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Liquified Petroleum Gas (LPG) is an oil refinery product that must adhere to quality specifications with respect to certain impurities. Refineries apply an LPG purification process that consists of a flow network with several process units (PUs). Current methods focus on optimising the performance of each PU separately; there exists no known approach for identifying the whole process optimum. In this paper, we present an approach for optimising the LPG purification process as a whole. We utilise operational scenarios to model the non-linear transformations of each PU. These scenarios enable us to devise a Mixed Integer Linear Program (MILP) that minimises energy consumption. The obtained solution is an approximation of the optimum but offers actionable support to refinery engineers. To enable the applicability of our approach at large scale, we propose two filters based on Pareto dominance and Data Envelopment Analysis (DEA) to identify the Pareto optimal and the Best Practice set of scenarios, respectively. By filtering out the rest, we reduce the solution space of the corresponding MILP. Further, we provide computational evidence that the application of these filters vastly improves solution time and enables applicability under real production conditions. [ABSTRACT FROM AUTHOR]

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In this paper, we extend the Dai-Liao conjugate gradient method to vector optimization. Firstly, we analyze the global convergence of the direct extension version of the Dai-Liao conjugate gradient method for K-strongly convex vector functions. Secondly, we investigate the global convergence of the vector version of restricted non-negative Dai-Liao conjugate gradient method for general vector functions. Additionally, we discuss the global convergence of the vector version of modified Dai-Liao conjugate gradient method for general vector functions. Finally, numerical experiments demonstrate that the proposed conjugate gradient methods are effective for solving vector optimization problems. In particular, these methods can effectively generate the Pareto frontiers for the test problems. [ABSTRACT FROM AUTHOR]

The minimum connected dominating set problem is a well-known NP-hard combinatorial optimization problem in graph theory, with various fields of application including wireless sensor networks, optical networks, and systems biology. This paper presents an adaptive multiobjective simulated annealing approach to address a variant of the minimum connected dominating set problem known as the Minimum Weight Minimum Connected Dominating Set Problem. This approach combines a multiobjective Pareto set with a greedy simulated annealing algorithm to tackle the problem by simultaneously optimizing two objectives, namely the cardinality and the total weight of the connected dominating set. Experimental results compared to those obtained by current state-of-the-art approaches show the superiority of our method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel Many-Objective Whale Optimization Algorithm (MaOWOA) is proposed to overcome the challenges of large-scale many-objective optimization problems (LSMOPs) encountered in diverse fields such as engineering. Existing algorithms suffer from curse of dimensionality i.e., they are unable to balance convergence with diversity in extensive decision-making scenarios. MaOWOA introduces strategies to accelerate convergence, balance convergence and diversity in solutions and enhance diversity in high-dimensional spaces. The prime contributions of this paper are—development of MaOWOA, incorporation an Information Feedback Mechanism (IFM) for rapid convergence, a Reference Point-based Selection (RPS) to balance convergence and diversity and a Niche Preservation Strategy (NPS) to improve diversity and prevent overcrowding. A comprehensive evaluation demonstrates MaOWOA superior performance over existing algorithms (MaOPSO, MOEA/DD, MaOABC, NSGA-III) across LSMOP1-LSMOP9 benchmarks and RWMaOP1-RWMaOP5 problems. Results validated using Wilcoxon rank sum tests, highlight MaOWOA excellence in key metrics such as generational distance, spread, spacing, runtime, inverse generational distance and hypervolume, outperforming in 71.8% of tested scenarios. Thus, MaOWOA represents a significant advancement in many-objective optimization, offering new avenues for addressing LSMOPs and RWMaOPs’ inherent challenges. This paper details MaOWOA development, theoretical basis and effectiveness, marking a promising direction for future research in optimization strategies amidst growing problem complexity.

This study analyzes the conditional gradient method for constrained multiobjective optimization problems, also known as the Frank–Wolfe method. We assume that the objectives are continuously differentiable, and the constraint set is convex and compact. We employ an average-type nonmonotone line search, which takes the average of the recent objective function values. The asymptotic convergence properties without convexity assumptions on the objective functions are established. We prove that every limit point of the sequence of iterates that is obtained by the proposed method is a Pareto critical point. An iteration-complexity bound is provided regardless of the convexity assumption on the objective functions. The effectiveness of the suggested approach is demonstrated by applying it to several benchmark test problems. In addition, the efficiency of the proposed algorithm in generating approximations of the entire Pareto front is compared to the existing Hager–Zhang conjugate gradient method, the steepest descent method, the monotone conditional gradient method, and a nonmonotone conditional gradient method. In finding empirical comparison, we utilize two commonly used performance matrices—inverted generational distance and hypervolume indicators. [ABSTRACT FROM AUTHOR]

What is the relation between the notion of Nash equilibria and Pareto-optimal points? It is well known that Nash equilibria do not need to be Pareto optimal, and Pareto points do not need to be Nash equilibria. However, the paper "Characterizing and Computing the Set of Nash Equilibria via Vector Optimization" by Feinstein and Rudloff takes a deeper look at the relation. It is shown that it is possible to characterize the set of all Nash equilibria as the set of all Pareto-optimal solutions of a certain vector optimization problem. This is accomplished by carefully designing the objective function and the ordering cone of the vector optimization problem such that both notions coincide. This characterization holds for all noncooperative games (nonconvex, convex, linear). It opens up a new way of computing Nash equilibria, as one can now use techniques and algorithms from vector optimization to compute the set of all Nash equilibria, which is in contrast to the classical fixed-point iterations that find just a single Nash equilibrium. Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work, we show that it is possible to characterize the set of all Nash equilibria for any noncooperative game as the Pareto-optimal solutions of a certain vector optimization problem. To accomplish this task, we increase the dimensionality of the objective function and formulate a nonconvex ordering cone under which Nash equilibria are Pareto efficient. We demonstrate these results, first, for shared-constraint games in which a joint constraint is applied to all players in a noncooperative game. In doing so, we directly relate our proposed Pareto-optimal solutions to the best response functions of each player. These results are then extended to generalized Nash games, where, in addition to providing an extension of the above characterization, we deduce two vector optimization problems providing necessary and sufficient conditions, respectively, for generalized Nash equilibria. Finally, we show that all prior results hold for vector-valued games as well. Multiple numerical examples are given and demonstrate that our proposed vector optimization formulation readily finds the set of all Nash equilibria. [ABSTRACT FROM AUTHOR]

Recent advancements in the realm of deep generative models focus on generating samples that satisfy multiple desired properties. However, prevalent approaches optimize these property functions independently, thus omitting the trade-offs among them. In addition, the property optimization is often improperly integrated into the generative models, resulting in an unnecessary compromise on generation quality (i.e., the quality of generated samples). To address these issues, we formulate a constrained optimization problem. It seeks to optimize generation quality while ensuring that generated samples reside at the Pareto front of multiple property objectives. Such a formulation enables the generation of samples that cannot be further improved simultaneously on the conflicting property functions and preserves good quality of generated samples.Building upon this formulation, we introduce the ParetO-gUided Diffusion model (PROUD), wherein the gradients in the denoising process are dynamically adjusted to enhance generation quality while the generated samples adhere to Pareto optimality. Experimental evaluations on image generation and protein generation tasks demonstrate that our PROUD consistently maintains superior generation quality while approaching Pareto optimality across multiple property functions compared to various baselines [ABSTRACT FROM AUTHOR]

When examining the economic impact of a change in policy regime, one may elect to conduct a positive analysis that considers the effect of such a policy change on the allocations supported as a market equilibrium. An alternative approach would be to perform a normative analysis that examines the effect of the regime change on the set of Pareto optimal allocations in the economy. In settings where the Fundamental Welfare Theorems hold, the isomorphism between equilibrium and Pareto efficient allocations implies that the choice of approach is largely a matter of convenience. When this isomorphism fails to hold, as in settings with hidden information or hidden actions, the equilibrium allocations may not be efficient so that a normative analysis of the alternative efficiency frontiers is required to determine whether the policy change is desirable in the sense of permitting potential Pareto improvements. If so, then an equilibrium analysis may be used to determine the extent to which such improvements may be realized by market participants. [ABSTRACT FROM AUTHOR]

Traditional integer-order admittance control is widely used in industrial scenarios requiring force control, but integer-order models often struggle to accurately depict fractional-order-controlled objects, leading to precision bottlenecks in the field of precision machining. For robotic precision polishing scenarios, to enhance the stability of the control process, we propose a more physically accurate five-parameter fractional-order admittance control model. To reduce contact impact, we introduce a method combining the rear fastest tracking differential with fractional-order admittance control. The optimal parameter identification for the fractional-order system is completed through Pareto optimality and a time–frequency domain fusion analysis of the control system. We completed the optimal parameter identification in a simulation, which is applied to the robotic precision polishing scenario. This method significantly enhanced the force control precision, reducing the error margin from 15% to 5%. [ABSTRACT FROM AUTHOR]

In a pure-exchange economy with no aggregate uncertainty, we characterize in closed form and full generality Pareto-optimal allocations between two agents who maximize (nonconcave) rank-dependent utilities (RDU). We then derive a necessary and sufficient condition for Pareto optima to be no-betting allocations (i.e., deterministic allocations or full insurance allocations). This condition depends only on the probability weighting functions of the two agents and not on their (concave) utility of wealth. Hence, with RDU preferences, it is the difference in probabilistic risk attitudes given common beliefs rather than heterogeneity or ambiguity in beliefs that is a driver of betting behavior. As by-product of our analysis, we answer the question of when sunspots matter in this economy. Funding: M. Ghossoub acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada [Grant 2018-03961]. [ABSTRACT FROM AUTHOR]

Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the Hilbert space setting. In this manuscript, we consider nonconvex minimum norm problems that arise from Bioengineering and reformulate them in such a way that the solution to their reformulation is already known. In particular, we tackle the problem of min ∥ x ∥ subject to ∥ R k (x) ∥   ≥   a k for k   =   1 , ... , l , where x ∈ X and R k : X → Y are continuous linear operators between real normed spaces X , Y , and a k   >   0 for k   =   1 , ... , l . Notice that the region of constraints of the previous problem is neither convex nor balanced. However, it is additively symmetric, which is also the case for the objective function, due to the properties satisfied by norms, which makes possible the analytic resolution of such a nonconvex minimization. The recent literature shows that the design of optimal coils for electronics applications can be achieved by solving problems like this. However, in this work, we apply our analytical solutions to design an optimal coil for an electromagnetic sensor. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of insolvency prediction in Spanish SMEs from a binary classification perspective. From a dataset containing more than 325 dependent variables of different natures (including demographic and economic-financial) and 17562 SMEs, a decision tree has been fitted that with a 0.93 accuracy predicts the state of a company and allows it to identify the most relevant variables in such prediction. The results obtained indicate that, in general, insolvency can be predicted from very few financial variables and with an anticipation of more than 10 years before the insolvency event. As a result, it is possible to provide early warnings to SMEs based on the indicators identified. [ABSTRACT FROM AUTHOR]

In this work, an inexact proximal point algorithm is proposed for solving unconstrained multiobjective optimization problems with locally Lipschitz and quasi-convex objective functions. In this algorithm, we use quasi-distance in the regularization term and consider the ε -approximate solution of the scalarization subproblem as well as the ε -subdifferential in the optimality condition of the subproblem. This algorithm is shown to be well-defined. Then, it is proved that each accumulation point, if any, of the sequence generated by the algorithm is a Pareto-Clarke critical point of the problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear. [ABSTRACT FROM AUTHOR]

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish a local superlinear rate of convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration to address the lack of convexity assumption. Numerical results shows that the introduced modifications preserve the practical efficiency of the BFGS method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inexact projected gradient method equipped with a nonmonotone line search rule for smooth constrained multiobjective optimization. In this method, a new nonmonotone line search technique proposed here is employed and the relative errors on the search direction is admitted. We demonstrate that this method is well-defined. Then, we prove that each accumulation point of the sequence generated by this method is Pareto stationary and analyze the convergence rate of the algorithm. When the objective function is convex, the convergence of the sequence to a weak Pareto optimal point of the problem is established. [ABSTRACT FROM AUTHOR]

In this work, we propose an inexact proximal point method for solving unconstrained quasiconvex multiobjective optimization problems. Two error criteria (the absolute one and the relative one) of the algorithm are considered, and it is proved under some mild assumptions that the sequence generated by the algorithm in both cases converges to a Pareto stationary point when the objective functions are continuously differentiable, while to a weak Pareto optimal point of the problem when the objective functions are proper convex and lower semicontinuous. Moreover, by using an additional growth condition, we show that the convergence rate of the method under the relative error criteria is linear if the regularization parameters are bounded, and further superlinear if these parameters converge to zero. The main results established in the present work generalize and improve some corresponding ones existing in the literature. Some numerical experiments are also presented. [ABSTRACT FROM AUTHOR]

Objective: Aiming at the shortcomings of artificial surgical path planning for the thermal ablation of liver tumors, such as the time-consuming and labor-consuming process, and relying heavily on doctors' puncture experience, an automatic path-planning system for thermal ablation of liver tumors based on CT images is designed and implemented. Methods: The system mainly includes three modules: image segmentation and three-dimensional reconstruction, automatic surgical path planning, and image information management. Through organ segmentation and three- dimensional reconstruction based on CT images, the personalized abdominal spatial anatomical structure of patients is obtained, which is convenient for surgical path planning. The weighted summation method based on clinical constraints and the concept of Pareto optimality are used to solve the multi-objective optimization problem, screen the optimal needle entry path, and realize the automatic planning of the thermal ablation path. The image information database was established to store the information related to the surgical path. Results: In the discussion with clinicians, more than 78% of the paths generated by the planning system were considered to be effective, and the efficiency of system path planning is higher than doctors' planning efficiency. Conclusion: After improvement, the system can be used for the planning of the thermal ablation path of a liver tumor and has certain clinical application value. [ABSTRACT FROM AUTHOR]

Particle swarm optimization, one of the modern global optimization methods, is attracting widespread interest because it overcomes the difficulties of conventional inversion techniques, such as trapping at a local minimum and/or initial model dependence. The main characteristic of particle swarm optimization is the large search space of parameters, which in a sense allows the exploration of the entire objective function space if the input parameters are properly chosen. However, in the case of a high‐dimensional model space, the numerical instability of the solution may increase and lead to unrealistic models and misinterpretations due to the sampling problem of particle swarm optimization. Therefore, smoothness‐constrained regularization techniques used for the objective function or model reduction techniques are required to stabilize the solution. However, weighting and combining objective function terms is partly a subjective process, as the regularization parameter is generally chosen based on some kind of criteria of how the smoothing constraints affect the data misfits. This means that it cannot be completely predefined but needs to be adjusted during the inversion process, which begins with the response of an initial model. In this paper, a new modelling approach is proposed to obtain a smoothness‐constrained model from magnetotelluric data utilizing multi‐objective particle swarm optimization based on the Pareto optimality approach without using a regularization parameter and combining several objective function terms. The presented approach was verified on synthetic models and an application with field data set from the Çanakkale–Tuzla geothermal field in Turkey. Findings from these analyses confirm the usefulness of the method as a new approach for all constrained inversions of geophysical data without the need to combine the objective function terms weighted by a regularization parameter. [ABSTRACT FROM AUTHOR]

A multi-objective social group optimization (MOSGO) is proposed in this study as a method for resolving problems with multiple objectives. The initial step is to use an external chronicle with a predetermined size to store the existing non-dominated Pareto optimum solutions. Following that, solutions are chosen from this repository using a roulette wheel mechanism based on the coverage of solutions to guide individuals in the direction of promising regions of multi-objective search spaces. The proposed method is tested on ten CEC2009 multi-objective benchmark problems and it has been compared to two well-known meta-heuristics: the multi-objective evolutionary algorithm based on decomposition (MOEA/D) algorithm and the multi-objective particle swarm optimization (MOPSO) algorithm. It is essential to the machining processes to choose the optimum machining parameters in order to guarantee product quality, lower machining costs, boost productivity, and preserve resources for sustainability. Hence, MOSGO, a posterior multi-objective optimization method, is used in this study to tackle the multi-objective optimization problems of three machining processes, including turning, wire-electric-discharge machining, and laser cutting. The results of the MOSGO algorithm are compared with the results obtained using GA, NSGA-II, PSO, and iterative search methods and are found to be comparable. Here it has been observed that the MOSGO algorithm achieved the Pareto-optimal set of solutions in a very less number of function evaluations as compared to other algorithms showing a higher convergence speed. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal sets of solutions are helpful for real production systems and will aid the decision-maker in tumultuous situations. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the domain of decreasing marginal valuations and show that in the presence of budget-constrained bidders there is no multi-unit auction that satisfies the following four properties: incentive compatibility, Pareto optimality, individual rationality and no positive transfers. This result strengthens the impossibility results of two previous studies. [ABSTRACT FROM AUTHOR]

This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place, the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation (MF-FSDE), and a mean-field backward stochastic differential equation (MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results. [ABSTRACT FROM AUTHOR]

Despite advances in security technology, it is impractical to entirely prevent intrusion threats. Consequently, developing effective service migration strategies is crucial to maintaining the continuity of network services. Current service migration strategies initiate the migration process only upon detecting a loss of service functionality in the nodes, which increases the risk of service interruptions. Moreover, the migration decision-making process has not adequately accounted for the alignment between tasks and node resources, thereby amplifying the risk of system overload. To address these shortcomings, we introduce a Quality-Driven Resource Migration Strategy (QD-RMS). Specifically, QD-RMS initiates the migration process at an opportune moment, determined through an analysis of service quality. Subsequently, it employs a method combining Pareto optimality and the simulated annealing algorithm to identify the node most suitable for migration. This approach not only guarantees seamless service continuity but also ensures optimal resource distribution and load balancing. The experiments demonstrate that, in comparison with conventional migration strategies, QD-RMS achieves superior service quality and an approximate 20% increase in maximum task capacity. This substantiates the strategic superiority and technological advancement of the proposed strategy. [ABSTRACT FROM AUTHOR]

The current research trend is not only focused on advanced techniques to intensify the extraction of bioactive compounds from plants, but also on the optimization process. The objective of this work was the implementation of the multiple criteria analysis using navigation on Pareto sets to determine the optimal parameters for the microwave-assisted extraction of Levisticum officinale WDJ Koch roots in order to obtain the maximum efficiency of the antioxidant potential of the extracts. The optimized parameters were extraction time, microwave power, and plant biomass/solvent ratio, while the evaluation criteria were based on the total phenols, flavonoids, reducing sugars, and antioxidant capacity. It was shown that the process parameters analyzed, i.e., biomass/solvent ratio, process time, and microwave power, determined the extraction efficiency of total phenolic content (TPC). A different observation was made for the analysis of total flavonoid content (TFC) and total antioxidant potential (TAA). Compared to the assessment of TFC and TAA, a completely different trend was observed for the analysis of total reducing sugars (RSC). Sets of Pareto optimal, compromise, and preferred solutions were identified that will maximize the efficiency of the extraction of bioactive compounds from biomass. Due to the determined number of Pareto optimal solutions, an approach related to the introduction of preferences in the optimization procedure was applied. It was shown that for a satisfactory level of bioactive compounds, extraction should be carried out at a maximum microwave power of 750 W. Preferred solutions were obtained for root biomass to water ratios ranging from 0.0536 g/mL to 0.0679 g/mL. The preferred optimal time for microwave-assisted water extraction ranged from 64.2857 to 85.7143 s. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is an emerging distributed learning technique through which models can be trained using the data collected by user devices in resource-constrained situations while protecting user privacy. However, FL has three main limitations: First, the parameter server (PS), which aggregates the local models that are trained using local user data, is typically far from users. The large distance may burden the path links between the PS and local nodes, thereby increasing the consumption of the network and computing resources. Second, user device resources are limited, but this aspect is not considered in the training of the local model and transmission of the model parameters. Third, the PS-side links tend to become highly loaded as the number of participating clients increases. The links become congested owing to the large size of model parameters. In this study, we propose a resource-efficient FL scheme. We follow the Pareto optimality concept with the biased client selection to limit client participation, thereby ensuring efficient resource consumption and rapid model convergence. In addition, we propose a hierarchical structure with location-based clustering for device-to-device communication using k-means clustering. Simulation results show that with prate at 0.75, the proposed scheme effectively reduced transmitted and received network traffic by 75.89% and 78.77%, respectively, compared to the FedAvg method. It also achieves faster model convergence compared to other FL mechanisms, such as FedAvg and D2D-FedAvg. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to improving the detection of mild cognitive impairment (MCI) through the use of super-resolved structural magnetic resonance imaging (MRI) and optimized deep learning models. The study introduces enhancements to the perceptual quality of super-resolved 2D structural MRI images using advanced loss functions, modifications to the upscaler part of the generator, and experiments with various discriminators within a generative adversarial training setting. It empirically demonstrates the effectiveness of super-resolution in the MCI detection task, showcasing performance improvements across different state-of-the-art classification models. The paper also addresses the challenge of accurately capturing perceptual image quality, particularly when images contain checkerboard artifacts, and proposes a methodology that incorporates hyperparameter optimization through a Pareto optimal Markov blanket (POMB). This approach systematically explores the hyperparameter space, focusing on reducing overfitting and enhancing model generalizability. The research findings contribute to the field by demonstrating that super-resolution can significantly improve the quality of MRI images for MCI detection, highlighting the importance of choosing an adequate discriminator and the potential of super-resolution as a preprocessing step to boost classification model performance. [ABSTRACT FROM AUTHOR]

The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism. [ABSTRACT FROM AUTHOR]

This paper addresses a class of discrete-time Markov decision processes in Borel spaces with a finite number of cost constraints. The constrained control model considers costs of discounted type with state-dependent discount factors which are subject to external disturbances. Our objective is to prove the existence of optimal control policies and characterize them according to certain optimality criteria. Specifically, by rewriting appropriately our original constrained problem as a new one on a space of occupation measures, we apply the direct method to show solvability. Next, the problem is defined as a convex program, and we prove that the existence of a saddle point of the associated Lagrangian operator is equivalent to the existence of an optimal control policy for the constrained problem. Finally, we turn our attention to multi-objective optimization problems, where the existence of Pareto optimal policies can be obtained from the existence of saddle-points of the aforementioned Lagrangian or equivalently from the existence of optimal control policies of constrained problems. [ABSTRACT FROM AUTHOR]

Abstract The Internet of Things (IoT) devices are not able to execute resource-intensive tasks due to their limited storage and computing power. Therefore, Mobile edge computing (MEC) technology has recently been utilized to provide computing and storage capabilities to those devices, enabling them to execute these tasks with less energy consumption and low latency. However, the edge servers in the MEC network are located at fixed positions, which makes them unable to be adjusted according to the requirements of end users. As a result, unmanned aerial vehicles (UAVs) have recently been used to carry the load of these edge servers, making them mobile and capable of meeting the desired requirements for IoT devices. However, the trajectories of the UAVs need to be accurately planned in order to minimize energy consumption for both the IoT devices during data transmission and the UAVs during hovering time and mobility between halting points (HPs). The trajectory planning problem is a complicated optimization problem because it involves several factors that need to be taken into consideration. This problem is considered a multiobjective optimization problem since it requires simultaneous optimization of both the energy consumption of UAVs and that of IoT devices. However, existing algorithms in the literature for this problem have been based on converting it into a single objective, which may give preference to some objectives over others. Therefore, in this study, several multiobjective trajectory planning algorithms (MTPAs) based on various metaheuristic algorithms with variable population size and the Pareto optimality theory are presented. These algorithms aim to optimize both objectives simultaneously. Additionally, a novel mechanism called the cyclic selection mechanism (CSM) is proposed to manage the population size accurately, optimizing the number of HPs and the maximum function evaluations. Furthermore, the HPs estimated by each MTPA are associated with multiple UAVs using the k-means clustering algorithm. Then, a low-complexity greedy mechanism is used to generate the order of HPs assigned to each UAV, determining its trajectory. Several experiments are conducted to assess the effectiveness of the MTPAs with variable population size and cyclic selection mechanisms. The experimental findings demonstrate that the MTPAs with the cyclic selection mechanism outperform all competing algorithms, achieving better outcomes.

The optimization design problem of nuclear reactor radiation shield is a typical multi-objective optimization problem with almost 10 sub-objectives and the sub-objectives are always demanded to be under tolerable limits. In this paper, a design method combining multi-objective optimization algorithms with paralleling discrete ordinate transportation code is developed and applied to shield design of the Savannah nuclear reactor. Three approaches are studied for light-weighted and compact design of radiation shield. Comparing with directly optimization with 10 objectives and the single-objective optimization, the approach by setting sub-objectives representing weight and volume as optimization objectives while treating other sub-objectives as constraints has the best performance, which is more suitable to reactor shield design.

Clearly arranged visualizations are needed in multiobjective optimization problems with a large number of objective functions, when a large number of Pareto optimal outcome vectors (vectors of objective function values) must be compared during the decision making processes. This paper contributes to visualizing such outcome vectors independent of how they have been generated. Parallel coordinate plots are a widely used visualization technique to represent different outcome vectors.We propose a novel visualization technique called SCORE bands to be used with parallel coordinate plots to support the decision maker in simultaneously identifying patterns in outcome vectors and correlations among the objective functions in a meaningful way. To do so, amongst others, we change the ordering of objective functions and modify the distances among them in parallel coordinate plots. SCORE bands also have interactive capabilities allowing the decision maker to first study general trends among the outcome vectors as bands and then zoom-in and move about different groups of outcome vectors of interest. The novelty of our approach lies in proposing a visually appealing way to support the decision maker in dealing with large amounts of information. We demonstrate the benefits of SCORE bands with different examples.

The change in public awareness always directly affects people’s behavior. When an epidemic breaks out in a population, a severe epidemic situation can cause panic among people, while a less severe epidemic may lead to its harmful effects being overlooked. This paper has established a nonlinear infectious disease model based on mean field evolutionary game theory, aimed at exploring the impact of the epidemic scale on people’s vaccination behavior. Additionally, based on this nonlinear infectious disease model, we have developed an optimal control system to explore vaccination behavior under optimal control. To enhance the practicality of the model, we have introduced multiple convex structured parameters, leading to a variety of epidemic prevention strategies. This provides decision-makers with two types of epidemic prevention strategies based on vaccination: aggressive and conservative.

This paper proposes an algorithm for solving multiobjective optimization problems using the attack technique of the Grey Wolf. It is a metaheuristic method called a Multiobjective Optimizer based on Grey Wolf Attack Technique (MOGWAT). In fact, it is inspired by the modified Hybrid Grey Wolf Optimizer and Genetic Algorithm (HmGWOGA), which is a single objective optimization algorithm specially designed for positive objective functions. The MOGWAT method combines the multiple objective functions of the initial problem into a single objective function, and then penalizes constraint functions to get an unconstrained single-objective optimization. The use of an effective single-objective optimizer allows reaching the optimal solutions. These solutions are also the Pareto optimal solutions of the initial problem according to some parameters. Through some theorems, we have established the theoretical foundation and performance of our method. Furthermore, in order to highlight the numerical performance of the method, we have tackled three groups of problems: 16 test problems from the Zitzler-Deb-Thiele benchmarks, 2 instances from the CEC 2009 benchmarks, and 2 real-world problems from literature. Our numerical results have been compared to the ones obtained with the NSGA-II method. This comparison was made using some computed performance parameters. The outcomes of the comparison have enabled us to prove the effectiveness and efficiency of our new approach in terms of speed and convergence. [ABSTRACT FROM AUTHOR]

This paper introduces a Riemannian BFGS method to address multiobjective optimization problems with strongly retraction-convex objective functions. This method is a natural extension of the Euclidean version and produces a sequence of iterates that converges to a Pareto optimal point regardless of the initial point. The main component of our globalization strategy is a generalized Wolfe line search. Numerical experiments demonstrate the superiority and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The field of visual search has gained significant attention recently, particularly in the context of web search engines and e-commerce product search platforms. However, the abundance of web images presents a challenge for modern image retrieval systems, as they need to find both relevant and diverse images that maximize users' satisfaction. In response to this challenge, we propose a non-dominated visual diversity re-ranking (NDVDR) method based on the concept of Pareto optimality. To begin with, we employ a fast binary hashing method as a coarse-grained retrieval procedure. This allows us to efficiently obtain a subset of candidate images for subsequent re-ranking. Fed with this initial retrieved image results, the NDVDR performs a fine-grained re-ranking procedure for boosting both relevance and visual diversity among the top-ranked images. Recognizing the inherent conflict nature between the objectives of relevance and diversity, the reranking procedure is simulated as the analytical stage of a multi-criteria decision-making process, seeking the optimal tradeoff between the two conflicting objectives within the initial retrieved images. In particular, a non-dominated sorting mechanism is devised that produces Pareto non-dominated hierarchies among images based on the Pareto dominance relation. Additionally, two novel measures are introduced for the effective characterization of the relevance and diversity scores among different images. We conduct experiments on three popular real-world image datasets and compare our re-ranking method with several state-of-the-art image search re-ranking methods. The experimental results validate that our re-ranking approach guarantees retrieval accuracy while simultaneously boosting diversity among the top-ranked images. [ABSTRACT FROM AUTHOR]

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The Internet of Things (IoT) devices are not able to execute resource-intensive tasks due to their limited storage and computing power. Therefore, Mobile edge computing (MEC) technology has recently been utilized to provide computing and storage capabilities to those devices, enabling them to execute these tasks with less energy consumption and low latency. However, the edge servers in the MEC network are located at fixed positions, which makes them unable to be adjusted according to the requirements of end users. As a result, unmanned aerial vehicles (UAVs) have recently been used to carry the load of these edge servers, making them mobile and capable of meeting the desired requirements for IoT devices. However, the trajectories of the UAVs need to be accurately planned in order to minimize energy consumption for both the IoT devices during data transmission and the UAVs during hovering time and mobility between halting points (HPs). The trajectory planning problem is a complicated optimization problem because it involves several factors that need to be taken into consideration. This problem is considered a multiobjective optimization problem since it requires simultaneous optimization of both the energy consumption of UAVs and that of IoT devices. However, existing algorithms in the literature for this problem have been based on converting it into a single objective, which may give preference to some objectives over others. Therefore, in this study, several multiobjective trajectory planning algorithms (MTPAs) based on various metaheuristic algorithms with variable population size and the Pareto optimality theory are presented. These algorithms aim to optimize both objectives simultaneously. Additionally, a novel mechanism called the cyclic selection mechanism (CSM) is proposed to manage the population size accurately, optimizing the number of HPs and the maximum function evaluations. Furthermore, the HPs estimated by each MTPA are associated with multiple UAVs using the k-means clustering algorithm. Then, a low-complexity greedy mechanism is used to generate the order of HPs assigned to each UAV, determining its trajectory. Several experiments are conducted to assess the effectiveness of the MTPAs with variable population size and cyclic selection mechanisms. The experimental findings demonstrate that the MTPAs with the cyclic selection mechanism outperform all competing algorithms, achieving better outcomes. [ABSTRACT FROM AUTHOR]

This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of LPFD and HLPFD to modelling cooperative games in strategic form is explored. The resulted framework provides a unified view on Nash equilibrium, Pareto optimality and the core. The philosophical relevance of these game-theoretical notions to discussions of collective agency is made explicit. Some key connections with other logics are also revealed, for example, the coalition logic, the logic of functional dependence and the logic of ceteris paribus preference. [ABSTRACT FROM AUTHOR]

Cloud computing is one of the emerging technologies that expands the boundaries of the internet by using centralized servers to maintain data and resources. It allows users and consumers to use various applications provided by the cloud provider, but one of the major issues is task scheduling. Task scheduling is employed for the purpose of mapping the requests of users to the appropriate resources available. This paper provides a detailed survey of the available scheduling techniques for cloud environments based on six common metaheuristic algorithms. Those algorithms are the Cuckoo Search Algorithm (CSA), Chicken Swarm Optimization (CSO), Genetic Algorithm (GA), Bat Algorithm (BA), Whale Optimization Algorithm (WOA), and Grey Wolf Optimization (GWO). The literature is analyzed from three perspectives: task type, objectives to be optimized, simulation environment, and quality of service performance metrics. In addition, the research gaps and future directions for future investigation are presented. [ABSTRACT FROM AUTHOR]

The maximally entangled (ME) Eisert–Wilkens–Lewenstein (EWL) quantization scheme efficiently solves the classical prisoner's dilemma (PD). Despite the intensive research on the EWL scheme, little is known about the role of the arbiter in controlling the scheme properties. We redefine the EWL scheme by introducing an arbitrary phase shift into the ME initial state. Four basic initial states were analyzed in this study. It is found that the arbiter completely controls the characteristics of the arbitrary ME quantum PD. The arbiter can adjust the ME initial state to obtain an efficient symmetric Nash equilibrium. In contrast, the arbiter can nullify the quantization advantages. Moreover, it can preserve/violate the symmetry of the game or even turn it into a potential game. [ABSTRACT FROM AUTHOR]