthermore, a scenario analysis for considering changes in the harvest periods is carried out by considering three possible scenarios. This analysis is required because these periods can change every year due to different factors, such as weather conditions and agricultural practices, among others. The results show that the harvest costs and fruit loss increase, on average, 87% and 100%, respectively, when the harvest period is short, that is, one day. Finally, managerial insights about the information obtained by the MOLP model are discussed.

Bi-Level Inverse Robust Optimization Dispatch of Wind Power and Pumped Storage Hydropower Complementary Systems

This paper presents a bi-level inverse robust economic dispatch optimization model consisting of wind turbines and pumped storage hydropower (PSH). The inner level model aims to minimize the total generation cost, while the outer level introduces the optimal inverse robust index (OIRI) for wind power output based on the ideal perturbation constraints of the objective function. The OIRI represents the maximum distance by which decision variables in the non-dominated frontier can be perturbed. Compared to traditional methods for quantifying the worst-case sensitivity region using polygons and ellipses, the OIRI can more accurately quantify parameter uncertainty. We integrate the grid multi-objective bacterial colony chemotaxis algorithm and the bisection method to solve the proposed model. The former is adopted to solve the inner level problem, while the latter is used to calculate the OIRI. The proposed approach establishes the relationship between the maximum forecast deviation and the minimum generation cost associated with each non-dominated solution in the optimal load allocation. To demonstrate its economic viability and effectiveness, we simulate the proposed approach using real power system operation data and conduct a comparative analysis.

Growing Neural Gas Network-based surrogate-assisted Pareto set learning for multimodal multi-objective optimization

The key issue in handling multimodal multi-objective optimization problems (MMOPs) is to find multiple Pareto sets (PSs) corresponding to one Pareto front (PF). Therefore, learning the PSs is critical to facilitate solving MMOPs while unfortunately, current research only focuses on PF learning which is helpless in finding multiple PSs by the information of one PF. Moreover, since the PSs of an MMOP are usually non-functional, traditional approximative function model-based PF learning is inapplicable. Consequently, developing new PS learning techniques is desired. Inspired by data-driven evolutionary algorithms, data can be used to train surrogate models to assist the algorithm. This article proposes an online data-driven PSs learning technique that aims to learn the topologies of PSs through a surrogate model to facilitate the search for PSs. Specifically, the Growing Neural Gas network is trained using non-dominated solutions to learn the topologies of PSs during the evolutionary process. Then, the nodes of the network are used to generate new solutions and adopted as reference points for environmental selection. A new algorithm is developed based on the PS learning technique for MMOPs. Experimental studies on three benchmark test suites and two different real-world applications demonstrate the superiority of our method over six state-of-the-art algorithms dedicated to MMOPs. The PSs learning technique can obtain the topologies of PSs and facilitate the search for them.

Using multiobjective optimization to reconstruct interferometric data

Context. In very long baseline interferometry (VLBI), signals recorded at multiple antennas are combined to form a sparsely sampled virtual aperture with an effective diameter set by the largest separation between the antennas. Due to the sparsity of the sampled aperture, VLBI imaging constitutes an ill-posed inverse problem. Various algorithms have been employed to deal with the VLBI imaging, including the recently proposed multiobjective evolutionary algorithm by decomposition (MOEA/D) described in the first paper of this series. Aims. Among the approaches to the reconstruction of the image features in total intensity from sparsely sampled visibilities, extensions to the polarimetric and the temporal domain are of great interest for the VLBI community in general and the Event Horizon Telescope Collabroration (EHTC) in particular. Based on the success of MOEA/D in presenting an alternative claim of the image structure in a unique, fast, and largely unsupervised way, we study the extension of MOEA/D to polarimetric and time dynamic reconstructions in this paper. Methods. To this end, we utilized the multiobjective, evolutionary framework introduced for MOEA/D, but added the various penalty terms specific to total intensity imaging time-variable and polarimetric variants, respectively. We computed the Pareto front (the sample of all non-dominated solutions) and identified clusters of close proximities. Results. We tested MOEA/D with synthetic data sets that are representative for the main science targets and instrumental configuration of the EHTC and its possible successors. We successfully recovered the polarimetric and time-dynamic signature of the ground truth movie (even with relative sparsity) and a set of realistic data corruptions. Conclusions. MOEA/D has been successfully extended to polarimetric and time-dynamic reconstructions and, specifically, in a setting that would be expected for the EHTC. It offers a unique alternative and independent claim to the already existing methods, along with a number of additional benefits, namely: it is the first method that effectively explores the problem globally and compared to regularized maximum likelihood (RML) methods. Thus, it waives the need for parameter surveys. Hence, MOEA/D is a novel, useful tool to characterize the polarimetric and dynamic signatures in a VLBI data set robustly with a minimal set of user-based choices. In a consecutive work, we will address the last remaining limitation for MOEA/D (the number of pixels and numerical performance), so that MOEA/D can firmly solidify its place within the VLBI data reduction pipeline.

Multi-objective optimization for impeller structure parameters of fuel cell air compressor using linear-based boosting model and reference vector guided evolutionary algorithm

As a pivotal part of cathode air supply system, centrifugal air compressors play a central position in ensuring efficient operations of onboard fuel cells. To improve the overall performance of compressors, comprehensive performance tests were conducted and an integrated simulation model was developed by using computational fluid dynamics (CFD) methods. On this basis, the prediction performance of Linear-based Boosting models was investigated, and multi-objective optimization of impeller structural parameters was carried out through the Reference Vector Guided Evolutionary Algorithm (RVEA). Simulation results indicate that the impeller of the original compressor exhibits significant entropy increase, insufficient gas compression and serious energy dissipation, highlighting considerable room for design optimization. The eXtreme Gradient Boosting (XGBoost) model with 29 estimators has superior generalization ability and prediction performance, making it the preferred Boosting model for the compressor. Multi-objective optimizations have strong universality and rationality, resulting in a well-distributed and diversified final non-dominated solution set. The isentropic efficiency and pressure ratio of the Max_σ solution are improved by 18.7% and 70.1%, while those of the Max_ηc solution are enhanced by 23.0% and 48.9%, respectively. After optimization, the gas experiences reduced shock loss, diminished entropy increase and enhanced flow stability. These findings can provide data support, theoretical basis and directional guidance for performance improvement of centrifugal air compressors.

Multi-objective optimization of reactive power dispatch problem using fuzzy tuned mayfly algorithm

The recent multi-objective optimization problems are very complex which require an effective and robust evolutionary method for obtaining a global Pareto-optimal solutions. Most of these multi-objective evolutionary techniques are population-based methods which usually work on random search approaches and often trapped into local minima during their execution. A new fuzzy tuned mayfly algorithm (FTMA) is presented in this paper, to obtain the Pareto-optimal solutions for any complex multi-objective power system problem. It has a self-adapting global exploration capability to get the best Pareto-optimal solutions by varying two crucial parameters i.e., crossover (Pc) and mutation Pm probabilities. Moreover, a model of Pareto-dominance is employed to rank non-dominating solutions to maintain the diversity within the populations. The proposed evolutionary approach is examined on a standard ZDT benchmark test suite and its algorithmic performance is statistically compared with a few of the recent optimization techniques such as NSGA-II, NSGA-III, MMODE, MOAVOA and MMA algorithm. It is further applied to minimize two distinct objective functions (i.e., total transmission loss and voltage stability index) for IEEE-118 bus system and IEEE-24 bus RTS. A comprehensive statistical analysis is presented for the obtained numerical results, which proves that proposed FTMA has better convergence with better solution diversity in comparison to the other competing algorithms. A comprehensive analysis based on statistical results reveal that the proposed FTMA is superior for obtaining better non-dominating pareto-fronts as compared to other competing methods.

A Decentralized Optimization Algorithm for Multi-Agent Job Shop Scheduling with Private Information

The optimization of job shop scheduling is pivotal for improving overall production efficiency within a workshop. In demand-driven personalized production modes, achieving a balance between workshop resources and the diverse demands of customers presents a challenge in scheduling. Additionally, considering the self-interested behaviors of agents, this study focuses on tackling the problem of multi-agent job shop scheduling with private information. Multiple consumer agents and one job shop agent are considered, all of which are self-interested and have private information. To address this problem, a two-stage decentralized algorithm rooted in the genetic algorithm is developed to achieve a consensus schedule. The algorithm allows agents to evolve independently and concurrently, aiming to satisfy individual requirements. To prevent becoming trapped in a local optimum, the search space is broadened through crossover between agents and agent-based block insertion. Non-dominated sorting and grey relational analysis are applied to generate the final solution with high social welfare. The proposed algorithm is compared using a centralized approach and two state-of-the-art decentralized approaches in computational experiments involving 734 problem instances. The results validate that the proposed algorithm generates non-dominated solutions with strong convergence and uniformity. Moreover, the final solution produced by the developed algorithm outperforms those of the decentralized approaches. These advantages are more pronounced in larger-scale problem instances with more agents.

An integrated model of supply chain resilience considering supply and demand uncertainties

AbstractThe complexity of the global supply chain has increased dramatically over the past few decades as a result of uncertainty caused by various factors. This paper studies the optimal strategy for supply chain resilience models considering supply disruptions and demand fluctuations. We present two‐stage stochastic programming models based on different scenarios, including a risk‐neutral model that considers the expected total cost, a risk‐averse model that considers the conditional value‐at‐risk measure, and a responsiveness model that considers the service level. We also propose multiobjective mathematical programming that considers all three models simultaneously and suggests the solution approach. Finally, we present the results of computational experiments and demonstrate how to cope with uncertainty through flexibility and redundancy. We offer a set of nondominated solutions from the multiobjective model and derive managerial insights, which suggest a decision‐making strategy between the disruption risk, expected total cost, and service level.

MOFS-REPLS: A large-scale multi-objective feature selection algorithm based on real-valued encoding and preference leadership strategy

Multi-objective feature selection (MOFS) has emerged as a crucial step in constructing efficient machine-learning models. While multi-objective evolutionary algorithms often yield satisfactory sub-optimal solutions, enhancing these algorithms' global optimization capacity remains a central challenge in the field of engineering optimization. To improve the quality of solutions to problems, there is an imperative need for an algorithm with superior optimization capability. This study introduces a large-scale MOFS algorithm based on real-valued encoding and a preference leadership strategy, named MOFS-REPLS, which aims to address the challenge of large-scale sparse feature selection (FS). First, we propose a novel encoding scheme to facilitate broader population exploration. During the population initialization phase, we integrate a ReliefF-guided approach with roulette wheel selection to create the initial population. Second, we introduce a preference leadership strategy that directs individuals toward their respective areas in the Pareto front. Finally, we devise an adaptive learning strategy incorporating ReliefF-guided methods to steer the evolution of the population, thereby mitigating performance deficiencies due to the algorithm's lack of prior knowledge. MOFS-REPLS employs a dual-archive mechanism to maintain diversity within the algorithm and to preserve non-dominated solutions for further exploration. Through experimental assessment using 20 UCI datasets and 10 state-of-the-art algorithms, we demonstrate the effectiveness of MOFS-REPLS. The results show that our proposed algorithm not only maintains high accuracy but also selects a smaller, more relevant set of features, significantly outperforming other FS algorithms in comparison.

Multi-Criteria Decision under Uncertainty as Applied to Resource Allocation and Its Computing Implementation

This research addresses the problem of multi-objective resource allocation or resource deficits, offering robust answers to planning decisions that involve the elementary question: “How is it done?”. The solution to the problem is realized using the general scheme of multi-criteria decision-making in uncertain conditions. The bases of the proposed scheme are associated with the possibilistic approach, which involves the generalization of fuzzy sets from the classical approach to process the uncertainty of information to produce robust (non-dominated) solutions in multi-criteria analysis. Applying this general scheme makes it possible to reduce regions of decision uncertainty through the maximum use of available quantitative information. In the case where quantitative information analysis is insufficient to obtain a unique solution, the proposed approach presupposes the appropriation of qualitative data extracted from experts, who express their opinions considering their knowledge, experience, and intuition. The information on the qualitative character can be represented in diverse preference formats processed by transformation functions to provide homogeneous information for decision procedures used at the final decision stage. The presented results have been implemented within the system of multi-criteria decision-making under uncertain conditions described in the paper. Its functioning is illustrated by solving the typical problem in investment planning activities.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

A many-objective evolutionary algorithm based on learning assessment and mapping guidance of historical superior information

Abstract Multi-objective optimization algorithms have shown effectiveness on problems with two or three objectives. As the number of objectives increases, the proportion of non-dominated solutions increases rapidly, resulting in insufficient selection pressure. Nevertheless, insufficient selection pressure usually leads to the loss of convergence, too intense selection pressure often results in a lack of diversity. Hence, balancing the convergence and diversity remains a challenging problem in many-objective optimization problems. To remedy this issue, a many-objective evolutionary algorithm based on learning assessment and mapping guidance of historical superior information, referred to here as MaOEA-LAMG, is presented. In the proposed algorithm, an effective learning assessment strategy according to historical superior information based on an elite archive updated by indicator ${I}_{\varepsilon + }$ is proposed, which can estimate the shape of the Pareto front and lay the foundation for subsequent fitness and acute angle-based similarity calculations. From this foundation, to balance the convergence and diversity dynamically, a mapping guidance strategy based on the historical superior information is designed, which contains clustering, associating, and proportional selection. The performance of the proposed algorithm is validated and compared with ten state-of-the-art algorithms on 24 test instances with various Pareto fronts and real-world water resource planning problem. The empirical studies substantiate the efficacy of the results with competitive performance.

A Lagrangian bounding and heuristic principle for bi-objective discrete optimization

Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems with complicating side constraints. Its aim is often twofold; first, it provides bounds for the optimal value, and, second, it can be used to heuristically find near-optimal feasible solutions, the quality of which can be assessed by the bounds. We consider bi-objective discrete optimization problems with complicating side constraints and extend this Lagrangian bounding and heuristic principle to such problems. The Lagrangian heuristic here produces non-dominated candidates for points on the Pareto frontier, while the bounding forms a polyhedral outer approximation of the Pareto frontier, which can be used to assess the quality of the candidate points. As an illustration example we consider a facility location problem in which both CO2 emission and cost should be minimized. The computational results are very encouraging, both with respect to bounding and the heuristically found non-dominated solutions. In particular, the Lagrangian bounding is much stronger than the outer approximation given by the Pareto frontier of the problem’s linear programming relaxation.

Constrained multi-objective trans-media maneuver trajectory optimization for morphing unmanned aerial-underwater vehicles

In this study, the challenge of optimizing trans-media maneuver trajectories is addressed through the introduction of a Constrained Multi-Objective Grey Wolf Optimizer (CMOGWO). The objective function has been refined to assess solutions more accurately based on their feasibility and adherence to constraints. Three distinct Archives have been employed for categorizing and optimizing dominant, non-dominant, and feasible non-dominant solutions, each benefiting from specifically tailored optimization strategies. A hybrid search method, complemented by a watch-based strategy, is proposed for effectively guiding the population towards the Pareto front, ensuring the discovery of potential optimal solutions. Investigations have been conducted into the impact of initial altitude on trajectory optimization, with comparative simulations revealing the effectiveness of the proposed CMOGWO in managing unmanned aerial-underwater vehicle trajectories. The results demonstrate the potential of the CMOGWO in enhancing the reliability and feasibility of trajectory optimization in complex environmental conditions.

An improved NSGA‐II for the dynamic economic emission dispatch with the charging/discharging of plug‐in electric vehicles and home‐distributed photovoltaic generation

AbstractThis paper investigates four energy utilization scenarios with or without home‐distributed photovoltaic generation (HDPG) to reduce the generation cost and pollutant emission of the dynamic economic emission dispatch with the charging/discharging of plug‐in electric vehicles (DEED‐PEV). The first scenario considers valley filling for the charging of PEVs. The second scenario combines valley filling and peak shaving for the charging and discharging of PEVs. The third scenario adds peak shaving of HDPG to the first scenario, followed by the peak shaving with the discharging of PEVs. The fourth scenario rearranges the distribution of photovoltaic (PV) power for the third scenario, and the PV power in the afternoon is stored by a photovoltaic energy storage system (PESS) and consumed in the evening. A universal procedure is designed for the valley filling and peak shaving of the four scenarios, which is beneficial for determining the filled and shaved loads with respect to certain time intervals. An NSGA‐II method based on a modified crossover and an elimination of individuals (NSGA‐II‐MCEI) is proposed for the multiobjective optimization of DEED‐PEV. The modified crossover can improve the convergence of NSGA‐II‐MCEI, and the elimination operator can maintain the evenness of the nondominated solutions. According to experimental results, scenario 4 achieves cost savings of 95386.62 $, 85636.87 $, and 6776.85 $, respectively, for Scenarios 1, 2, and 3, and it reaches emission reductions of 27617.64 kg, 17252.71 kg, and 220.98 kg, respectively, for scenarios 1, 2, and 3. Also, scenario 4 outperforms the other three scenarios for three weather conditions such as sunny day, cloudy day, and rainy day.

A novel technique for multi-objective sustainable decisions for pavement maintenance and rehabilitation

To maintain pavement in good condition while considering financial costs and sustainability, it is necessary to develop a comprehensive pavement management plan. Pavement Maintenance and Rehabilitation (M&R) consists of two essential components: firstly, predicting the pavement condition within a specified timeframe, and secondly, employing an appropriate optimization algorithm. This study utilized three ensemble learning techniques including extreme gradient boosting, categorical boosting, and light gradient boosting machine to develop accurate predictions about the pavement condition. Subsequently, the most accurate prediction technique, which was extreme gradient boosting, was combined with non-dominated sorting genetic algorithm III which is a multi-objective metaheuristic optimization algorithm, resulting in a hybrid technique that offers highly accurate multi-objective maintenance and rehabilitation planning. Although previous studies neglected important criteria such as road closure in the optimization process, this study takes into account four objective functions including greenhouse gas emission, M&R cost, pavement condition, and road closure to be minimized over a 5-year program. This process generated 52 non-dominated optimal solutions known as the Pareto front. To compare and rank various optimal maintenance and rehabilitation plans, grey relational analysis was employed. The results suggested that there is a direct correlation between M&R costs and GHG emissions. Minimizing only pavement conditions in the planning can significantly increase GHG emissions, M&R costs, and road closure. Implementing preventive M&R actions can reduce M&R costs and overall road closure while light and medium rehabilitation actions are recommended to optimize the condition of pavements.

Multi-objective optimization model for railway heavy-haul traffic: Addressing carbon emissions reduction and transport efficiency improvement

This paper establishes a multi-objective optimization model for railway heavy-haul trains, focusing on reducing carbon emissions and improving transport efficiency. The model integrates optimization of the route and the vehicle load rate, significantly reducing carbon emissions and enhancing transport efficiency. It addresses the challenges and characteristics of heavy-haul trains, introducing multi-objective optimization problems related to transport carbon emissions and efficiency. Using a pigeon-inspired optimization algorithm, the model considers joint constraints between carbon emissions and transport efficiency objectives. To overcome challenges in multi-objective transportation problems, the paper proposes a forward-learning pigeon-inspired optimization algorithm based on a surrogate-assisted model. This approach calculates the quality of the candidate solution using a surrogate model, reducing time costs. The algorithm employs a forward-learning strategy to enhance learning from non-dominant solutions. Experimental validation with benchmark functions confirms the effectiveness of the model and offers optimized solutions. The proposed method reduces carbon emissions while maintaining transport efficiency, contributing innovative ideas for the development of sustainable heavy-duty trains.

A time-varying competitive swarm optimizer for integrated flight recovery with multi-objective and priority considerations

Integrating aircraft and crew recovery is a growing topic in providing an efficient recovery system after a disruption. Most existing models only conduct from airline perspective and treat all disturbed flights homogeneously. However, in a realistic operation, the decision objectives are multiple with the interplay of stakeholders. Moreover, flights with first-aid items hold special priority. Thus, this paper presents a new Integrated Aircraft and Crew Recovery with Multi-objective and Priority, namely IACR_MP. To solve IACR_MP efficiently, an ad-hoc particle swarm optimization-based optimizer is designed. Time-varying tri-competition with different evolutionary mechanisms is developed to achieve a balance between exploitation and exploration capacities. Three repair schemes are built to prevent low feasibility caused by high constraints, and a self-exploration strategy is used to detect the potential zones of contemporary non-dominated solutions. Finally, six instances with different scales are used for algorithm performance analyses. Results illustrate that our algorithm has good solution quality and significantly outperforms its competitors in solving the IACR_MP. Moreover, our framework can provide a series of specific recovery schemes, providing decision support with more choices to airline managers.