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We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra's projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra's projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations. [ABSTRACT FROM AUTHOR]

The problem of finding optimal block designs can be formulated as a combinatorial optimization, but its resolution is still a formidable challenge. This paper presents a general and user-friendly algorithm, namely Modified Particle Swarm Optimization (MPSO), to construct optimal or near-optimal block designs. It can be used for several classes of block designs such as binary, non-binary and test-control block designs with correlated or uncorrelated observations. In order to evaluate the algorithm, we compare our results with the optimal designs presented in some published papers. An advantage of our algorithm is its independency to the sizes of blocks and the structure of correlations. [ABSTRACT FROM AUTHOR]

The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream model, the state-of-the-art single-pass semi-streaming algorithm for it is still a simple greedy algorithm that computes a maximal matching, and this way obtains 1 / 2 -approximation. Some previous works described two/three-pass algorithms that improve over this approximation ratio by using their second and third passes to improve the above mentioned maximal matching. One contribution of this paper continues this line of work by presenting new three-pass semi-streaming algorithms that work along these lines and obtain improved approximation ratios of 0.6111 and 0.5694 for triangle-free and general graphs, respectively. Unfortunately, a recent work Konrad and Naidu (Approximation, randomization, and combinatorial optimization. Algorithms and techniques, APPROX/RANDOM 2021, August 16–18, 2021. LIPIcs, vol 207, pp 19:1–19:18, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.19) shows that the strategy of constructing a maximal matching in the first pass and then improving it in further passes has limitations. Additionally, this technique is unlikely to get us closer to single-pass semi-streaming algorithms obtaining a better than 1 / 2 -approximation. Therefore, it is interesting to come up with algorithms that do something else with their first pass (we term such algorithms non-maximal-matching-first algorithms). No such algorithms were previously known, and the main contribution of this paper is describing such algorithms that obtain approximation ratios of 0.5384 and 0.5555 in two and three passes, respectively, for general graphs. The main significance of our results is not in the numerical improvements, but in demonstrating the potential of non-maximal-matching-first algorithms. [ABSTRACT FROM AUTHOR]

Terrain visibility analysis is vital in geospatial research, employing computer geometry and graphics principles for computing and visualizing visibility between observation and target points. The observation point setup problem is crucial for tasks like sentry point selection and signal base station placement. This problem involves choosing the minimum viewpoints on terrain for optimal joint view coverage, presenting a combinatorial optimization challenge. As technology advances, data can be acquired with increasing precision, the number of viewpoints that can be extracted from the same area is gradually increasing as well, obtaining candidate viewpoints and determining optimal combinations become challenging. This paper proposes a novel method, Stepwise Maximum Viewshed (SMV), addressing observation point setup by stepwise filtering the maximum viewshed and can customize the size of the observation point combination. In complex mountainous terrain, the SMV algorithm demonstrates superior joint view coverage compared to Candidate Viewpoints Filtering (CVF) and Simulated Annealing (SA) algorithms. Experimental results reveal up to 5.59% improvement over CVF and a maximum of 12.52% over SA in joint viewshed coverage. [ABSTRACT FROM AUTHOR]

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to feature noises, outlier nodes, and global transformation (e.g. rotation). In this paper, we propose a graph neural network (GNN) based approach to combine the advantage of data-driven and traditional methods. In the GNN framework, we transform traditional graph matching solvers as single-channel GNNs on the association graph and extend the single-channel architecture to the multi-channel network. The proposed model can be seen as an ensemble method that fuses multiple algorithms at every iteration. Instead of averaging the estimates at the end of the ensemble, in our approach, the independent iterations of the ensembled algorithms exchange their information after each iteration via a 1 × 1 channel-wise convolution layer. Experiments show that our model improves the performance of traditional algorithms significantly. In addition, we propose a random sampling strategy to reduce the computational complexity and GPU memory usage, so that the model is applicable to matching graphs with thousands of nodes. We evaluate the performance of our method on three tasks: geometric graph matching, semantic feature matching, and few-shot 3D shape classification. The proposed model performs comparably or outperforms the best existing GNN-based methods. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) have been extensively researched and deployed in both military and civilian applications due to their tiny size, low cost, and great ease. Although UAVs working together on complicated jobs can significantly increase productivity and reduce costs, they can cause major issues with path planning. In complex environments, the path planning problem, which is a multiconstraint combinatorial optimization problem and hard to settle, requires considering numerous constraints and limitations and generates the best paths for each UAV to accomplish group tasks. In this paper, we study the path planning problem for multiple UAVs and propose a reinforcement learning algorithm: PERDE‐MADDPG based on prioritized experience replay (PER) and delayed update skills. First, we adopt a PER mechanism based on temporal difference (TD) error to enhance the efficiency of experience utilization and accelerate the convergence speed of the algorithm. Second, we use delayed updates in the process of updating network parameters to ensure stability in training multiple agents. Finally, we propose the PERDE‐MADDPG algorithm based on PER and delayed update skills, which is evaluated against the MATD3, MADDPG, and SAC methods in simulation scenarios to confirm its efficacy. [ABSTRACT FROM AUTHOR]

We consider the weighted k-set packing problem, where, given a collection S of sets, each of cardinality at most k, and a positive weight function w : S → Q > 0 , the task is to find a sub-collection of S consisting of pairwise disjoint sets of maximum total weight. As this problem does not permit a polynomial-time o (k log k) -approximation unless P = N P (Hazan et al. in Comput Complex 15:20–39, 2006. https://doi.org/10.1007/s00037-006-0205-6), most previous approaches rely on local search. For twenty years, Berman's algorithm SquareImp (Berman, in: Scandinavian workshop on algorithm theory, Springer, 2000. https://doi.org/10.1007/3-540-44985-X%5f19), which yields a polynomial-time k + 1 2 + ϵ -approximation for any fixed ϵ > 0 , has remained unchallenged. Only recently, it could be improved to k + 1 2 - 1 63 , 700 , 993 by Neuwohner (38th International symposium on theoretical aspects of computer science (STACS 2021), Leibniz international proceedings in informatics (LIPIcs), 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.53). In her paper, she showed that instances for which the analysis of SquareImp is almost tight are "close to unweighted" in a certain sense. But for the unit weight variant, the best known approximation guarantee is k + 1 3 + ϵ (Fürer and Yu in International symposium on combinatorial optimization, Springer, 2014. https://doi.org/10.1007/978-3-319-09174-7%5f35). Using this observation as a starting point, we conduct a more in-depth analysis of close-to-tight instances of SquareImp. This finally allows us to generalize techniques used in the unweighted case to the weighted setting. In doing so, we obtain approximation guarantees of k + ϵ k 2 , where lim k → ∞ ϵ k = 0 . On the other hand, we prove that this is asymptotically best possible in that local improvements of logarithmically bounded size cannot produce an approximation ratio below k 2 . [ABSTRACT FROM AUTHOR]

The quantum alternating operator ansatz (QAOA) and its predecessor, the quantum approximate optimization algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet no rigorous proof of convergence for the QAOA, we provide one in this paper. The proof involves retracing the connection between the quantum adiabatic algorithm and the QAOA, and naturally suggests a refined definition of the 'phase separator' and 'mixer' keywords. [ABSTRACT FROM AUTHOR]

In this paper, we study the knapsack problem with conflict pair constraints. After a thorough literature survey on the topic, our study focuses on the special case of bipartite conflict graphs. For complete bipartite (multipartite) conflict graphs, the problem is shown to be NP-hard but solvable in pseudo-polynomial time, and it admits an FPTAS. Extensions of these results to more general classes of graphs are also presented. Further, a class of integer programming models for the general knapsack problem with conflict pair constraints is presented, which generalizes and unifies the existing formulations. The strength of the LP relaxations of these formulations is analyzed, and we discuss different ways to tighten them. Experimental comparisons of these models are also presented to assess their relative strengths. This analysis disclosed various strong and weak points of different formulations of the problem and their relationships to different types of problem data. This information can be used in designing special purpose algorithms for KPCC involving a learning component. [ABSTRACT FROM AUTHOR]

As a classical combinatorial optimization problem, the traveling salesman problem (TSP) has been extensively investigated in the fields of Artificial Intelligence and Operations Research. Due to being NP-complete, it is still rather challenging to solve both effectively and efficiently. Because of its high theoretical significance and wide practical applications, great effort has been undertaken to solve it from the point of view of intelligent search. In this paper, we propose a two-stage probe-based search optimization algorithm for solving both symmetric and asymmetric TSPs through the stages of route development and a self-escape mechanism. Specifically, in the first stage, a reasonable proportion threshold filter of potential basis probes or partial routes is set up at each step during the complete route development process. In this way, the poor basis probes with longer routes are filtered out automatically. Moreover, four local augmentation operators are further employed to improve these potential basis probes at each step. In the second stage, a self-escape mechanism or operation is further implemented on the obtained complete routes to prevent the probe-based search from being trapped in a locally optimal solution. The experimental results on a collection of benchmark TSP datasets demonstrate that our proposed algorithm is more effective than other state-of-the-art optimization algorithms. In fact, it achieves the best-known TSP benchmark solutions in many datasets, while, in certain cases, it even generates solutions that are better than the best-known TSP benchmark solutions. [ABSTRACT FROM AUTHOR]

In this paper, we focus on Hitting-Set , a fundamental problem in combinatorial optimization, through the lens of sublinear time algorithms. Given access to the hypergraph through a subset query oracle in the query model, we give sublinear time algorithms for Hitting-Set with almost tight parameterized query complexity. In parameterized query complexity , we estimate the number of queries to the oracle based on the parameter k , the size of the Hitting-Set. The subset query oracle we use in this paper is called Generalized d -partite Independent Set query oracle (GPIS) and it was introduced by Bishnu et al. (ISAAC'18). GPIS is a generalization to hypergraphs of the Bipartite Independent Set query oracle (BIS) introduced by Beame et al. (ITCS'18 and TALG'20) for estimating the number of edges in graphs. Since its introduction GPIS query oracle has been used for estimating the number of hyperedges independently by Dell et al. (SODA'20 and SICOMP'22) and Bhattacharya et al. (STACS'22), and for estimating the number of triangles in a graph by Bhattacharya et al. (ISAAC'19 and TOCS'21). Formally, GPIS is defined as follows: GPIS oracle for a d-uniform hypergraph H takes as input d pairwise disjoint non-empty subsets A 1 , ... , A d of vertices in H and answers whether there is a hyperedge in H that intersects each set A i , where i ∈ { 1 , 2 , ... , d }. For d = 2 , the GPIS oracle is nothing but BIS oracle. We show that d - Hitting-Set , the hitting set problem for d -uniform hypergraphs, can be solved using O ˜ d (k d log ⁡ n) GPIS queries. Additionally, we also showed that d - Decision-Hitting-Set , the decision version of d - Hitting-Set can be solved with O ˜ d (min ⁡ { k d log ⁡ n , k 2 d 2 }) GPIS queries. We complement these parameterized upper bounds with an almost matching parameterized lower bound that states that any algorithm that solves d - Decision-Hitting-Set requires Ω (( k + d d )) GPIS queries. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the Bees Algorithm (BA) called Bees Algorithm with 2-parameter (BA2), which is a population-based metaheuristic algorithm designed to solve continuous and combinatorial optimisation problems. The proposed algorithm simplified the BA's parameters by combining exploration and exploitation strategies while preserving the algorithm's core principles to efficiently search for optimal solutions. The paper provides a detailed description of the algorithm's core principles and its application to two engineering problems, the air-cooling system design (ACSD) and the printed circuit board assembly sequence optimisation (PASO). The results show that BA2 outperforms previous versions of the basic BA in terms of convergence speed and solution quality. However, the authors acknowledge that further research is needed to test the scalability and generalisability of the algorithm to larger and more diverse optimisation problems. Overall, this paper provides valuable insights into the potential of metaheuristics for solving real-world optimisation problems. [ABSTRACT FROM AUTHOR]

The mathematical side of applied problems in multiple subject areas (biology, pattern recognition, etc.) is reduced to the problem of discrete optimization in the following mathematical method. We were provided a network and graphs in its leaves, for which we needed to find a rearrangement of graphs by non-leaf nodes, in which the given functional reached its minimum. Such a problem, even in the simplest case, is NP-hard, which means unavoidable restrictions on the network, on graphs, or on the functional. In this publication, this problem is addressed in the case of all graphs being so-called "structures", meaning directed-loaded graphs consisting of paths and cycles, and the functional as the sum (over all edges in the network) of distances between structures at the endpoints of every edge. The distance itself is equal to the minimal length of sequence from the fixed list of operations, the composition of which transforms the structure at one endpoint of the edge into the structure at its other endpoint. The list of operations (and their costs) on such a graph is fixed. Under these conditions, the given discrete optimization problem is called the reconstruction problem. This paper presents novel algorithms for solving the reconstruction problem, along with full proofs of their low error and low polynomial complexity. For example, for the network, the problem is solved with a zero error algorithm that has a linear polynomial computational complexity; and for the tree the problem is solved using an algorithm with a multiplicative error of at most two, which has a second order polynomial computational complexity. [ABSTRACT FROM AUTHOR]

Cost is the foremost factor in decision-making for profit-driven organizations. However, hybrid flow shop scheduling (HFSS) research rarely prioritizes cost as its optimization objective. Existing studies primarily focus on electricity costs linked to machine utilization. This paper introduces a comprehensive cost-based HFSS model, encompassing electricity, labor, maintenance, and penalty costs. Next, the Tiki-Taka Algorithm (TTA) is improved by increasing the exploration capability to optimize the problem. The cost-based HFSS model and TTA algorithm have been tested using benchmark and case study problems. The results indicated that the TTA consistently outperforms other algorithms. It delivers the best mean fitness and better solution distribution. In industrial contexts, the TTA able to reduces costs by 2.8% to 12.0% compared to other approaches. This holistic cost-based HFSS model empowers production planners to make more informed decisions. Furthermore, the improved TTA shows promise for broader applicability in various combinatorial optimization domains. [ABSTRACT FROM AUTHOR]

Genetic Algorithms (GAs) are known for their efficiency in solving combinatorial optimization problems, thanks to their ability to explore diverse solution spaces, handle various representations, exploit parallelism, preserve good solutions, adapt to changing dynamics, handle combinatorial diversity, and provide heuristic search. However, limitations such as premature convergence, lack of problem-specific knowledge, and randomness of crossover and mutation operators make GAs generally inefficient in finding an optimal solution. To address these limitations, this paper proposes a new metaheuristic algorithm called the Genetic Engineering Algorithm (GEA) that draws inspiration from genetic engineering concepts. GEA redesigns the traditional GA while incorporating new search methods to isolate, purify, insert, and express new genes based on existing ones, leading to the emergence of desired traits and the production of specific chromosomes based on the selected genes. Comparative evaluations against state-of-the-art algorithms on benchmark instances demonstrate the superior performance of GEA, showcasing its potential as an innovative and efficient solution for combinatorial optimization problems. [ABSTRACT FROM AUTHOR]

Outlier detection is of great significance in the domain of data mining. Its task is to find those target points that are not identical to most of the object generation mechanisms. The existing algorithms are mainly divided into density-based algorithms and distance-based algorithms. However, both approaches have some drawbacks. The former struggles to handle low-density modes, while the latter cannot detect local outliers. Moreover, the outlier detection algorithm is very sensitive to parameter settings. This paper proposes a new two-parameter outlier detection (TPOD) algorithm. The method proposed in this paper does not need to manually define the number of neighbors, and the introduction of relative distance can also solve the problem of low density and further accurately detect outliers. This is a combinatorial optimization problem. Firstly, the number of natural neighbors is iteratively calculated, and then the local density of the target object is calculated by adaptive kernel density estimation. Secondly, the relative distance of the target points is computed through natural neighbors. Finally, these two parameters are combined to obtain the outlier factor. This eliminates the influence of parameters that require users to determine the number of outliers themselves, namely, the top-n effect. Two synthetic datasets and 17 real datasets were used to test the effectiveness of this method; a comparison with another five algorithms is also provided. The AUC value and F1 score on multiple datasets are higher than other algorithms, indicating that outliers can be found accurately, which proves that the algorithm is effective. [ABSTRACT FROM AUTHOR]

The Digital Annealer is a CMOS hardware designed by Fujitsu Laboratories for high-speed solving of Quadratic Unconstrained Binary Optimization (QUBO) problems that could be difficult to solve by means of existing general-purpose computers. In this paper, we present a mathematical description of the first-generation Digital Annealer's Algorithm from the Markov chain theory perspective, establish a relationship between its stationary distribution with the Gibbs-Boltzmann distribution, and provide a necessary and sufficient condition on its cooling schedule that ensures asymptotic convergence to the ground states. [ABSTRACT FROM AUTHOR]

Nodes localization has been a critical subject in wireless sensor network (WSN) field. As far as existing localization algorithms are concerned, distance vector hop (DV-Hop) has the advantages of no extra hardware and implementation simplicity, however its localization accuracy cannot meet some specific requirements. In order to enhance the accuracy of WSN nodes localization, a DV-Hop based localization algorithm based on nodes negotiation and multi communication radii (NNMCR DV-Hop) is proposed in this paper. Firstly, the hop counts between WSN nodes is modified from an integer to a decimal by changing communication radius of anchor nodes through nodes negotiation. By refining the hop counts, the accuracy of the estimated distance from the unknown to the anchor nodes is improved. Secondly, the calculation of the average hop size of the anchor node is abstracted into a combinatorial optimization problem which is solved by using binary particle swarm optimization (BPSO) to improve the accuracy of the estimated distance which is between the anchor and the unknown node. Finally, when calculating the coordinates of unknown nodes, only the anchor nodes with smaller hop counts are selected to participate in the calculation. Simulation experiments show that compared with the original DV-Hop as well as other improved algorithms based on DV-Hop, NNMCR DV-Hop greatly improves the localization accuracy of unknown nodes without additional hardware. [ABSTRACT FROM AUTHOR]

Whale optimization algorithm is a new swarm intelligence optimization algorithm inspired by humpback whale hunting behavior, and its performance is far better than the traditional algorithms. In order to track the latest research results and promote the research in the field of swarm intelligence optimization algorithm, this paper firstly introduced the basic principle of whale optimization algorithm, briefly described its implementation steps, and compared and analyzed its pe1formance characteristics. In view of its shortcomings of slow convergence speed and low convergence accuracy, this paper summarized and analyzed the improved methods including other intelligent optimization algorithms, Levy flight strategy, chaos strategy, as well as their advantages and limitations. Then, it described its applications and effect in combinatorial optimization, image segmentation, data prediction, and so on. Finally, this paper summarized and prospected the future development trend. [ABSTRACT FROM AUTHOR]

Recently, substantial progress has been made in developing efficient algorithms for solving combinatorial optimization problems. In this paper, following this direction, the problem of designing supply chains which is an important combinatorial optimization problem is considered. The structural properties of supply chain models are investigated to transform such models into a generalized network optimization model. The transformation to a generalized network optimization model reduces the algorithms' solution time. Moreover, this paper proposes a new efficient hybrid algorithm based on tabu search and generalized network simplex algorithm (GN-TSA) for designing multi-objectives supply chain models. The developed algorithm's parameters are tuned properly, validated, and evaluated. The algorithm's performance is then compared to an exact algorithm embedded in the General Algebraic Modeling System (GAMS) and two metaheuristic algorithms, namely a linear programming simplex algorithm integrated with the tabu search approach (LP-TSA) and simulated annealing. The findings indicated that the GN-TSA obtains solutions very close to the exact algorithm with less computation time. In addition, the proposed algorithm outperforms the LP-TSA and simulated annealing in terms of computation time, while the quality of the solutions is the same as solutions obtained by LP-TSA and better than simulated annealing. On average, the results revealed that the reduction in computational time is more than 26.30% using GN-TSA compared to LP-TSA and simulated annealing. [ABSTRACT FROM AUTHOR]

This paper presents a Q-learning-based algorithm for sequence and orientation optimization toward the 2D rectangular strip packing problem. The width-filled skyline is used to represent the interior packing state, and a constructive rectangular packing algorithm with the commonly adopted fitness evaluation for placement is designed. Then, the consecutive item packing is simulated as Markov Decision Process, where the state is defined as the set of already packed items, and the action is defined as the rectangle selected to be packed along with its orientation. We propose the reverse updating of Q-value in the paradigm of Q-learning and use the algorithm to optimize the sequence and orientation of the rectangles. The decreasing-size-choice mechanism in Q-learning is studied on randomly generated problems to optimize the setting of ε-greedy policy. We also test the Q-learning-based algorithm on the benchmark instances of C21, N13, N-series from NT, Cgcut and Beng. Compared with a few state-of-the-art algorithms, the computational results show that the proposed algorithm can produce good packing quality when adequate execution time allowed. [ABSTRACT FROM AUTHOR]

As a meta-heuristic algorithm, the ant colony algorithm has been successfully used to solve various combinatorial optimization problems. However, the existing algorithm that takes the power of ants to solve distributed constraint optimization problems (ACO_DCOP) is easy to fall into local optima. To deal with this issue, this paper presents an adaptive ant colony algorithm based on local information entropy to solve distributed constraint optimization problems, named LIEAD. In LIEAD, the local information entropy is introduced to help agents adaptively select the pheromone update strategy and value selection strategy, which improves the convergence speed and the quality of the solution. Moreover, a restart mechanism is designed to break the accumulation state of pheromone, which increases the population diversity and helps the algorithm jump out of the local optima. The extensive experimental results indicate that LIEAD can significantly outperform ACO_DCOP and is competitive with the state-of-the-art DCOPs algorithms. [ABSTRACT FROM AUTHOR]

A hybrid algorithm combines two or more individual algorithms in order to integrate the advantages of these individual algorithms. In recent years, a huge number of hybrid algorithms have been proposed, and their efficiencies have been demonstrated by experimental studies. However, few theoretical results that support the experimental conclusions are available. In this paper, we focus on theoretical investigation about the efficiency of hybrid algorithms for combinatorial optimization problems. We first analyze the runtime of three specific hybrid algorithms and their component algorithms on two instances. One is a well-known pseudo-Boolean function, and the other is an instance of a classical combinatorial optimization problem. We then theoretically investigate the relationship between the upper bounds of the expected runtime of three kinds of general hybrid algorithms and their component algorithms. [ABSTRACT FROM AUTHOR]

The rectangular layout problem with balance constraints is a combinatorial optimization problem, which is difficult to solve when the problem scale increases. To improve the performance, this paper designed a bee colony algorithm. By analyzing the distribution of solutions, it provided a greedy initialization scheme for the population, selected an effective mutation operator, and limited the search space around the optimal solution. In addition, it designed a local search module to further improve the quality of the solution. On 10 open test cases, the algorithm was compared with the best known existing algorithms, and the performance of the proposed algorithm exceeded the existing algorithms on 9 large-scale cases. The theoretical analysis and experimental results show that the proposed algorithm can significantly improve the efficiency of solution. [ABSTRACT FROM AUTHOR]

In the scenario of device-free localization under multiple effects, the accuracy of localization based on compressed sensing theory is severely affected. Most existing localization techniques directly ignore multiple path effects. However, it is not practical to ignore the multiple path effect due to its high signal strength, which can provide localization information. In this paper, we formulate the sensing matrix optimization problem in compressed sensing for device-free localization scenarios based on multiple reflections. To solve this problem, we model it as a constrained combinatorial optimization problem and propose a hybrid meta-heuristic algorithm. First, smart reflection surfaces and virtual node models are used to construct the desired communication links. Second, we iteratively improve the properties of the measurement matrix by using K-means clustering to obtain reasonable thresholds, and use a meta-heuristic algorithm to optimize the sensing matrix. Finally, the simulation results show that the proposed method efficiently optimizes the sensing matrix and achieves fast and high-precision localization while conserving communication resources. [ABSTRACT FROM AUTHOR]

• The adaptive bulk search is a QUBO solver alternative to quantum annealing. • The cyclic-min algorithm is a SA-like algorithm without random number generation. • The bit permutated cyclic-min algorithm provides near-optimal solutions for QUBO. • Our scalable implementation attains linear improvement of the search rate. A wide range of combinatorial optimization problems can be reduced to the Ising model, and equivalently the quadratic unconstrained binary optimization (QUBO) problem. Thus, in recent years, researchers have proposed to solve QUBO on FPGAs, GPUs, and special-purpose processors. The adaptive bulk search (ABS) is a previously-proposed framework for solving QUBO in parallel on multiple GPUs. In the ABS, a CPU host performs a GA-based global search while GPUs asynchronously perform many local searches in parallel. An original ABS adopts a simple local search algorithm called a cyclic-min algorithm, which does not use pseudo random numbers. However, the lack of randomness may cause a potential drawback of restricted bit-flipping operations in a local search. To avoid this drawback, this paper proposes a cyclic-min algorithm with randomly-generated multiple bit permutations, which enables a more effective local search with random number generation in CPUs (not in GPUs). Furthermore, this paper introduces a scalable implementation of the ABS with MPI and OpenMP. Our experimental results on TSUBAME3.0 show that the solution quality improves and the throughput linearly increases as the number of GPUs increases; with 256 GPUs, it evaluates 20.1 × 10 12 solutions per second. [ABSTRACT FROM AUTHOR]

The two-dimension strip packing problem (2DSPP) is an NP-hard combinatorial optimization problem, and it has a wide range of applications. The order in which the rectangles are placed in the strip is the key to solving the 2DSPP. In this paper, the corner increment multi-level scoring strategy and the two-step selection strategy are proposed to make the selection of rectangles more reasonable. The hierarchical construction strategy is used to improve the constructive heuristic algorithm to expand the search space of the rectangle selection. Based on this, this paper proposes a multi-strategy rectangle selection algorithm TSMSA for solving 2DSPP. Comparing experiments with 7 excellent algorithms for solving 2DSPP on 737 instances of the benchmark dataset shows that the instance number of the optimal solution obtained by TSMSA is 1.05~2.9 times that of the other 7 algorithms. [ABSTRACT FROM AUTHOR]

Message propagation algorithms from statistical physics are widely used in various fields of artificial intelligence, especially in solving combinatorial optimization problems. According to the related literatures of message propagation algorithm, this paper summarized the history of message propagation algorithm and its related application. According to the development of message propagation algorithm, it introduced the concepts of information propagation algorithm for solving the satisfiability problem, which mainly involved the warning propagation algorithm, the belief propagation algorithm and the survey propagation algorithm. This paper described the convergence and effectiveness research of the three kind of algorithms, summarized the application of each algorithm in related fields, and summarized the research path and application direction of message propagation algorithm. [ABSTRACT FROM AUTHOR]

Recently, graph neural network (GNN)-based algorithms were proposed to solve a variety of combinatorial optimization problems [M. J. Schuetz, J. K. Brubaker, H. G. Katzgraber, Nat. Mach. Intell. 4, 367-377 (2022)].GNNwas tested in particular on randomly generated instances of these problems. The publication [M. J. Schuetz, J. K. Brubaker, H. G. Katzgraber, Nat. Mach. Intell. 4, 367-377 (2022)] stirred a debate whether the GNN-based method was adequately benchmarked against best prior methods. In particular, critical commentaries [M. C. Angelini, F. Ricci-Tersenghi, Nat. Mach. Intell. 5, 29-31 (2023)] and [S. Boettcher, Nat. Mach. Intell. 5, 24-25 (2023)] point out that a simple greedy algorithm performs better than the GNN. We do not intend to discuss the merits of arguments and counterarguments in these papers. Rather, in this note, we establish a fundamental limitation for running GNN on random instances considered in these references, for a broad range of choices of GNN architecture. Specifically, these barriers hold when the depth of GNN does not scale with graph size (we note that depth 2 was used in experiments in [M. J. Schuetz, J. K. Brubaker, H. G. Katzgraber, Nat. Mach. Intell. 4, 367-377 (2022)]), and importantly, these barriers hold regardless of any other parameters of GNN architecture. These limitations arise from the presence of the overlap gap property (OGP) phase transition, which is a barrier for many algorithms, including importantly local algorithms, of which GNN is an example. At the same time, some algorithms known prior to the introduction of GNN provide best results for these problems up to the OGP phase transition. This leaves very little space for GNN to outperform the known algorithms, and based on this, we side with the conclusions made in [M. C. Angelini, F. Ricci-Tersenghi, Nat. Mach. Intell. 5, 29-31 (2023)] and [S. Boettcher, Nat. Mach. Intell. 5, 24-25 (2023)]. [ABSTRACT FROM AUTHOR]

The maximum internal spanning tree (MIST) problem is to find a spanning tree with maximum number of internal node for an undirected graph. It is a variation of the well-known minimum spanning tree problem and is NP-hard. Evolutionary algorithms (EAs) have been successfully applied to solve many NP-hard combinatorial optimization problems in numerical empirical studies. However, researchers know little about their performance guarantees from theory aspect. This paper designs a valid fitness function to guide the well-studied evolutionary algorithm, (1 + 1) EA , to optimize the MIST problem, and presents theoretical analysis to show that it can obtain a performance guarantee of 2 and 5/3 in expected runtime O (n m 2) and O (n m 4) , respectively. Moreover, this paper proves that the (1+1) EA can achieve a performance guarantee of 3 for a variation of the MIST problem, where each vertex is associated with a weight. In addition, comparison analyses on two family instance graphs are presented to show that (1 + 1) EA is better than two local search algorithms. This theoretical study provides insight into the process of (1 + 1) EA constructing a performance guarantee solution for the MIST problem. [ABSTRACT FROM AUTHOR]

Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, which utilize the particular structure of this class of problems, to obtain more efficient algorithms than those offered by general SDP solvers. For certain applications, such as those described in this paper, it may be desirable to obtain sparse dual solutions, i.e., those with support size (almost) independent of the number of primal constraints. In this paper, we give an algorithm that finds such solutions, which is an extension of a logarithmic-potential based algorithm of Grigoriadis et al. [SIAM J. Optim. 11 (2001), pp. 1081-1091] for packing/covering linear programs. [ABSTRACT FROM AUTHOR]

The knapsack problem (KP) is a discrete combinatorial optimization problem that has different utilities in many fields. It is described as a non-polynomial time (NP) problem and has several applications in many fields. The differential evolution (DE) algorithm has been successful in solving continuous optimization problems, but it needs further work to solve discrete and binary optimization problems and avoid local optima. According to the literature, no DE search operator or algorithm is optimal for all optimization tasks. As a result, using more than one search operator in a single algorithm architecture, called multi-operator-based algorithms, is a solution to address this problem. These methods outperformed single-based methods for continuous optimization problems. Thus, in this paper, a binary multi-operator differential evolution (BMODE) approach is presented to tackle the 0–1 KP. The presented methodology utilizes multiple differential evolution (DE) mutation strategies with complementary characteristics, with the best mutation operator being asserted utilizing the produced solutions' quality and the population's diversity. In BMODE, two types of transfer functions (TFs) (S-shaped and V-shaped) are used to transfer the continuous solutions to binary ones to be able to calculate the fitness function value. To handle the capacity constraints, a feasibility rule is utilized and some of the infeasible solutions are repaired. The performance of BMODE is tested by solving 40 instances with multiple dimensions, i.e., low, medium, and high. Experimental results of the proposed BMODE are compared with well-known state-of-the-art 0–1 knapsack algorithms. Based on Wilcoxon's nonparametric statistical test ( α = 0.05 ), the proposed BMODE can obtain the best results against the rival algorithms in most cases, and can work well on stability and computational accuracy. [ABSTRACT FROM AUTHOR]

In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. This paper aims to contribute to this endeavor by examining the impact of solution initialization methods on the performance of a hybrid algorithm applied to the set union knapsack problem (SUKP). Three distinct solution initialization methods, random, greedy, and weighted, have been proposed and evaluated. These have been integrated within a sine cosine algorithm employing k-means as a binarization procedure. Through testing on medium- and large-sized SUKP instances, the study reveals that the solution initialization strategy influences the algorithm's performance, with the weighted method consistently outperforming the other two. Additionally, the obtained results were benchmarked against various metaheuristics that have previously solved SUKP, showing favorable performance in this comparison. [ABSTRACT FROM AUTHOR]

The discounted {0-1} knapsack problem (DKP) is an NP-hard problem that is more challenging than the classical knapsack problem. In this paper, an enhanced version of the sine-cosine algorithm (SCA) called TMHSCA is proposed to solve the DKP. The SCA is a novel metaheuristic algorithm based on sine-cosine theory. Three effective improvements are proposed for the SCA to enhance the convergence speed and exploitation capability of the algorithm. First, by dividing the initial population into three subpopulations using random, greedy and opposition-based learning (OBL) strategies, the diversity of the population can be effectively enhanced. Furthermore, a forward-inverse sine-cosine search that expands the search space by utilizing the worst solution as another target is proposed. The proposed forward-inverse sine-cosine search strategy facilitates the algorithm to explore the easily ignored solution space. The last improvement includes the use of an OBL mutation and the mutation operator of differential evolution at a two-stage mutation, which increases the algorithm's convergence speed and fitness. In our proposed two-stage mutation, the number of mutations can be adaptively adjusted based on the optimization capabilities of the optimal individual. Additionally, a reshuffling repair strategy for repairing infeasible solutions by sorting items into groups to obtain the weight-to-value ratio is proposed. Extensive experiments are conducted on 40 publicly available datasets and are compared to the greedy algorithm, 3 SCAs and 8 competitive baseline methods. The experimental results demonstrate that our method achieves a state-of-the-art performance. [ABSTRACT FROM AUTHOR]

• Formulate a non-cooperative game with both UEs and MECs as players. • Prove the existence of and convergence to a Nash equilibrium. • Develop a set of algorithms to find the Nash equilibrium. • Demonstrate numerical examples of non-cooperative games with and without MECs' participation. In a newly emerged fog computing environment, various user equipments (UE) enhance their computing power and extend their battery lifetime by computation offloading to mobile edge cloud (MEC) servers. Such an environment is distributed and competitive in nature. In this paper, we take a game theoretical approach to computation offloading optimization in a fog computing environment. Such an approach captures and characterizes the nature of a competitive environment. The main contributions of the paper can be summarized as follows. First, we formulate a non-cooperative game with both UEs and MECs as players. Each UE attempts to minimize the execution time of its tasks with an energy constraint. Each MEC attempts to minimize the product of its power consumption for computation and execution time for allocated tasks. Second, we develop a heuristic algorithm for a UE to determine its "heuristically" best response to the current situation, an algorithm for an MEC to determine its best response to the current situation, and an iterative algorithm to find the Nash equilibrium. Third, we prove that our iterative algorithm converges to a Nash equilibrium. We demonstrate numerical examples of our non-cooperative games with and without MECs' participation. We observe that our iterative algorithm always quickly converges to a Nash equilibrium. The uniqueness of our non-cooperative games is that the strategy set of a player can be discrete and the payoff function of a player can be obtained by a heuristic algorithm for combinatorial optimization. To the best of the author's knowledge, there has been no such investigation of non-cooperative games based on combinatorial optimization for computation offloading optimization in a fog computing environment. [ABSTRACT FROM AUTHOR]

This paper studies a shuffled linear regression problem. As a variant of ordinary linear regression, it requires estimating not only the regression variable, but also permutational correspondences between the covariates and responses. While existing formulations require the underlying ground-truth correspondences to be an ideal bijection such that all pieces of data should match, such a requirement barely holds in real-world applications due to either missing data or outliers. In this work, we generalize the formulation of shuffled linear regression to a broader range of conditions where only a part of the data should correspond. To this end, the effective recovery condition and NP-hardness of the proposed formulation are also studied. Moreover, we present a simple yet effective algorithm for deriving the solution. Its global convergence property and convergence rate are also analyzed in detail. Distinct tasks validate the effectiveness of our proposed formulation and the solution method. [ABSTRACT FROM AUTHOR]

In this paper, we describe the first parallel Branch-and-Bound (B&B) algorithm with a history-based domination technique. Although history-based domination substantially speeds up a B&B search, it makes parallelization much more challenging. Our algorithm is the first parallel exact algorithm for the Sequential Ordering Problem using a pure B&B approach. To effectively explore the solution space, we have developed three novel parallelization techniques: thread restart, parallel history domination, and history-table memory management. The proposed algorithm was experimentally evaluated using the SOPLIB and TSPLIB benchmarks on multi-core processors. Using 32 threads with a time limit of one hour, the algorithm gives geometric-mean speedups of 72x and 20x on the medium-difficulty SOPLIB and TSPLIB instances, respectively. On the hard instances, it solves 12 instances that the sequential algorithm does not solve, with geometric-mean speedups of 16x on SOPLIB and 32x on TSPLIB. Super-linear speedups up to 366x are seen on 16 instances. • We propose the first parallel B&B algorithm that involves a history-based domination technique. • The proposed algorithm includes three novel parallelization techniques: thread restart, parallel history-based domination, and history-table memory management. • The proposed algorithm is the first parallel B&B algorithm for the Sequential Ordering Problem, which is an NP-hard sequencing problem with precedence constraints. • We present a thorough experimental evaluation of the proposed parallel algorithm on SOPLIB and TSPLIB. The results show that super-linear speedup is not an anomaly; it can be achieved on many instances. We report a speedup ratio as high as 285 on a 32-core processor. [ABSTRACT FROM AUTHOR]

The three-dimensional path planning problem is a combinatorial optimization problem to find the optimal path be- tween the starting point and the destination in the interference environment. Aiming at the shortcomings of traditional swarm in- telligence algorithm in solving this problem,such as low convergence accuracy and easy to fall into local optimum, this paper proposed an adaptive moth-flame optimization algorithm to solve the problem. By introducing the dynamic adjustment strategy of the flight direction and the position intersection strategy,the improved algorithm continuously generated new individuals while dynamically adjusting the flight direction of the moth, which effectively avoided the algorithm from falling into local optimum ; by adaptively adjusting the number of flames, so as to the algorithm enhanced population diversity in the global exploration stage a- void premature convergence. It used the adaptive moth-flame optimization algorithm and other swarm intelligence algorithms to solve the three-dimensional path planning problem. The experimental results show that the improved adaptive moth-flame opti- mization algorithm has the smallest cost value and the fastest convergence speed among all algorithms. The algorithm has better solution ability in 3D path planning problem. [ABSTRACT FROM AUTHOR]

• Connect quadratic assignment model (QAP) with network design problem. • Reformulate time-dependent synchronized service design as network-based quadratic assignment problem. • Propose extended Gilmore-Lawler Bound (EGLB) in the generic QAP network. • Develop Branch & Bound algorithm with an effective lower bound estimator using EGLB. A new modeling framework is developed in this paper to design a class of synchronized transportation services that can be formulated as a time-dependent synchronized service network design problem. The framework is established using a generic network representation for the quadratic assignment problem (QAP). As one of the fundamental combinatorial optimization problems, the QAP was introduced by Koopmans and Beckman (KB-QAP), in 1957, in the context of locating economic activities. Our proposed network-based QAP (NET-QAP) model not only linearizes the KB-QAP model but also generalizes the traditional QAP model as a special case with a symmetric network structure. The NET-QAP is utilized to formulate a time-dependent synchronized service network design problem to obtain an optimal schedule for both inbound and outbound services in a transshipment area, where commodities are collected from origins using the inbound services and distributed to their final destinations using the outbound services (after sorting and storage). From the view of the Gilmore-Lawler Bound (GLB), this paper explores a new branch and bound framework to solve the synchronizing NET-QAP problem. An extended GLB (E-QAP) is adopted in this research as a lower bound estimator for the first-stage assignment costs, based on several relaxed subproblems in the second-stage assignment. Then, the framework can also be applied to estimate the cost of sub-decisions that are involved in making a broader decision-making problem. Numerical experiments are conducted to demonstrate the effectiveness and applicability of the proposed modeling and computational framework. [ABSTRACT FROM AUTHOR]

This paper presents an exact algorithm for the team formation problem, in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems, and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modeling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application and a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. The team formation problem (TFP) aims to construct a capable team that can communicate and collaborate effectively. The cost of communication is quantified using the proximity of the potential members in a social network. We study a TFP with two measures for communication effectiveness; namely, we minimize the sum of communication costs, and we impose an upper bound on the largest communication cost. This problem can be formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-size instances, which are intractable for the solver. Summary of Contribution: This paper presents an exact algorithm for the Team Formation Problem (TFP), in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modelling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application as well as a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the one-machine scheduling problem with release and delivery times with the minimum makespan objective. Both heuristics and branch-and-bound algorithms have been formulated for the problem. One such branch-and-bound algorithm solves the problem and a variation that requires a delay between the completion of one job and the start of another (delayed precedence constraints). This paper analyzes key components of this branch-and-bound algorithm and proposes an improved heuristic to be used in conjunction with a different search strategy. Computational experiments demonstrate that the modifications lead to substantial improvements in running time and number of iterations on the one-machine problem instances both with and without delayed precedence constraints. [ABSTRACT FROM AUTHOR]

The minimum cost and large flow problem is a combinatorial optimization problem, which has important research significance and application value in the fields of economy and industry. In view of the low efficiency of the algorithm for solving part of the minimum cost and maximum flow problem,according to the linear programming equation of the minimum cost and maximum flow problem, this paper mapped the problem model to the corresponding factor graph model, improved the description function, gave the iteration equation, and designed the minimum cost belief propagation algorithm for maximum flow problem. It used the iterative equation to perform convergence calculation on the maximum feasible flow eigenvalue firstly, and obtained the maximum flow, and set the maximum flow threshold. On this basis, the minimum cost calculation was performed to obtain the optimal solution of the problem. Finally, this paper selected a number of weighted directed graph models for numerical experiments to verify the feasibility and effectiveness of the algorithm. The results show that the algorithm is superior to some algorithms in terms of solving efficiency. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining all optimal integer solutions of a linear integer network flow problem, which we call the all optimal integer flow (AOF) problem. We derive an O (F (m + n) + m n + M) time algorithm to determine all F many optimal integer flows in a directed network with n nodes and m arcs, where M is the best time needed to find one minimum cost flow. We remark that stopping Hamacher's well-known method for the determination of the K best integer flows (Hamacher, 1995) at the first sub-optimal flow results in an algorithm with a running time of O (F m (n log n + m) + M) for solving the AOF problem. Our improvement is essentially made possible by replacing the shortest path sub-problem with a more efficient way to determine a so-called proper zero cost cycle using a modified depth-first search technique. As a byproduct, our analysis yields an enhanced algorithm to determine the K best integer flows that runs in O (K n 3 + M). Besides, we give lower and upper bounds for the number of all optimal integer and feasible integer solutions. Our bounds are based on the fact that any optimal solution can be obtained by an initial optimal tree solution plus a conical combination of incidence vectors of all induced cycles with bounded coefficients. [ABSTRACT FROM AUTHOR]

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has m identical copies. The case m = 2 has already been completely solved by several authors using different methods, but the case m > 2 had not been satisfactorily solved yet. Here, under the conjecture of certain (very likely true) uniform convergence results, we provide an efficient algorithm to compute the optimal threshold and the probability of success for every m. Moreover, we give a method to determine their asymptotic values based on the solution of a system of m ODEs. [ABSTRACT FROM AUTHOR]

In many cities and regions, decision makers independently develop Train Operation Plan (TOP) for each line in the rail transit network, resulting in a lack of TOP Synchronization (TOPS). Considering the entire network as a whole, researchers have realized that synchronous optimization is of great significance. In this paper, we formulate two Mixed-Integer Linear Programming (MILP) models to optimize demand-driven TOP in the network. The former is an Asynchronous TOP Optimization (ATOPO) model, while the latter is a Synchronous TOP Optimization (STOPO) model. The bi-objective models simultaneously determine train frequency, train timetable, and rolling stock circulation under small-granularity passenger demand to minimize trains' total cost and passengers' total time. Then, we propose the Nondominated Sorting Coevolutionary Memetic Algorithm (NSCMA) to solve the combinatorial optimization problems. The hybrid heuristic algorithm incorporates Coevolutionary Memetic Algorithm (CMA) into Advanced and Adaptive Nondominated Sorting Genetic Algorithm II (AANSGA-II) to ameliorate the evolution process for elite individuals. On this basis, we study the case of Shenyang Metro to verify the models and the algorithm. The results demonstrate that the STOPO model is better than the ATOPO model in reducing trains' total cost and passengers' total time. In addition, NSCMA is better than AANSGA-II in obtaining elite individuals. [ABSTRACT FROM AUTHOR]

Randomized search heuristics such as evolutionary algorithms are frequently applied to dynamic combinatorial optimization problems. Within this paper, we present a dynamic model of the classic weighted vertex cover problem and analyze the runtime performances of the well-studied algorithms randomized local search and (1 + 1) EA adapted to it, to contribute to the theoretical understanding of evolutionary computing for problems with dynamic changes. In our investigations, we use an edge-based representation based on the dual form of the Linear Programming formulation for the problem and study the expected runtime that the adapted algorithms require to maintain a 2-approximate solution when the given weighted graph is modified by an edge-editing or weight-editing operation. Considering the weights on the vertices may be exponentially large with respect to the size of the graph, the step size adaption strategy is incorporated, with or without the 1/5-th rule that is employed to control the increasing/decreasing rate of the step size. Our results show that three of the four algorithms presented in the paper can recompute 2-approximate solutions for the studied dynamic changes in polynomial expected runtime, but the (1 + 1) EA with 1/5-th rule requires pseudo-polynomial expected runtime. [ABSTRACT FROM AUTHOR]

• An advanced shuffled frog leaping algorithm (DSSRLFLA) is developed for model evaluation and feature selection. • A dynamic step size adjustment strategy based on historical information is designed to balance exploration and exploitation. • Specular reflection learning mechanism increases the possibility of searching for valid solutions and enhances the search ability. • An improved simulated annealing strategy is executed for each memetic to improve the efficiency of local exploitation. • DSSRLFLA can obtain higher quality optimal solutions compared to some competitive algorithms. The shuffled frog leaping algorithm is a new optimization algorithm proposed to solve the combinatorial optimization problem, which effectively combines the memetic algorithm based on a memetic algorithm and the particle swarm algorithm based on population behavior. The algorithm is widely used because it is easy to implement and requires few parameters to be adjusted. However, there are still some characteristics of this method that need to be improved because it is easy to fall into local optimization or poor search ability. To alleviate this limitation, a new version of the improved SFLA is proposed in this paper, which incorporates a dynamic step size adjustment strategy based on historical information, a specular reflection learning mechanism, and a simulated annealing mechanism based on chaotic mapping and levy flight. Firstly, the dynamic step size adjustment strategy based on historical information effectively helps to balance local exploration and global exploitation and alleviates the problem of falling into local optimum. Second, the specular reflection learning mechanism increases the possibility of searching for valid solutions in feasible domains and enhances the search ability of individuals in the population. Finally, an improved simulated annealing strategy is executed for each memetic, which improves the efficiency of local exploitation. In order to test the performance of the proposed algorithm, 31 test functions were selected from IEEE CEC2014 and 23 essential benchmark functions, and comparative experiments were carried out from the two dimensions of 30 and 100. Furthermore, a series of competing algorithms are selected, which involve nine classical standard algorithms, including PSO, BA, SSA, FA, SCA, WOA, GWO, MFO, and SFLA, as well as, six well-known improved algorithms, including LSFLA, DDSFLA, GOTLBO, ALCPSO, BLPSO, CLPSO. Furthermore, Wilcoxon signed-rank test and Friedman test are used as testing tools to illustrate the scalability of the proposed algorithm. From the analysis of the results, it can be seen that this proposed method has been effectively improved concerning stability and the quality of the optimal solution obtained from the search, both in low and high dimensions, and the ability to jump out of the local optimum has also been enhanced. In addition, to prove that this method has a reliable performance in discrete problems and continuous problems, DSSRLFLA is mapped into a discrete space, and 24 UCI data sets are also selected to evaluate the performance of the new feature selection method. The experimental results illustrate that this improved method can obtain fewer features and higher classification accuracy than some well-known feature selection methods. [ABSTRACT FROM AUTHOR]

The rapid growing number of web services has posed new challenges for service composition computing. How to combine services that meet the needs of users in the least amount of time from a huge number of candidate services is a hot topic of research today. As a meta-heuristic algorithm for solving optimization problems, salp swarm algorithm (SSA) has been widely applied to case scenarios in different fields due to its simple structure and high performance. However, QoS-aware service composition is a discrete problem and existing methods are not suitable for it. Therefore, in this paper, we propose an improved SSA integrating chaotic mapping method for QoS service composition selection, named CSSA. Through the randomness and ergodicity of chaos, reducing the possibility of falling into local optimum and strengthening the exploitation capability of the algorithm. In addition, a fuzzy continuous neighborhood search method is used to enhance the local search capability of the algorithm which makes the discrete space of service composition in a way similar to continuous space. Finally, two well-known datasets are used to verify the effectiveness of CSSA compared to three advanced algorithms and original SSA. The test results demonstrate that CSSA has significant advantages and it also has satisfactory performance in large scale scenarios. [ABSTRACT FROM AUTHOR]

Given an undirected graph G = (V,E) with a nonnegative edge length function and an integer p, 0 < p < |V |, the p-centdian problem is to find p vertices (called the centdian set) of V such that the eccentricity plus median-distance is minimized, in which the eccentricity is the maximum (length) distance of all vertices to their nearest centdian set and the median-distance is the total (length) distance of all vertices to their nearest centdian set. The eccentricity plus median-distance is called the centdian-distance. The purpose of the p-centdian problem is to find p open facilities (servers) which satisfy the quality-of-service of the minimum total distance (median-distance) and the maximum distance (eccentricity) to their service customers, simultaneously. If we converse the two criteria, that is given the bound of the centdian-distance and the objective function is to minimize the cardinality of the centdian set, this problem is called the converse centdian problem. In this paper, we prove the p-centdian problem is NP-Complete. Then we design the first non-trivial brute force exact algorithms for the p-centdian problem and the converse centdian problem, respectively. Finally, we design two approximation algorithms for both problems. [ABSTRACT FROM AUTHOR]