This study addresses the problem of finding an anti-Berge equilibrium in a bimatrix game based on a global search algorithm. Finding the anti-Berge equilibrium reduces equivalently to a quadratic programming with an indefinite matrix and linear constraints, which belongs to a class of global optimization. To solve the problem numerically, we develop a modified parallel tangent algorithm. The proposed algorithm uses the one-dimensional nonlocal search procedure based on the Strongin and parabolas methods. The stop criterion of the algorithm is the sufficient condition for anti-Berge equilibrium. The proposed algorithm is implemented and numerically tested on a range of bimatrix games.
The quality, accessibility, and stability of the business environment directly affect the competitiveness and growth of enterprises. Therefore, this study aims to classify Mongolia’s business environment using machine learning techniques and identify each cluster’s specific characteristics and key influencing factors. The research utilizes data from 4,073 enterprises operating in Mongolia as of 2020, comprising 104 variables related to the business environment. Since the original dataset contained many missing values, imputation was necessary. Mode and K-Nearest Neighbors (KNN) imputation methods—commonly used in research—were tested. Their mean absolute errors (MAE) were evaluated against the original data, and KNN (MAE = 0.0119) demonstrated higher accuracy than Mode (MAE = 0.0438). As a result, the KNN-imputed dataset was used for further analysis. Five clustering algorithms were applied to group the data, and their performance was assessed using three metrics: Silhouette Score, Davies-Bouldin Index, and Calinski-Harabasz Score. Among these, the HDBSCAN model yielded the best results (Silhouette Score = 0.435, DB Index = 0.409), and after removing 1,051 enterprises classified as noise, the remaining 2,852 enterprises were grouped into three clusters. Additionally, Random Forest classification and SHAP analysis were used to identify the most influential features in cluster formation. The study showed that bank interest rates, the effectiveness of government policies, and household living standards had the most significant impact on cluster differentiation. By identifying these key drivers, this study provides scientifically grounded insights that support evidence-based decision-making for policymakers and researchers seeking to improve the business environment.
Critical node detection involves identifying key nodes whose removal significantly disrupts network connectivity or performance. The evaluation of vulnerability in networks is crucial because many real-world problems are represented as graphs with uncertainty, including social networks, communication infrastructures, epidemiological models, and transportation systems. In this paper, we consider a stochastic Critical Node Detection Problem (SCNDP) with edge uncertainty, aiming to minimize the expected pairwise connectivity (EPC) in the resulting residual network. We propose a heuristic method for the SCNDP and compare it with the existing algorithm. Experimental results performed on random graphs with different edge-probability configurations demonstrate the effectiveness of the heuristics.
The n-dimensional folded hypercube FQ_n is a well-known extension of the n-dimensional hypercube that can be constructed by adding an edge to every pair of vertices with complementary addresses. The existence of the Hamiltonian cycle provides advantages for implementing algorithms that require a ring structure. In addition, k (≥ 2) edge-disjoint Hamiltonian cycles also provide higher transmission efficiency for all-to-all communication algorithms and provide fault-tolerant routing for network transmission. This paper proves that there exist two edge-disjoint Hamiltonian cycles on FQ_n while n ≥ 3 ; and for k edge-disjoint Hamiltonian cycles on FQ_n , the maximum k is 2 while n ∈{3, 4} and 3 while n ∈{5, 6} .
Submodular optimization is an important topic in the field of combinatorial optimization. The k-submodular function is a generalization of the submodular function. Many machine learning problems, such as placing k types of sensors, can be formulated as maximizing a monotone k-submodular function. In real-world optimization problems where the constraints involve random components, chance constraints are often used to limit the probability of constraint violations due to random factors. In this paper, we investigate the problem of maximizing a monotone k-submodular function under the chance constraint. Specifically, each element e is assigned a random weight independently sampled from a uniform distribution. We study two distinct cases, in which the weights are drawn from a common uniform distribution or from element-specific uniform distributions, all with the same dispersion. For the first case, this paper designs a threshold-decreasing algorithm with an approximation ratio of 1/2-ϵ . For the second case, this paper first designs a deterministic algorithm, which uses the method of dividing the ground set into two parts, and then combines its output solution with the threshold-greedy algorithm to design an algorithm with an approximation ratio of 1/3-ϵ .
