Journal of Combinatorial Optimization最新文献

Cloud computing has a powerful capability to handle a large number of tasks. However, this capability comes with significant energy requirements. It is critical to overcome the challenge of minimizing energy consumption within cloud service platforms without compromising service quality. In this paper, we propose a heuristic energy-saving scheduling algorithm, called Real-time Multi-workflow Energy-efficient Scheduling (RMES), which aims to minimize the total energy consumption in a container-based cloud. RMES schedules tasks in the most parallelized way to improve the resource utilization of the running machines in the cluster, thus reducing the time of the global process and saving energy. This paper also considers the affinity constraints between containers and machines, and RMES has the ability to satisfy the resource quantity and performance requirements of containers during the scheduling process. We introduce a re-scheduling mechanism that automatically adjusts the scheduling decisions of remaining tasks to account for the dynamic system states over time. The results show that RMES outperforms other scheduling algorithms in energy consumption and success rate. In the higher arrival rate scenario, the proposed algorithm saves energy consumption by more than 19.42%. The RMES approach can enhance the reliability and efficiency of scheduling systems.

Consider a set of items, X, with a total of n items, among which a subset, denoted as (Isubseteq X), consists of defective items. In the context of group testing, a test is conducted on a subset of items Q, where (Q subset X). The result of this test is positive, yielding 1, if Q includes at least one defective item, that is if (Q cap I ne emptyset ). It is negative, yielding 0, if no defective items are present in Q. We introduce a novel method for deriving lower bounds in the context of non-adaptive randomized group testing. For any given constant j, any non-adaptive randomized algorithm that, with probability at least 2/3, estimates the number of defective items |I| within a constant factor requires at least

tests. Our result almost matches the upper bound of (O(log n)) and addresses the open problem posed by Damaschke and Sheikh Muhammad in (Combinatorial Optimization and Applications - 4th International Conference, COCOA 2010, pp 117–130, 2010; Discrete Math Alg Appl 2(3):291–312, 2010). Furthermore, it enhances the previously established lower bound of (Omega (log n/log log n)) by Ron and Tsur (ACM Trans Comput Theory 8(4): 15:1–15:19, 2016), and independently by Bshouty (30th International Symposium on Algorithms and Computation, ISAAC 2019, LIPIcs, vol 149, pp 2:1–2:9, 2019). For estimation within a non-constant factor (alpha (n)), we show: If a constant j exists such that (alpha >{log log {mathop {cdots }limits ^{j}}log n}), then any non-adaptive randomized algorithm that, with probability at least 2/3, estimates the number of defective items |I| to within a factor (alpha ) requires at least

In this case, the lower bound is tight.

Consider a simple (edge weighted) graph (G = left( {V,E} right)) with (left| V right| = n) and (left| E right| = m). Let (xy in E). The domination of a vertex (z in V) by an edge (xy) is defined as (z) belonging to the closed neighborhood of either (x) or (y). An edge set (W) is considered as an edge-vertex dominating set of (G) if each vertex of (V) is dominated by some edge of (W). The (weighted) edge-vertex domination problem aims to find an edge-vertex dominating set of (G) with the minimum cardinality. Let (M subseteq V) and (N subseteq E). Given a positive integer (p), if a vertex (z) is dominated by (p) edges in set (N), then set (N) is called a (p) edge-vertex dominating set of graph (G) with respect to (M). This study investigates the edge-vertex domination problem and the (p) edge-vertex domination problem, presents an algorithm with a time complexity of (Oleft( {nm^{2} } right)) for solving the weighted edge-vertex domination problem on unit interval graphs. Moreover, algorithms have been developed with time complexities of (Oleft( {mlg m + pleft| M right| + n} right)) and (Oleft( {nleft| M right|} right)) for identifying a minimum (p) edge-vertex dominating set of an interval graph (G) and a tree (T), respectively, with respect to any subset (M subseteq V).

Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. In this paper, we are concerned with determining the smallest value of g such that a given graph G has an embedding on the orientable surface of genus g. In particular, we consider the Cartesian product of graphs since this is a well studied graph operation which is often used for modeling interconnection networks. The s-cube (Q_i^{(s)}) is obtained by taking the repeated Cartesian product of i complete bipartite graphs (K_{s,s}). We determine the genus of the Cartesian product of the 2r-cube with the repeated Cartesian product of cycles and of the Cartesian product of the 2r-cube with the repeated Cartesian product of paths.

In this paper we study a scheduling problem with release dates and submodular rejection penalties on multiple (parallel) identical serial-batch machines. For this problem, each machine processes jobs in batches, jobs in a common batch start and finish simultaneously, and the duration of a batch is equal to the sum of a setup time and the total processing time of jobs in it. Some jobs are accepted and processed on the machines, while the left jobs are rejected with penalty and the total rejection penalty is determined by a submodular function. The objective function to be minimized is the sum of the makespan of accepted jobs and the total rejection penalty. For the scenario of an arbitrary number of machines and submodular rejection penalties, we give a 2-approximation algorithm by which the objective function value of the obtained schedule is no more than twice that of the optimal schedule. For the scenario of a fixed number of machines and linear rejection penalties, we give a pseudo-polynomial-time dynamic programming exact algorithm and a fully polynomial-time approximation scheme.

In this paper, a reduced quadratic surface support vector machine (RQSSVM) classification model is proposed and solved using the augmented Lagrange method. The new model can effectively handle nonlinearly separable data without kernel function selection and parameter tuning due to its quadratic surface segmentation facility. Meanwhile, the maximum margin term is replaced by an (L_2) regularization term and the Hessian of the quadratic surface is reduced to a diagonal matrix. This simplification significantly reduces the number of decision variables and improves computational efficiency. The (L_1) loss function is used to transform the problem into a convex composite optimization problem. Then the transformed problem is solved by the Augmented Lagrange method and the non-smoothness of the subproblems is handled by the semi-smooth Newton algorithm. Numerical experiments on artificial and public benchmark datasets show that RQSSVM model not only inherits the superior performance of quadratic surface SVM for segmenting nonlinear surfaces, but also significantly improves the segmentation speed and efficiency.

Solving the optimal order quantity for products with stock-dependent demand is a challenging task as both exact values of multiple parameters and complicated procedures are required. Motivated by this practical dilemma, this paper develops a new method to overcome the above-mentioned two challenges simultaneously. This new method, referred as two-stage AEOQ (adaptive economic order quantity) policy, includes the following two merits when managing products with stock-dependent demand and variable holding cost rate. First, it is feasible even when the values of underlying parameters are unknown. Second, it is easy-to-implement as decisions are made via adaptively recalibrating the inputs of classical EOQ formula by observable variables in the previous period. Theoretical analysis and numerical example show that this two-stage AEOQ policy could obtain the optimal order quantity. Moreover, this two-stage AEOQ policy is robust to parameter misestimation, and performs better than the traditional solution method when the underlying parameters are volatile. Finally, it is shown that this two-stage AEOQ policy could be further simplified when the fixed ordering cost is negligible. Therefore, this study provides a feasible order policy when the exact values of underlying parameters are unable to gain or when the economic environment is volatile.

The performance of machine learning algorithms is significantly influenced by the quality of the underlying dataset, which often comprises a mix of essential and redundant features. Feature selection, which identifies and discards these redundant features, plays a pivotal role in reducing computational and storage overheads. Current methodologies for this task primarily span filter-based and wrapper-based techniques. While Ant Colony Optimization, a popular bio-inspired meta-heuristic technique, has been extensively used for feature selection, employing mutual information as a principal heuristic measure, traditional mutual information is primarily suited for categorical features. To address this limitation, this study introduces an Embedded-Filter Ant Colony Optimization feature selection strategy that incorporates Clustering-Based Mutual Information. This integration offers enhanced support for classification tasks involving continuous features. To validate the efficiency of the proposed approach, various datasets were used, and a diverse range of machine learning algorithms were employed to evaluate the derived feature subsets. In addition to comparing the proposed method with Grey Wolf Optimization and Cuckoo Search Optimization-based feature selection approaches, a comprehensive evaluation was also carried out against established Ant Colony Optimization wrapper techniques. Experimental results indicate that the proposed Embedded-Filter Ant Colony Optimization consistently selects the minimal yet most relevant feature set while largely maintaining the efficacy of machine learning algorithms.

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

For a connected graph G, an instance I is a set of pairs of vertices and a corresponding routing R is a set of paths specified for all vertex-pairs in I. Let (mathfrak {R}_I) be the collection of all routings with respect to I. The undirected optical index of G with respect to I refers to the minimum integer k to guarantee the existence of a mapping (phi :Rrightarrow {1,2,ldots ,k}), such that (phi (P)ne phi (P')) if P and (P') have common edge(s), over all routings (Rin mathfrak {R}_I). A natural lower bound of the undirected optical index is the edge-forwarding index, which is defined to be the minimum of the maximum edge-load over all possible routings. Let w(G, I) and (pi (G,I)) denote the undirected optical index and edge-forwarding index with respect to I, respectively. In this paper, we derive the inequality (w(T,I_A)<frac{3}{2}pi (T,I_A)) for any tree T, where (I_A:={{x,y}:,x,yin V(T)}) is the all-to-all instance.