Journal of Combinatorial Optimization最新文献

Diagnosis of thyroid disease is a most important cause in the field of medicinal research and it is a complex onset axiom. Secretion of Thyroid hormone plays a major role in the regulation of metabolism. Hence, it is very significant to predict thyroid disease in the initial stage, which is helpful for preventing more serious health complications due to thyroid cancer. The diagnostic accuracy of machine leaning-based approaches is greater but these techniques require large amounts of data for the diagnosis process. In the conventional approaches, the time needed for the prediction process is also high. Feature engineering is less investigated in conventional models and hence error produced during the prediction process is high. Hence, in this research work, a machine learning-aided thyroid disease prediction technique is designed to provide higher prediction accuracy and reliability. Initially, the thyroid data is gathered from the standard benchmark resources. Next, the data transformation process is carried out to make the data usable for analysis and visualization. After, the features are extracted using Principal Component Analysis (PCA), “One-Dimensional Convolutional Neural Network Model (1DCNN). Moreover, the statistical features are also extracted for getting more relevant information from the data. The three sets of features such as PCA-based, 1DCNN-based and statistical are concatenated and fed to the “optimal weighted feature selection” process, where the optimal features and weights are tuned by an Improved Archimedes Optimization Algorithm (IAOA). Next, the selected optimally fused features are given to the Ensemble Learning (EL) for predicting the thyroid diseases, where the EL with be suggested by incorporating stacking classifier, XGboost, and Multivariate regression classifier. Ensembling of three different classifiers provides higher thyroid disease prediction accuracy and it makes the decision about normal and abnormal classes. Here, the same IAOA is used for optimizing the parameters of every classifier. The investigational outcomes demonstrate that the proposed ensemble classifier provides higher performance than others. Experimental results prove that the thyroid prediction accuracy of the developed EL approach is 96.30%, precision is 99.67% and F1-score is 97.93%, which is more extensive than the state-of-the-art approaches.

In a graph G, the normal k-edge coloring (sigma ) is defined as the conventional edge coloring of G using the color set (left[ k right] =left{ 1,2,cdots ,k right} ). If the condition (Sleft( u right) ne Sleft( v right) ) holds for any edge (uvin Eleft( G right) ), where (Sleft( u right) =sum nolimits _{uvin Eleft( G right) }{sigma left( uv right) }), then (sigma ) is termed a neighbor sum distinguishable k-edge coloring of the graph G, abbreviated as k-VSDEC. The minimum number of colors ( k ) needed for this type of coloring is referred to as the neighbor sum distinguishable edge chromatic number of ( G ), represented as ( chi '_{varSigma }(G) ). This paper examines neighbor sum distinguishable k-edge colorings in the joint graphs of an h-order path ({{P}_{h}}) and an (left( z+1 right) )-order star ({{S}_{z}}), providing exact values for their neighboring and distinguishable edge coloring numbers, which are either (varDelta ) or (varDelta +1).

In recent years, k-submodular functions have garnered significant attention due to their natural extension of submodular functions and their practical applications, such as influence maximization and sensor placement. Influence maximization involves selecting a set of nodes in a network to maximize the spread of information, while sensor placement focuses on optimizing the locations of sensors to maximize coverage or detection efficiency. This paper first proposes two randomized algorithms aimed at improving the approximation ratio for maximizing monotone k-submodular functions under matroid constraints and individual size constraints. Under the matroid constraints, we design a randomized algorithm with an approximation ratio of (frac{nk}{2nk-1}) and a complexity of (O(rn(text {RO}+ktext {EO}))), where n represents the total number of elements in the ground set, k represents the number of disjoint sets in a k-submodular function, r denotes the size of the largest independent set, (text {RO}) indicates the time required for the matroid’s independence oracle, and (text {EO}) denotes the time required for the evaluation oracle of the k-submodular function.Meanwhile, under the individual size constraints, we achieve an approximation factor of (frac{nk}{3nk-2}) with a complexity of O(knB), where n is the total count of elements in the ground set, and B is the upper bound on the total size of the k disjoint subsets, belonging to (mathbb {Z_{+}}). Additionally, this paper designs two double randomized algorithms to accelerate the algorithm’s running speed while maintaining the same approximation ratio, with success probabilities of ((1-delta )), where (delta ) is a positive parameter input by the algorithms. Under the matroid constraint, the complexity is reduced to (O(nlog rlog frac{r}{delta }(text {RO}+ktext {EO}))). Under the individual size constraint, the complexity becomes (O(k^{2}nlog frac{B}{k}log frac{B}{delta })).

Today, artificial bee colony (ABC) algorithm is one of the most popular swarm intelligence based optimization techniques. Although it was originally introduced to work on continuous space for numerical optimization problems, several researchers also successfully use the ABC for other problem types. In this study, variants of the ABC for scheduling problems are surveyed. Since the scheduling problems are combinatorial type problems, generally some modifications related to the solution representation or neighborhood search operators are introduced in these studies. Additionally, several enhancement ideas are also presented for the ABC algorithm such as the improvements of initialization, employed bee, onlooker bee, scout bee phases and hybrid usage with other metaheuristics or local search methods. This paper evaluates the literature, provides some analyses on its current state and gaps, and addresses possible future works. It is hoped that this review study would be beneficial for the researchers interested in this field.

In the A-Multi3-Hitting Set problem (A-M3HS), where (A subseteq {1,2,3}), the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k, and the goal is to decide if there is a set S of at most k vertices such that (|S cap e| in A) for every hyperedge e. In this paper we give (O^*(2.027^k))-time algorithms for ({1})-M3HS and ({1,3})-M3HS, and an (O^*(1.381^k))-time algorithm for ({2})-M3HS.

Green manufacturing is used to describe an environmentally friendly manufacturing approach, which explicitly considers the impact of production on the environment and resources. Therefore, the production scheduling of solving energy conscious is in line with the focus of green manufacturing. In this paper, we consider the scheduling problems with rejection in the green manufacturing industry. The objective is to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs, subject to the constraint that the total machine cost of the processed jobs is not more than a given threshold. We present pseudo-polynomial time algorithms and 2-approximation algorithms for the single-machine and the parallel-machine problems, respectively.

The cubic knapsack problem (CKP) is a combinatorial optimization problem, which can be seen both as a generalization of the quadratic knapsack problem (QKP) and of the linear Knapsack problem (KP). This problem consists of maximizing a cubic function of binary decision variables subject to one linear knapsack constraint. It has many applications in biology, project selection, capital budgeting problem, and in logistics. The QKP is known to be strongly NP-hard, which implies that the CKP is also NP-hard in the strong sense. Unlike its linear and quadratic counterparts, the CKP has not received much of attention in the literature. Thus the few exact solution methods known for this problem can only handle problems with up to 60 decision variables. In this paper, we propose a deterministic dynamic programming-based heuristic algorithm for finding a good quality solution for the CKP. The novelty of this algorithm is that it operates in three different space variables and can produce up to three different solutions with different levels of computational effort. The algorithm has been tested on a set of 1570 test instances, which include both standard and challenging instances. The computational results show that our algorithm can find optimal solutions for nearly 98% of the standard test instances that could be solved to optimality and for 92% for the challenging instances. Finally, the computational experiments present comparisons between our algorithm, an existing heuristic algorithm for the CKP found in the literature, as well as adaptations to the CKP of some heuristic algorithms designed for the QKP. The results show that our algorithm outperforms all these methods.

In this paper, we focus on analyzing the 3-path vertex cover (3PVC) problem in a number of graph classes. Let (G=(V,E)) be a simple graph. A set (C subseteq V) is called a k-path vertex cover of G, if each path of order k in G, contains at least one vertex from C. In the k-path vertex cover problem, we are given a graph G, and asked to find a k-path vertex cover of minimum size. For (k=3), the problem becomes the well-known 3PVC problem. A problem that is closely related to the 3PVC problem is the dissociation set (DS) problem. Given a graph (G=(V,E)), a dissociation set is any (D subseteq V), such that the vertex-induced subgraph (G'= (D,E')) consists of vertices having degree 0 or 1. In the dissociation set problem, we are required to find a dissociation set of maximum cardinality. Both these problems have also been studied extensively as per the literature. In this paper, we focus on pipartite (planar and bipartite) graphs for the most part. We first show that the 3PVC problem is NP-hard, even in pipartite graphs having maximum degree 4. We then show that the 3PVC problem on this class of graphs admits a linear time (frac{8}{5})-approximation algorithm. Next, we show that the 3PVC problem is APX-complete in bipartite graphs having maximum degree 4 and cubic graphs. Finally, we discuss an elegant and alternative proof for the APX-completeness of the vertex cover problem in cubic graphs and establish lower bounds for the 3PVC problem in special graph classes. It is important to note that our work is the first of its kind to establish APX-completeness of the 3PVC problem in graphs.

This work considers a semi-online version of scheduling on m identical machines, where the objective is to minimize the makespan. In the variant studied here, jobs are presented sorted by non-increasing sizes, and a buffer of size k is available for storing at most k jobs. Every arriving job has to be either placed into the buffer until its assignment, or else it has to be assigned immediately to a machine. We prove a lower bound greater than 1 on the competitive ratio of the problem for any m and any buffer size. To complement this negative result, we design a simple algorithm for any m whose competitive ratio tends to 1 as the buffer size grows. Using those results, we show the best possible competitive ratio is (1+Theta (frac{m}{k})). We provide additional bounds for small values of m. In particular, we show that for (m=2) the case (k=1) is not different from the case without a buffer, while (k=2) admits an improved competitive ratio.

Chaos optimization algorithm (COA) is an interesting alternative in a global optimization problem. Due to the non-repetition and ergodicity of chaos, it can explore the global search space at higher speeds than stochastic searches that depend on probabilities. To adjust the solution obtained by COA, guided local search algorithm (GLS) is integrated with COA to form a hybrid algorithm. GLS is a metaheuristic optimization algorithm that combines elements of local search with strategic guidance to efficiently explore the solution space. This study proposes a chaotic guided local search algorithm to search for global solutions. The proposed algorithm, namely COA-GLS, contributes to optimization problems by providing a balance between quick convergence and good solution quality. Its combination of local refinement, strategic guidance, diversification strategies, and adaptability makes it a powerful metaheuristic capable of efficiently navigating complex solution spaces and finding high-quality solutions in a relatively short amount of time. Simulation results show that the present algorithms significantly outperform the existing methods in terms of convergence speed, numerical stability, and a better optimal solution than other algorithms.