Journal of Combinatorial Optimization最新文献

Customer segmentation, a critical strategy in marketing, involves grouping consumers based on shared characteristics like age, income, and geographical location, enabling firms to effectively establish different strategies depending on the target group of customers. Clustering is a widely utilized data analysis technique that facilitates the identification of diverse groups, each distinguished by their unique set of characteristics. Traditional clustering techniques often lack in handling the complexity of consumer data. This paper introduces a novel approach employing the Flying Fox Optimization algorithm, inspired by the survival strategies of flying foxes, to determine customer segments. Applied to two different datasets, this method demonstrates superior capability in identifying distinct customer groups, thereby facilitating the development of targeted marketing strategies. Our comparative analysis with existing state-of-the-art as well as recently developed clustering methods reveals that the proposed method outperforms them in terms of segmentation capabilities. This research not only presents an innovative clustering technique in market segmentation but also showcases the potential of computational intelligence in improving marketing strategies, enhancing their alignment with each customer’s needs.

With the rapid development of network architectures and application technologies, there is an increasing number of latency-sensitive tasks generated by user devices, necessitating real-time processing on edge servers. During peak periods, user devices compete for limited edge resources to execute their tasks, while different edge servers also compete for transaction opportunities. This article focus on resource allocation problems in competitive edge networks with multiple participants. Considering the decreasing value of tasks over time, a Greedy Method with Priority Order (GMPO) mechanism based on auction theory is designed to maximize the overall utility of the entire network. This mechanism consists of a short-slot optimal resource allocation phase, a winner determination phase that ensures monotonicity, and a pricing phase based on critical prices. Theoretical analysis demonstrates that the GMPO mechanism can prevent user devices from engaging in dishonest transactions. Experimental results indicate that it significantly enhances the overall utility of competitive edge networks.

In this work, we consider the Submodular Maximization under Knapsack ((textsf{SMK})) constraint problem over the ground set of size n. The problem recently attracted a lot of attention due to its applications in various domains of combinatorial optimization, artificial intelligence, and machine learning. We improve the approximation factor of the fastest deterministic algorithm from (6+epsilon ) to (5+epsilon ) while keeping the best query complexity of O(n), where (epsilon >0) is a constant parameter. Our technique is based on optimizing the performance of two components: the threshold greedy subroutine and the building of two disjoint sets as candidate solutions. Besides, by carefully analyzing the cost of candidate solutions, we obtain a tighter approximation factor.

In the field of optimization algorithms, nature-inspired techniques have garnered attention for their adaptability and problem-solving prowess. This research introduces the Arctic Fox Algorithm (AFA), an innovative optimization technique inspired by the adaptive survival strategies of the Arctic fox, designed to excel in dynamic and complex optimization landscapes. Incorporating gradient flow dynamics, stochastic differential equations, and probability distributions, AFA is equipped to adjust its search strategies dynamically, enhancing both exploration and exploitation capabilities. Through rigorous evaluation on a set of 25 benchmark functions, AFA consistently outperformed established algorithms particularly in scenarios involving high-dimensional and multi-modal problems, demonstrating faster convergence and improved solution quality. Application of AFA to real-world problems, including wind farm layout optimization and financial portfolio optimization, highlighted its ability to increase energy outputs by up to 15% and improve portfolio Sharpe ratios by 20% compared to conventional methods. These results showcase AFA’s potential as a robust tool for complex optimization tasks, paving the way for future research focused on refining its adaptive mechanisms and exploring broader applications.

In order to maximize full-view coverage of moving targets in Camera Sensor Networks (CSNs), a novel method known as “group set cover” is presented in this research. Choosing the best camera angles and placements to accomplish full-view coverage of the moving targets is one of the main focuses of the research in CSNs. Discretize the target into multiple views of [0, 2(pi )], use a set of views of targets to represent the sensing direction of the camera sensor, and use a group set of views of targets to represent the position of the camera sensor. The total number of targets in a dynamic time window that is visible in full view is calculated. A mixed integer linear programming formulation is employed, which is then approximated using a random rounding method. This approximation approach offers a global estimation of local optimality, particularly for non-submodular optimization problems. Two methods for maximizing overall full-view coverage within a dynamic time window are proposed TSC-FTC-DTW and FTC-TW-DTW. Finally, the proposed methods are verified through experiments.

The neighbor-connectivity of a graph G, denoted by (kappa _{NB}(G)), is the least number of vertices such that removing their closed neighborhoods from G results in a graph that is empty, complete, or disconnected. In the paper, we show that for any graph G of order n, (kappa _{NB}(G)le lceil sqrt{2n} rceil -2). We pose a conjecture that (kappa _{NB}(G)le lceil sqrt{n} rceil -1) for a graph G of order n. For supporting it, we show that the conjecture holds for any triangle-free graphs, Cartesian, direct, lexicographic product of any two graphs.

This paper studies a due-window assignment scheduling problem with deterioration effects on a single-machine. Under different due-window assignment, i.e., the due-window of a job without any restriction, our goal is to make a decision on the optimal due-window and sequence of all jobs to minimize the weighted sum of earliness and tardiness, number of early and delayed, due-window starting time and size. We present properties of the optimal solutions, for some special cases, we prove that the problem can be solved in polynomial time. For the general case, we present a lower bound and an upper bound (i.e., a heuristic algorithm), then a branch-and-bound algorithm is proposed.

A k-edge coloring (varphi ) of a graph G is injective if (varphi (e_1)ne varphi (e_3)) for any three consecutive edges (e_1, e_2) and (e_3) of a path or a triangle. The injective chromatic index (chi _i'(G)) of G is the smallest k such that G admits an injective k-edge coloring. By discharging method, we demonstrate that any graph with maximum degree (Delta le 5) has (chi _i'(G)le 12) (resp. 13) if its maximum average degree is less than (frac{20}{7}) (resp. 3), which improves the results of Zhu (2023).

We study the non-submodular maximization problem, whose objective function can be expressed as the Difference between two Set (DS) functions or the Ratio between two Set (RS) functions. For the cardinality-constrained and unconstrained DS maximization problems, we present several deterministic algorithms and our analysis shows that the algorithms can provide provable approximation guarantees. As an application, we manage to derive an improved approximation bound for the DS minimization problem under certain conditions compared with existing results. As for the RS maximization problem, we show that there exists a polynomial-time reduction from the approximation of RS maximization to the approximation of DS maximization. Based on this reduction, we derive the first approximation bound for the cardinality-constrained RS maximization problem. We also devise algorithms for the unconstrained problem and analyze their approximation guarantees. By applying our results to the problem of optimizing the ratio between two supermodular functions, we give an answer to the question posed by Bai et al. (in Proceedings of The 33rd international conference on machine learning (ICML), 2016). Moreover, we give an example to illustrate that whether the set function is normalized has an effect on the approximability of the RS optimization problem.