Journal of Combinatorial Optimization最新文献

The Probabilistic p-Center problem under Pressure (Min P p CP) is a variant of the usual Min p-Center problem we recently introduced in the context of wildfire management. The problem is to locate p shelters minimizing the maximum distance people will have to cover in case of fire in order to reach the closest accessible shelter. The landscape is divided into zones and is modeled as an edge-weighted graph with vertices corresponding to zones and edges corresponding to direct connections between two adjacent zones. The risk associated with fire outbreaks is modeled using a finite set of fire scenarios. Each scenario corresponds to a fire outbreak on a single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuation path cannot pass through the vertex on fire. Second, the fact that someone close to the fire may not take rational decisions when selecting a direction to escape is modeled using new kinds of evacuation paths. In this paper, we characterize the set of feasible solutions of Min P p CP-instance. Then, we propose some approximation results for Min P p CP. These results require approximation results for two variants of the (deterministic) Min p-Center problem called Min MAC p-Center and Min Partial p-Center.

In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to the next stage of production or distribution after its completion. The objective is to minimize the number of bins used and the spread of customer orders over the cutting process. The 2BPP-OS gains relevance in manufacturing environments that seek minimum waste solutions with satisfactory levels of customer service. We propose integer linear programming (ILP) models for variants of the 2BPP-OS that consider non-guillotine, 2-stage, restricted 3-stage, and unrestricted 3-stage patterns. We are not aware of integrated approaches for the 2BPP-OS in the literature despite its relevance in practical settings. Using a general-purpose ILP solver, the results show that the 2BPP-OS takes more computational effort to solve than the 2BPP, as it has to consider several symmetries that are often disregarded by the traditional 2BPP approaches. The solutions obtained by the proposed approaches have similar bin usage and significantly better metrics of customer satisfaction concerning the approaches that neglect the customer order spread.

With the advancement of electronic service platforms, customers exhibit various purchasing behaviors. Given the extensive array of options and minimal exit barriers, customer migration from one digital service to another has become a common challenge for businesses. Customer churn prediction (CCP) emerges as a crucial marketing strategy aimed at estimating the likelihood of customer abandonment. In this paper, we aim to predict customer churn intentions using a novel robust meta-classifier. We utilized three distinct datasets: transaction, telecommunication, and customer churn datasets. Employing Decision Tree, Random Forest, XGBoost, AdaBoost, and Extra Trees as the five base supervised classifiers on these three datasets, we conducted cross-validation and evaluation setups separately. Additionally, we employed permutation and SelectKBest feature selection to rank the most practical features for achieving the highest accuracy. Furthermore, we utilized BayesSearchCV and GridSearchCV to discover, optimize, and tune the hyperparameters. Subsequently, we applied the refined classifiers in a funnel of a new meta-classifier for each dataset individually. The experimental results indicate that our proposed meta-classifier demonstrates superior accuracy compared to conventional classifiers and even stacking ensemble methods. The predictive outcomes serve as a valuable tool for businesses in identifying potential churners and taking proactive measures to retain customers, thereby enhancing customer retention rates and ensuring business sustainability.

In this paper, we consider the following two-machine no-wait flow shop scheduling problem with two competing agents (F2~|~M_1rightarrow M_2,~ M_2,~ p_{ij}^{A} = p,~ notext{- }wait~|~C_{max }^A:~ C_{max }^B~le Q ): Given a set of n jobs (mathcal {J} = { J_1, J_2, ldots , J_n}) and two competing agents A and B. Agent A is associated with a set of (n_A) jobs (mathcal {J}^A = {J_1^A, J_2^A, ldots , J_{n_A}^A}) to be processed on the machine (M_1) first and then on the machine (M_2) with no-wait constraint, and agent B is associated with a set of (n_B) jobs (mathcal {J}^B = {J_1^B, J_2^B, ldots , J_{n_B}^B}) to be processed on the machine (M_2) only, where the processing times for the jobs of agent A are all the same (i.e., (p_{ij}^A = p)), (mathcal {J} = mathcal {J}^A cup mathcal {J}^B) and (n = n_A + n_B). The objective is to build a schedule (pi ) of the n jobs that minimizing the makespan of agent A while maintaining the makespan of agent B not greater than a given value Q. We first show that the problem is polynomial time solvable in some special cases. For the non-solvable case, we present an (O(n log n))-time ((1 + frac{1}{n_A +1}))-approximation algorithm and show that this ratio of ((1 + frac{1}{n_A +1})) is asymptotically tight. Finally, ((1+epsilon ))-approximation algorithms are provided.

In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are (d_{u_i}+d_{u_j}), if (u_i) is connected to (u_j); 0, otherwise, where (d_{u_i}) is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ((rho _1)) associated with this matrix. The lower and upper bounds of (rho _1) are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of (rho _1) is also explained.

The online graph exploration problem, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the origin), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.

This paper concerns online portfolio selection problem whose main feature is with no any statistical assumption on future asset prices. Since online portfolio selection aims to maximize the cumulative wealth, most existing online portfolio strategies do not consider risk factors into the model. To enrich the research on online portfolio selection, we introduce the risk factors into the model and propose two novel risk-adjusted online portfolio strategies. More specifically, we first choose several exponential gradient ((text {EG}(eta ))) with different values of parameter (eta ) to build an expert pool. Later, we construct two risk methods to measure performance of each expert. Finally, we calculate the portfolio by the weighted average over all expert advice. We present theoretical and experimental results respectively to analyze the performance of the proposed strategies. Theoretical results show that the proposed strategies not only track the expert with the lowest risk, but also are universal, i.e., they exhibit the same asymptotic average logarithmic growth rate as best constant rebalanced portfolio (BCRP) determined in hindsight. We conduct extensive experiments by using daily stock data collected from the American and Chinese stock markets. Experimental results show the proposed strategies outperform existing online portfolio in terms of the return and risk metrics in most cases.

In this work, we focus on maximizing the stochastic DS decomposition problem. If the constraint is a uniform matroid, we design an adaptive policy, namely Myopic Parameter Conditioned Greedy, and prove its theoretical guarantee (f(varTheta (pi _k))-(1-c_G)g(varTheta (pi _k))ge (1-e^{-1})F(pi ^*_A, varTheta (pi _k)) - G(pi ^*_A,varTheta (pi _k))), where (F(pi ^*_A, varTheta (pi _k)) = mathbb {E}_{varTheta }[f(varTheta (pi ^*_A)) vert varTheta (pi _k)]). When the constraint is a general matroid constraint, we design the Parameter Measured Continuous Conditioned Greedy to return a fractional solution. To round an integer solution from the fractional solution, we adopt the lattice contention resolution and prove that there is a ((b, frac{1-e^{-b}}{b})) lattice CR scheme under a matroid constraint. Additionally, we adopt the pipage rounding to obtain a non-adaptive policy with the theoretical guarantee (F(pi )-(1-c_G)G(pi ) ge (1-e^{-1}) F(pi ^*_A) - G(pi ^*_A) - O(epsilon )) and utlize the ((1,1-e^{-1}))-lattice contention resolution scheme (tau ) to obtain an adaptive solution (mathbb {E}_{tau sim varLambda } [f(tau (varTheta (pi )))- (1-c_G) g(tau (varTheta (pi )))] ge (1-e^{-1})^2F(pi ^*_A,varTheta (pi )) - (1-e^{-1}) G(pi ^*_A,varTheta (pi )) -O(epsilon )). Since any set function can be expressed as the DS decomposition, our framework provides a method for solving the maximization problem of set functions defined on a random variable set.

Göring–Helmberg–Wappler introduced optimization problems regarding embeddings of a graph into a Euclidean space and the first nonzero eigenvalue of the Laplacian of a graph, which are dual to each other in the framework of semidefinite programming. In this paper, we introduce a new graph-embedding optimization problem, and discuss its relation to Göring–Helmberg–Wappler’s problems. We also identify the dual problem to our embedding optimization problem. We solve the optimization problems for distance-regular graphs and the one-skeleton graphs of the (textrm{C}_{60}) fullerene and some other Archimedian solids.

Grey wolf optimizer (GWO) is one of the most popular metaheuristics, and it has been presented as highly competitive with other comparison methods. However, the basic GWO needs some improvement, such as premature convergence and imbalance between exploitation and exploration. To address these weaknesses, this paper develops a hybrid grey wolf optimizer (HGWO), which combines the Halton sequence, dimension learning-based, crisscross strategy, and Cauchy mutation strategy. Firstly, the Halton sequence is used to enlarge the search scope and improve the diversity of the solutions. Then, the dimension learning-based is used for position update to balance exploitation and exploration. Furthermore, the crisscross strategy is introduced to enhance convergence precision. Finally, the Cauchy mutation strategy is adapted to avoid falling into the local optimum. The effectiveness of HGWO is demonstrated by comparing it with advanced algorithms on the 15 benchmark functions in different dimensions. The results illustrate that HGWO outperforms other advanced algorithms. Moreover, HGWO is used to solve eight real-world engineering problems, and the results demonstrate that HGWO is superior to different advanced algorithms.