Under the combined impetus of the International Maritime Organization’s greenhouse gas reduction strategy, the European Union’s FuelEU Maritime initiative, and China’s dual-carbon goals, the shipping industry is accelerating its transition toward alternative fuels. Yet prevailing evaluation approaches are largely static and thus ill-suited to the dynamic uncertainties that characterize technological progress, economic conditions, and policy regimes. To address this gap, this study develops a dynamic multi-criteria decision-making framework capable of conducting intertemporal and cross-scenario assessments. A dynamic fuzzy matter‑element model is proposed for the comprehensive assessment of six principal alternative marine fuels—liquefied natural gas (LNG), methanol, ammonia, hydrogen, biofuels, and batteries. The evaluation framework is structured around six dimensions, namely technology readiness, safety, life‑cycle environmental performance, economics, supply‑chain maturity, and the fuel flexibility index. By incorporating time-evolving indicator values, scenario-driven dynamic weights, and trapezoidal membership functions, the model quantifies each fuel’s degrees of membership across graded performance levels. The study corroborates a long-term multi-fuel coexistence equilibrium in maritime decarbonization, with no single solution universally optimal across scenarios. The proposed dynamic fuzzy matter-element model offers decision-makers an effective quantitative instrument for crafting robust fuel-transition strategies under uncertainty. Methodologically, the research integrates temporal dynamics into fuzzy matter-element theory and introduces composite indicators such as the fuel flexibility index, thereby furnishing a novel analytical lens and decision support for charting green transition pathways in the shipping sector.
Path planning problems often involve multiple constraints that cannot always be simultaneously satisfiable in practice. Existing approaches focus on eliminating conflicts to restore feasibility, as they implicitly assume that conflict-free solutions exist. However, when constraints are inherently infeasible, these methods provide limited guidance in generating solutions. To address this limitation, we shifted path planning problems to minimum-violation optimization problems, where shift vectors are integrated into the objective function. Then, we proposed a minimum-violation optimization method that integrates Monte Carlo Tree Search with the augmented Lagrangian method, explicitly quantifying constraint violations by strongly convex measures. We further derived the method’s convergence rate and error bound, and validated it on benchmark instances of the Chinese Postman Problem with conflict constraints. In addition, we investigated the use of large language models as auxiliary components in the simulation phase and examined the conditions under which they are effective.
With the carbon peaking and carbon neutrality goals, the coverage of carbon cap-and-trade mechanism is incomplete and the carbon price is low. The timely introduction of carbon tax policy and the construction of a carbon pricing synergy mechanism (carbon cap and trade with carbon tax) of "mainly carbon market, supplemented by carbon tax" can effectively guide areas not covered by the carbon market to participate in carbon emission reduction and improve the efficiency of green supply chain management. This paper discussed the coordination of two-stage green supply chain composed of a small supplier and large manufacturer and constructed the supply chain coordination game model under four decision situations. The results show that: (1) Levying carbon tax on the basis of carbon cap-and-trade mechanism can decrease the carbon emission in the supply chain, but cause profit loss. A certain degree of coordination can be achieved by further considering government subsidies and cost sharing contracts. (2) Carbon price, consumer green sensitivity coefficient, government subsidy rate, and cost sharing rate have positive impacts on decision-making. The government should scientifically and rationally subsidize enterprises with significant emission reduction effects and coordinate with supply chain contracts to give full play to the synergy of carbon pricing mechanism.
In this paper, a new model of Binary Interdependent Networks with Weak Coupling (BINWC) is proposed based on the interdependence of nodes and edges in realistic complex networks. Unlike traditional models that focus solely on node-coupled or edge-coupled interdependent networks, this model introduces a mechanism where nodes depend on edges in heterogeneous networks. In this framework, a node failure will directly cause the failure of its dependent edge. Conversely, the failure of an edge affects the stability of its dependent node with a certain probability. This approach aligns more closely with the robustness characteristics observed in real networks. This paper presents a mathematical analysis framework based on percolation theory and the generating function method to study the percolation behavior of BINWC under random attacks. The accuracy of the theoretical analysis is verified through numerical solutions and computer simulations. Furthermore, we investigate the relationship between network robustness and the failure probabilities of both nodes and edges. It is demonstrated that the robustness of BINWC increases as the probability of both nodes and edges failure decreases. However, this improvement in robustness is less significant in BINWC with higher average degrees. Additionally, for both Random Regular (RR) and Erdős–Rényi (ER) networks, a first-order phase transition occurs at the average degree ⟨ k ⟩ = 3 , while a second-order phase transition is observed when ⟨ k ⟩ 3 . This study provides theoretical support for understanding binary interdependent networks and their robustness in realistic networks.
Game theory primarily investigates the interactions between formalized incentive structures, functioning as a mathematical theory and methodology for analyzing phenomena with competitive or confrontational attributes. With the extension of quantum physics research findings to other scientific fields, game theory has been expanded into the quantum domain, giving rise to the emerging interdisciplinary discipline of quantum game theory. This study focuses on bounded-rational Cournot oligopoly games, incorporating inter-advertiser competition into the cost function. A delayed bounded-rational Cournot oligopoly game model is constructed, verifying that the proposed model is a complex dynamical system exhibiting bifurcation and chaos. It is further confirmed that the time delay effect influences inter-firm games, advancing the occurrence of bifurcation and chaos within the system. Additionally, after quantizing the model, the stability of equilibrium points is quantitatively analyzed based on dynamical system theory. By establishing the local stability conditions for Nash equilibrium, the model’s dynamic behaviors are qualitatively explored via simulation methods, including bifurcation diagrams and phase portraits. Our findings reveal that quantum entanglement significantly modulates the competitive dynamics among enterprises. Qualitative analysis demonstrates that increasing the degree of quantum entanglement advances the emergence of system bifurcation and chaos, thereby affecting the outcome of the game.
In this paper, we investigate the mission planning problem for multiple Unmanned Aerial Vehicles (UAVs), where visit gains and the resource requirements for each mission are dependent on UAV types. This problem involves both mission allocation and path planning. Existing deep reinforcement learning (DRL) algorithms, particularly those utilizing graph attention networks (GAT), face challenges in extracting intricate state features. Additionally, these algorithms often lack practical applicability for mission planning problems where visit gains are highly dependent on UAV types. To address these issues, we propose an end-to-end DRL framework that employs a heterogeneous graph attention network (HAN) to derive the optimal scheduling strategy. Firstly, the problem is formulated as a Markov decision process (MDP). In this formulation, UAVs and missions are represented as a fully connected heterogeneous graph, which serves as the scheduling state across different time steps. We develop a heterogeneous graph neural network and integrate it with a multi-head attention mechanism to embed the latent relationships between various types of nodes and edges, ultimately yielding an overall graph embedding. The graph-level representation vector of the heterogeneous graph, along with the node vectors, is fed into a Transformer-based decoder to autoregressively generate the sequence of nodes to be visited. The reward function is designed to maximize the total visit gains while minimizing the total flight distance and flight time. Moreover, we propose a DRL training algorithm based on an Actor-Critic framework. The critic network estimates state-value functions by utilizing a fully connected HAN. Experimental results show that our proposed model exhibits a substantial advantage in solution efficiency, compared to CPLEX, several well-known heuristics, and a mainstream DRL framework. Specifically, when compared to the widely adopted mainstream GAT-based method (a representative architecture for neural combinatorial optimization), the average optimal gap for large-scale cases is reduced from 12.36
Crowdsourcing contests can gather group wisdom and open up new ways for companies to obtain innovative solutions. This paper studies crowdsourcing contests in a grouped mode where the organizer of the contest divides the participants into professional and amateur groups according to their level of expertise, holding a crowdsourcing contest for each group. Both crowdsourcing contests without entry fees and crowdsourcing contests with entry fees are considered. We use game theory models to conduct an in-depth study on how organizers should organize crowdsourcing contests in the grouped mode. The equilibrium effort of contestants and the benefits of organizers in the two modes are analyzed. The results show that when the number of participants is small or sufficiently large, and the entry fee is low enough, the organizer’s benefits with our proposed grouped mode are better than those with the non-grouped mode, regardless of whether the organizer focuses on the average performance or the best performance of the contestants. We verify our conclusions with numerical results.
Evolutionary games provide a very useful tool for analyzing how agents of population behave during the epidemic outbreak. Based on the fact that in the process of virus spreading, individuals may take different measures to inhibit virus spreading according to the environmental influences, we construct a two-stage evolutionary game process: the first stage is the choice of whether to vaccinate or not before the virus spreads, and the second stage is the process of virus spreading (SEIRD epidemic model). In the epidemic model, we analyze its basic reproduction number, the final epidemic size and the optimal control problem with efficacy of medicine as the control variable. At the level of the evolutionary game, we analyze the existence and stability of its equilibrium points and the effect of ℛ_0 on evolutionary stable strategies. Finally, a series of numerical experiments support the theoretical results obtained.
This work leverages the connection between dynamical systems and optimization algorithms to propose a Güler-type accelerated augmented Lagrangian method (GAALM) for solving convex optimization problems with linear equality constraints. The proposed GAALM is developed by formulating a second-order dual dynamical system associated with the dual formulation of the linearly constrained convex optimization problem and then discretizing it with a tunable parameter that balances implicit and explicit schemes. We establish a convergence rate of o(1/k^2) for the objective residual of the Lagrangian function (Lagrangian residual). Numerical experiments are also presented to illustrate the efficacy and advantages of the proposed method.
Iran ranks among the hottest countries in the world, offering high potential for solar energy absorption, making the use of solar power plants viable. One critical challenge in implementing solar power plants is site selection. This article aims to identify optimal locations for solar power plant construction through a case study in Kermanshah province. To achieve this goal, a two-step method was developed to evaluate the suitability of potential solar power plant sites. In the first step, initial input and output factors were identified through a literature review. The extended stepwise weight assessment ratio analysis (SWARA) method was then employed to determine the most relevant factors based on expert opinions. The input factors selected were air temperature, precipitation, and wind speed, while the output factors were elevation and irradiation, chosen for their importance as influential factors. In the second step, the performance of 14 potential solar power plant sites was assessed using data envelopment analysis (DEA) models. The results revealed that six locations—Sarpol-e Zahab, Mahidasht, Qasr-e Shirin, Kerend-e Gharb, Sonqor, and Harsin—exhibited both total and scale efficiency. Additionally, seven locations—Islamabad-e Gharb, Sarpol-e Zahab, Mahidasht, Qasr-e Shirin, Kerend-e Gharb, Sonqor, and Harsin—exhibited technical efficiency.
This technical note develops a complementary cooperative solution to the dynamic network game of the Fintech industry of Yeung et al. (J Oper Res Soc China. 12: 5–33, 2024). The solution satisfies the properties of individual rationality, group optimality, time consistency, and the fair gain-sharing principle. It entails two advantageous attributes over those of the Shapley value, including a gain-sharing principle based on the contributions of firms and a much simpler solution mechanism.
This paper investigates the online scheduling of unit jobs with rejection on two identical parallel machines. All jobs arrive sequentially in an online fashion, and upon each job’s arrival, an immediate decision must be made to either accept or reject it. The goal is to minimize the maximum quadratic completion time of accepted jobs plus the total rejection penalty of rejected jobs. For this problem, we present a deterministic online algorithm with the best-possible competitive ratio of 2.
This study presents an advanced two-step inertial proximal coordinate algorithm (TIPSCA) designed to minimize the sum of multiple separable nonconvex and potentially nonsmooth objective functions along with a single smooth, nonseparable function that may also be nonconvex. The proposed method, termed the two-step inertial proximal coordinate subgradient algorithm, iteratively refines the solution by applying the proximal subgradients of the separable functions at the current solution point. The algorithm’s global convergence is established under the framework of the Kurdyka–Łojasiewicz (KŁ) property and several reasonable auxiliary conditions. The convergence rate is determined based on the Łojasiewicz exponent, providing a theoretical foundation for the algorithm’s performance. To demonstrate the practical applicability and efficiency of the proposed method, two numerical experiments are conducted, showcasing its capabilities in handling complex optimization problems.
It is known that the sequential quadratic programming (SQP) method and the alternating direction method of multipliers (ADMM) are two kinds of very effective tools for solving smooth small-to-medium-scale optimization and large-scale separable optimization, respectively. This paper discusses a class of large-scale two-block optimization problems with linear equality-inequality constraints, where the objective function is smooth but not necessarily convex. Our aim is to design a novel ADMM-SQP method based on the fully augmented Lagrangian function (FALF for short, namely, both the equality constraints and the inequality constraints are considered in the augmented Lagrangian function). The main technical routes are as follows. First, based on FALF technique, transform the quadratic programming (QP) subproblem associated with the original problem to a piecewise QP (PQP) subproblem with simple constraints. Second, use the Gauss-Seidel splitting to divide the PQP into two small-scale PQP subproblems. And then, by linearizing the piecewise quadratic objective, reduce the PQP subproblems to two standard QP subproblems, which can yield two improved search directions corresponding to the primal two-block variables. Third, with the FALF of the original problem as a merit function, along the improved search directions, execute Armijo line search to generate the new iteration point. Fourth, the multipliers are updated by a new scheme different from ADMM. Based on a key inequality established in this paper, the global convergence and 𝒪(ε ^-2) iteration complexity of the proposed method can be obtained. Finally, a preliminary numerical test is carried out. To our knowledge, this is the first FALF-based method for equality-inequality constrained non-convex optimization.
This paper investigates the strategic interactions among policyholders, insurers, and reinsurers in the insurance market by proposing a two-layer hybrid game model to analyze the equilibrium strategies of the three parties. In this tripartite game, policyholders optimize their insurance strategies to minimize their risks and costs, while insurers determine optimal premium and risk allocation strategies based on the pricing strategies of reinsurers. Reinsurers, in turn, adjust their competitive reinsurance premium strategies to maximize their profits. Through theoretical derivation and analysis, this paper proves the existence and uniqueness of the equilibrium strategies and provides semi-explicit expressions for these strategies. Finally, numerical simulations reveal that the equilibrium strategies are influenced not only by risk preferences, but also by market structure and the interactions among participants.
Many experts have designed algorithms for the l(1-2)-minimization model and discussed their convergence. However, at present, convergence to a stable point, as defined in Definition of this paper, is only assured for convergent subsequences. On the other hand, the literature on the difference of convex functions algorithm (DCA) is extensive, but proving the convergence of the DCA algorithm requires the use of the Kurdyka-Lojasiewicz (KL) property. In this paper, drawing on the ideas of the DCA, we propose a novel algorithm whose entire sequence converges to a stable point. We establish this result without relying on the KL property. Additionally, we prove that the number of local minimum points of the l(1-2)-minimization model is finite. Leveraging this result, we demonstrate that when the initial point is in proximal to a minimum point of the objective function, the algorithm converges to one of these minimum points. This paper provides the necessary and sufficient conditions for local minimum point of l(1-2)-minimization. Furthermore, we establish the convergence of the subalgorithm utilized to solve an optimization problem within the main algorithm. Finally, our experiments demonstrate that the l(1-2) algorithm proposed in this paper outperforms several other existing algorithms.
We propose an optimization-based framework to define solutions for stochastic cooperative games. We construct excess-based preference functions that evaluate coalitional (or individual) dissatisfaction through the expected square and variance of excesses, with a parameter capturing risk aversion, neutrality and loving. Aggregating players’ preferences yields tractable optimization models, and solutions are defined as their minimizers under efficiency. We study two allocation paradigms: a decomposition rule that separates expected worth and residual uncertainty, and a cohesive proportional rule that distributes total random worth proportionally. For both paradigms, we derive optimal allocations, provide existence (uniqueness) conditions, and explain how risk attitudes shape risk sharing. Simple examples illustrate how the function measures risk attitudes and supports decision making in stochastic cooperative settings.
For convex smooth multiobjective optimization problems, certain inertial gradient systems accelerate convergence toward weakly Pareto optimal solutions. To achieve even faster convergence, we propose a multiobjective inertial gradient system with time scaling (MITS), formulated as a second-order differential equation comprising an inertial term, asymptotically vanishing damping, and a time-scaled gradient term. We first establish the existence of solution trajectories for MITS. Through Lyapunov analysis, we show that with suitable parameters, the trajectory attains a convergence rate of O(1/t^2β (t)) with respect to a merit function, where β (t) is a time scaling function. Specifically, choosing β (t)=t^p for 0⩽ p<α -3 yields the rate O(1/t^2+p) , enabling arbitrarily fast sublinear convergence by tuning p . We also prove that the trajectory converges to a weakly Pareto optimal solution. Furthermore, an implicit discretization of MITS leads to a multiobjective inertial proximal point method (MIPP), whose iterates share the O(1/k^2β _k) rate and converge to a weakly Pareto optimal solution under appropriate conditions. Numerical experiments support the theoretical findings.
