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- Synchronizing production planning and job scheduling: MILP models and
exact algorithms-
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Abstract: We address the synchronization of a resource production process with the consumption of related resources by jobs. Both processes interact through transfer transactions, which become the key components of the resulting scheduling problem. This Synchronized Resource Production/Job Processing problem (SRPJP) problem typically arises when the resource is a form of renewable energy (e.g., hydrogen, photovoltaic) stored in tanks or batteries. We first cast SRPJP into the Mixed-Integer Linear Programming (MILP) format and handle it through a branch-and-cut process involving specific No_Antichain constraints derived from the structure of the feasible transfer transactions. Subsequently, we explore another approach, which involves eliminating non-binary decision variables and applying a Benders decomposition scheme. Finally, we reformulate the SRPJP problem as a path search problem, which we efficiently handle by designing a tailored adaptation of the A* algorithm.
PubDate: 2025-07-03
- New Challenges in Combinatorial Optimization
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PubDate: 2025-07-03
- Algorithms for 2-balanced connected k-partition problem in graphs
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Abstract: Motivated by the result of balanced connected graph edge partition problem for trees, we investigate the 2-balanced connected graph vertex k-partition problem. This paper leverages the charity vertex method and proposes several algorithms for 2-balanced vertex-connected partitioning. Furthermore, we prove that these algorithms are polynomial-time solvable on degree-bounded graphs, thereby refining and extending the results of Caragiannis et al.
PubDate: 2025-07-03
- Single machine lot scheduling to minimize maximum weighted completion time
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Abstract: The development of artificial intelligence is a significant factor in the surge in demand for micro-products. Consequently, optimizing production scheduling for micro-products has become crucial in improving efficiency, quality, and competitiveness, which is essential for the sustainable development of the industry. In micro-product manufacturing, it is common for manufacturers to receive customized orders with varying quantities and priority levels. This work focuses on situations where orders are processed in lots with unified capacity on a single machine. Each lot has the potential to accommodate multiple orders, and if necessary, any order can be split and processed in consecutive lots. Each order is characterized by its size and weight. The objective of the problem is to minimize the maximum weighted completion time. In order to investigate the differences in the calculation of completion times for split orders, two mixed-integer linear programming models are established, and the optimal characteristics of these problems are subsequently analyzed. Furthermore, in consideration of the inherent unpredictability of order arrival over time in practice, we also explore the potential of online versions of these problems and propose an online algorithm for online problems. Finally, the experimental results assess the efficacy of the proposed optimality rules and the online algorithm and derive several managerial insights.
PubDate: 2025-07-03
- On the initial transition of graphs of Kirkman schedules by the partial
team swap-
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Abstract: Kirkman schedule is one of the typical single round-robin (abbrev. SRR) tournaments. The partial team swap (abbrev. PTS) is one of the typical procedures of changing from an SRR tournament to another SRR tournament, which is used in local search for solving the traveling tournament problem. An SRR of n teams (of even number) can be represented by a 1-factorization of the complete graph $$K_n$$. It is known that the 1-factorization of any Kirkman schedule is “perfect” when $$n=p+1$$ for prime numbers p, meaning that any pair of 1-factors in the 1-factorization forms a Hamilton cycle $$C_n$$ in $$K_n$$, called a 2-edge-colored Hamilton cycle. We are concerned with the cycle structure after applying the PTS to Kirkman schedules, that is, how a 2-edge-colored Hamilton cycle $$C_n$$ is decomposed into two 2-edge-colored cycles of length 2d and $$n-2d$$, say, $$C_{2d}$$ and $$C_{n-2d}$$ for some number $$d\in [n/2]$$. We characterize the numbers d such that any cycle $$C_{2d}$$ is not generated by any PTS. Moreover, in case that a cycle $$C_{2d}$$ is generated, we show that the number of $$C_{2d}$$ for any $$d\ne n/4$$ generated by any PTS is at most $$n-2$$. For the case of $$d=n/4$$ (i.e., $$C_{n/2}$$), the number of $$C_{n/2}$$ generated by any PTS is at most $$2(n-2)$$, and there is some PTS to achieve the upper bound.
PubDate: 2025-07-03
- Approximate maximin share allocation for indivisible goods under a
knapsack constraint-
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Abstract: The maximin share (MMS) allocation problem under a knapsack constraint is to allocate a set of indivisible goods to a set of n heterogeneous agents, such that the total cost of the allocated goods does not exceed the given budget, and the approximation ratio of the MMS allocation is as large as possible. For any $$\epsilon \in (0, 1)$$, we prove that $$(\frac{93}{95}+ \epsilon )$$-approximate MMS allocation does not always exist for two agents, while the MMS allocation problem without a knapsack constraint always has an MMS allocation for two agents. We propose a bag-filling based algorithm that can produce a $$\frac{n}{3n-2}$$-approximate MMS allocation. When $$n=2$$ and $$n=3$$, by more careful analysis, we improve the approximation ratios to $$\frac{2}{3}$$ and $$\frac{1}{2}$$, respectively.
PubDate: 2025-07-03
- Sufficient conditions for some graphical properties in terms of the
Lanzhou index and the ad-hoc Lanzhou index-
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Abstract: During the past decade, several research groups have published sufficient conditions for Hamiltonicity of graphs in terms of the first Zagreb index, the second Zagreb index and the forgotten topological index. The forgotten topological index (F-index) is defined as $$F(G)=\sum \limits _{uv\in E(G)}(d^{2}(u)+d^{2}(v))=\sum \limits _{v\in V(G)}d^{3}(v)$$. The forgotten topological coindex (F-coindex) is defined as $${\overline{F}}(G)=\sum \limits _{uv\notin E(G)}(d^{2}(u)+d^{2}(v))=\sum \limits _{v\in V(G)}d^{2}(v)(n-d(v)-1)$$ and it can be also called the Lanzhou index Lz(G). The Lanzhou index of the complement of G is the ad-hoc Lanzhou index and defined as $$\widetilde{Lz}(G)=\sum \limits _{v\in V(G)}d(v)(n-d(v)-1)^{2}$$. This paper mainly focuses on sufficient conditions for graphs to be traceable, Hamiltonian, Hamilton-connected, k-path-coverable, k-Hamiltonian, k-edge-Hamiltonian and k-leaf-connected in terms of the Lanzhou index and the ad-hoc Lanzhou index.
PubDate: 2025-06-22
- Fitting and analyzing data with convex-area-wise linear regression models
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Abstract: This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This regression model is highly interpretable for its close-form local models and boundaries, and it is able to interpolate any given finite datasets even when the underlying relationship between explanatory and response variables are non-linear and discontinuous. In order to construct CALR models for given datasets, accurate algorithms and an incremental algorithm are proposed under different assumptions. The analysis of correctness and time complexity of the algorithms are given, indicating that the problem can be solved in $$o(n^2)$$ time accurately when the input datasets have some special features, or be solved in $$O(T(n_s)+n(M+d^2))$$ time incrementally using an $$n_s$$-size initial subset to construct initial accurate model.
PubDate: 2025-06-19
- Approximation algorithms for the total dominating set problem
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Abstract: Given a network graph $$G=(V,E)$$, a subset $$T\subseteq V$$ is said to be a total dominating set (TDS) if every $$v\in V$$ is adjacent to at least one node in T. In this paper, we first present a distributed algorithm for the minimum TDS problem via the LP relaxation techniques. For a positive integer k and maximum degree $$\Delta $$, the proposed algorithm outputs a fractional total dominating set of expected size $$O(k\Delta ^\frac{2}{k}) TDS_{OPT} $$, where $$TDS_{OPT}$$ is an optimal TDS. The distributed algorithm runs in $$O(k^2)$$ communication rounds, and the algorithm uses messages of size $$O(\log \Delta )$$. Then we give a rounding algorithm. The fractional solution is rounded to obtain an integer total dominating set for the original problem.
PubDate: 2025-06-02
- The multiple steiner TSP with cyclic order on terminals: valid
inequalities and polyhedra-
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Abstract: This paper deals with a variant of the Traveling Salesman Problem (TSP), called the Multiple Steiner TSP with Order Constraints (MSTSPOC). Consider an undirected graph with nonnegative weights on the edges, and a set of salesmen such that with each salesman is associated a set of ordered terminals. The MSTSPOC consists in finding a minimum-weight subgraph containing for each salesman a tour going in order through its terminals. We study the polytope associated with the Integer Linear Programming (ILP) formulation proposed in Borne et al. (2013). We characterize when the basic inequalities define facets. We also describe new valid inequalities along with necessary conditions and sufficient conditions for these inequalities to be facet-defining. Further families of valid inequalities, coming from closely related problems, are also discussed. The theoretical results presented in this paper are computationally tested in a companion paper (Taktak 2024).
PubDate: 2025-06-02
- Finding a b-matching that embeds the maximum number of edge pairs
in a given set-
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Abstract: Given a set of edge pairs in a complete bipartite graph, the objective of the maximum edge-pair embedding bipartite b-matching problem (MEEBbM) is to find a bipartite b-matching that includes the maximum number of these edge pairs. The original problem, known as the maximum edge-pair embedding bipartite matching, was demonstrated to be NP-hard and inapproximable by Nguyen et al. in 2021. Building on this, and being inspired by the optimization of reconfigurable networks, we extend the problem in this paper to consider b-matchings, with a focus on scenarios where the number of edge pairs per node is bounded. Let $$ k $$ represent the maximum number of edge pairs that can be incident on a single node. We prove that when $$k > b$$, the problem is NP-hard. For the case when $$b = 2$$, we provide an exact algorithm for $$k = 1,2$$. Additionally, for any values of k and b, we provide a $$\Theta (k)$$-approximation algorithm for this problem.
PubDate: 2025-06-02
- Frequency allocation problem over an algebraic structure
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Abstract: In wireless telecommunication networks, where a multitude of communication links exist but only a restricted number of frequencies are available, the challenge of strategically assigning these frequencies to transmitters to minimize interference is known as the frequency allocation problem. This problem is commonly represented and approached through the lens of graph L(2, 1)-coloring, a recognized methodology for resolving such allocation challenges. In this paper, we consider frequency allocation as a graph L(2, 1)-coloring problem over an algebraic structure, a ring R with unity 1 not equal to zero. In L(2, 1)-coloring model of a network adjacent transceivers situated in very close proximity are assigned frequencies with a minimum difference of two. Meanwhile, transceivers in close vicinity are assigned frequencies that differ by at least one. This coloring scheme ensures effective frequency allocation while managing interference in wireless communication networks.
PubDate: 2025-05-29
- Refining waste and elevating customer service: assessing the efficacy of
reverse logistics strategies for product returns management-
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Abstract: To enhance the utilization rate of remanufactured products and further facilitate their widespread circulation, it is crucial to identify the responsible party for processing and refurbishing these items. This paper explores the potential contributions of various entities within a supply chain, including new product manufacturers, retailers, and third-party entities, in providing services for recycling and refurbishing remanufactured products. That is to say. It explores the question of which side of the production process of refurbished products can be done in a more economically and environmentally efficient way. The aim is to promote the rational use of resources and address the necessity to enhance the resilience of green supply chains. In this supply chain, remanufactured and new products are introduced to the market simultaneously. This research has developed three competitive cooperation models based on different recycling and refurbishment subjects for refurbished products by considering the return policy, the cost of new and remanufactured products, and the interaction between product prices. These include a model of competition between a separate manufacturer of new products and a separate manufacturer of refurbished products (Model A), a basic model in which a manufacturer of new products also carries on the business of refurbished products (Model B), and a model of competition and cooperation between a manufacturer of new products and a retailer that carries on the business of refurbished products (Model C). Based on a game theory framework, this study analyses in-depth the preference differences among members for different supply relationships of refurbished products in three supply chain models. In this model, owing to diverse return policies, refurbishment costs, and other factors, different members will undertake refurbishing products to maximize the interests of all parties involved. The findings of this paper indicate that the supplier favors Model B when the return policy (r) is small. However, for larger r values, the supplier will opt for either Model A or Model C. Additionally, this paper finds that retailers are more likely to choose Model C when the return policy reaches a specific value. Theoretically, this study extends the existing literature on the value of return policy and fills the gap in research on the impact of return policy on expanding green supply chains. Through developing a new game model, the impact mechanism of return policy in the competition between remanufactured and new products is analyzed in depth, providing academics with a fresh perspective on how to reshape supply chain structures to increase members' profitability. The study provides market management professionals and business managers with valuable insights for strategic decision-making, especially determining which party is responsible for recycling and refurbishing remanufactured products. In addition, the findings provide an important reference for government intervention to effectively expand the market for remanufactured products by adjusting the gap between product return policies, thereby optimizing resource utilization, promoting environmental protection, and enhancing the resilience and sustainability of green supply chains.
PubDate: 2025-05-29
- Integrated airline aircraft routing and crew pairing by alternating
Lagrangian decomposition-
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Abstract: For the aircraft routing and crew pairing problems, a sequential approach is usually used to solve they. When solving the crew pairing problem, the impact of aircraft routing problem is often neglected so that these two problems are independent. This approach reduces the complexity of the solution process, but it may obtain a suboptimal solution. In this paper, we consider an integrated aircraft routing and crew pairing problem. We propose an integrated model that integrates the aircraft routing and crew pairing problems. We propose a solution algorithm based on a heuristic alternating Lagrangian decomposition to address coupling constraint of the integrated model. The solution algorithm iterates between the first Lagrangian subproblem about aircraft routing and the second Lagrangian subproblem about crew pairing. These two Lagrangian subproblems are solved by a branch-and-price algorithm. In the branch-and-price algorithm, we present a heuristic branching strategy. The computational experiments are conducted on several real-world data sets.
PubDate: 2025-05-29
- Robust static and dynamic maximum flows
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Abstract: We study the robust maximum flow problem and the robust maximum flow over time problem where a given number of arcs $$\Gamma $$ may fail or may be delayed. Two prominent models have been introduced for these problems: either one assigns flow to arcs fulfilling weak flow conservation in any scenario, or one assigns flow to paths where an arc failure or delay affects a whole path. We provide a unifying framework by presenting novel general models, in which we assign flow to subpaths. These models contain the known models as special cases and unify their advantages in order to obtain less conservative robust solutions.We give a thorough analysis with respect to complexity of the general models. In particular, we show that the general models are essentially NP-hard, whereas, e.g., in the static case with $$\Gamma =1$$ an optimal solution can be computed in polynomial time. Further, we answer the open question about the complexity of the dynamic path model for $$\Gamma =1$$. We also compare the solution quality of the different models. In detail, we show that the general models have better robust optimal values than the known models and we prove bounds on these gaps.
PubDate: 2025-05-25
- Improved approximation algorithms for multiprocessor indivisible coflow
scheduling-
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Abstract: Coflow scheduling is a challenging optimization problem that underlies many data transmission and parallel computing applications. In this paper, we study the indivisible coflow scheduling problem on parallel identical machines with the objective to minimize the makespan, i.e., the completion time of the last flow. In our problem setting, the number of the input/output ports in each machine is a fixed constant, each port has a unit capacity, and all the flows inside a coflow should be scheduled on the same machine. We present a $$(2 + \epsilon )$$-approximation algorithm for the problem, for any $$\epsilon > 0$$, in which the number of machines can be either a fixed constant or part of the input.
PubDate: 2025-05-25
- Smart health system with deep kronecker network-based key generation for
privacy-aware aggregate authentication and access control in IoT-
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Abstract: The Internet of Things (IoT) application is an application and service that incorporates both the physical and information world. Similarly, it is difficult for existing health systems to provide privacy-aware aggregate authentication and fine-grained access control. To bridge the concern, a smart health system (SHS) with Deep Kronecker Network_key generation (DKN_keyGen) for privacy-aware aggregate authentication and access control in IoT is implemented. Here, entities employed for this model such as data owner (DO), registration center (RC), data user (DU) and cloud service provider (CSP). The method follows four steps, such as system initialization, user registration, Health data outsourcing and Health data access. Initially, the RC needs to initialize the security parameters, random parameters and public keys. After that, DO and DU must be registered in RC. Moreover, the smart health care data of DO generates the secret parameter and also obtains the secret parameter from the RC. The cloud storage stores and manages health care data in the health data outsourcing step. Finally, for health data access, the user gives appropriate parameters and access to the data which is implemented in the data access phase. The model is established considering different security functionalities including Encryption, ECC, XoR and hashing function. Here, the key is generated using DKN. The proposed model obtained a minimum computation time of 6.857 s, memory usage of 30 MB, and communication cost of 20.
PubDate: 2025-05-25
- The influence of carbon sink trading on carbon emission reduction in
agricultural supply chains-
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Abstract: As global climate change intensifies, the agricultural sector, responsible for over 30% of global greenhouse gas emissions, faces an urgent imperative to mitigate emissions and align with international climate commitments. Carbon sink trading, a market-based mechanism that incentivizes emission reductions through sequestration credits, has emerged as an important tool for accelerating carbon peaking and neutrality goals. This study investigates the influence of carbon sink trading on the strategic interactions between farmers and retailers in agricultural supply chains. Employing differential game theory, we construct three cooperative models: decentralized, Stackelberg leader-follower, and centralized, and derive equilibrium strategies for each using the Hamilton-Jacobi-Bellman framework. Through numerical simulations, we evaluate the influence of carbon sink trading on the emission reduction efforts of farmers and retailers, the extent of emission reductions in the supply chain, and the overall profits. Comparative analysis against baseline scenarios without carbon trading reveals that the integration of carbon sink markets enhances profit margins across all models and improves the level of emission reduction in the agricultural supply chain. In addition, our results show that the centralized model outperforms other configurations, followed by the Stackelberg model, with the decentralized model exhibiting the least effectiveness. These findings provide actionable insights for policymakers and supply chain managers to design carbon trading frameworks that harmonize economic incentives with ecological sustainability.
PubDate: 2025-05-25
- Approximating the maximum weight cycle/path partition in graphs with
weights one and two-
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Abstract: In this paper, we investigate the maximum weight k-cycle (k-path) partition problem (MaxWkCP/MaxWkPP for short). The input consists of an undirected complete graph $$G=(V,E)$$ with $$ V =kn$$, where k, n are positive integers, and a non-negative weight function on E, the objective is to determine n vertex disjoint k-cycles (k-paths), which are cycles (paths) containing exactly k vertices, covering all the vertices such that the total edge weight of these cycles (paths) is as large as possible. We propose improved approximation algorithms for the MaxWkCP/MaxWkPP in graphs with weights one and two. For the MaxWkCP in graphs with weights one and two, we obtain an approximation algorithm having an approximation ratio of $$\frac{37}{48}$$ for $$k=6$$, which improves upon the best available $$\frac{91}{120}$$-approximation algorithm by Zhao and Xiao 2024a. When $$k=4$$, we show that the same algorithm is a $$\frac{7}{8}$$-approximation algorithm and give a tight example. This ratio ties with the state-of-the-art result, also given by Zhao and Xiao 2024a. However, we demonstrate that our algorithm can be applied to the minimization variant of MaxWkCP in graphs with weights one and two and achieve a tight approximation ratio of $$\frac{5}{4}$$. For the MaxW5PP in graphs with weights one and two, we devise a novel $$\frac{19}{24}$$-approximation algorithm by combining two separate algorithms, each of which handles one of the two complementary scenarios of the optimal solution well. This ratio is better than the previous best ratio of $$\frac{3}{4}$$ due to Li and Yu 2023.
PubDate: 2025-05-25
- ZeSAI: AI vigilant malware detection in email security with zero
shot-based hybrid network and threat intelligence integration-
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Abstract: In this ever-evolving world of threats, e-mail security is becoming one of the biggest concerns because attackers are constantly searching for new techniques to bypass the existing security measures. Emails containing phishing, malware and other security threats have become far more common place, which is why there is a need to implement new and more efficient adaptive threat detection frameworks. Typically, email security products are outdated within these emerging threats hence the need to evolve into something more effective and smarter in the detection systems. In this regard, Zero Short learning based Artificial Intelligence (ZeSAI)-model is proposed as a new approach to improve threat identification in the context of email security. Initially, to ensure generalization and robust performance, the model uses three broad sets of input data: augmented data based on Context-Preserving Synthetic Email Generation (CPSEG) method and adversarial data, both generated from six datasets and Threat Intelligence feeds offering real-time updates. The proposed ZeSAI model enhances email threat detection through a structured workflow: eXtreme Language Network (XLNet) first generates bidirectional contextual embeddings from email content, capturing nuanced semantic relationships. The Recurrent GRU Network (RGN) then analyses temporal patterns in the email data, identifying complex relationships and variations over time. These RGN-extracted features are integrated with XLNet-generated semantic embeddings in the Cross-Modal Fusion Layer. Finally, Zero-Shot Learning (ZSL) utilizes these combined semantic descriptions and contextual insights to identify new threats based on their similarities to known threats, enabling robust and adaptive threat detection. The proposed approach yields good accuracy and other performance measures; precision, recall, and F1-score; under fivefold and tenfold cross-validation. An ablation study is also carried out to pinpoint the contribution of each module. Specifically, ZeSAI has accuracy of 98.51% in Business Email Compromise (BEC) threat detection, 96.8% in spam detection, 99.18% in phishing detection, 97.2% in malware attachment detection and 98.58% in detecting insider threats.
PubDate: 2025-05-25
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