Journal of Combinatorial Optimization最新文献

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.

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$K_n$. It is known that the 1-factorization of any Kirkman schedule is “perfect” when n=p+1$n=p+1$ for prime numbers p, meaning that any pair of 1-factors in the 1-factorization forms a Hamilton cycle C_n$C_n$ in K_n$K_n$, called a 2-edge-colored Hamilton cycle. We are concerned

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.

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.

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.

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.

For graphs G and H, the Ramsey number R(G, H) is the smallest r such that any red-blue edge coloring of (K_r) contains a red G or a blue H. The path-critical Ramsey number (R_{pi }(G,H)) is the largest n such that any red-blue edge coloring of (K_r setminus P_{n}) contains a red G or a blue H, where (r=R(G,H)) and (P_{n}) is a path of order n. In this note, we show a general upper bound for (R_{pi }(G,H)), and determine the exact values for some cases of (R_{pi }(G,H)).

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.

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.