Effective Heuristic Algorithm Research Articles

HSMVS: heuristic search for minimum vertex separator on massive graphs

In graph theory, the problem of finding minimum vertex separator (MVS) is a classic NP-hard problem, and it plays a key role in a number of important applications in practice. The real-world massive graphs are of very large size, which calls for effective approximate methods, especially heuristic search algorithms. In this article, we present a simple yet effective heuristic search algorithm dubbed HSMVS for solving MVS on real-world massive graphs. Our HSMVS algorithm is developed on the basis of an efficient construction procedure and a simple yet effective vertex-selection heuristic. Experimental results on a large number of real-world massive graphs present that HSMVS is able to find much smaller vertex separators than three effective heuristic search algorithms, indicating the effectiveness of HSMVS. Further empirical analyses confirm the effectiveness of the underlying components in our proposed algorithm.

Balancing the cardinality of clusters with a distance constraint: a fast algorithm

AbstractLogistics companies partition the customers they serve into delivery zones as a tactical decision and manage the customers assigned to each zone as a cluster for the purpose of routing, workload allocation, etc. Frequently, this partition is made in accordance with customers’ geographical location, which can result in very unbalanced clusters in terms of the number of customers they include. In addition, in the day-to-day operations, not necessarily all customers need to be served every day so, even if the clusters originally created are balanced, daily needs may lead to unbalanced clusters. Given an a priori assignment of customers to clusters, improving the balance between clusters in advance of workload management is therefore a key issue. This paper addresses the problem of balancing clusters, when there is a distance constraint that prevents reassigning customers to clusters far away from their original pre-assignment. This problem is formulated as a lexicographic biobjective optimization model. The highest priority objective function minimizes the variance of the number of customers in the clusters. The second ranked objective function minimizes the total distance resulting from all reassignments. A fast and effective heuristic algorithm is developed, based on exploring customer reassignments, either by comparing clusters two by two or by extending the search to allow for sequential customer swaps among clusters. Both the quality of the solution and the computational time required encourage the use of this algorithm by logistics companies to balance clusters in real scenarios.

Integer optimization models and algorithms for the multi-period non-shareable resource allocation problem

The resource allocation problem (RAP) determines a solution to optimally allocate limited resources to several activities or tasks. In this study, we propose a novel resource allocation problem referred to as multi-period non-shareable resource allocation problem (MNRAP), which is motivated by the characteristics of resources considered in the stem cell culture process for producing stem cell therapeutics. A resource considered in the MNRAP has the following three characteristics: (i) resource consumption required to perform an activity and available resource capacity may change over time; (ii) multiple activities cannot share one resource; and (iii) resource requirements can be satisfied through the combination of different types of resources. The MNRAP selects some of the given activities to maximize the overall profit under limited resources with these characteristics. To address this problem, pattern-based integer programming formulations based on the concept of resource patterns are proposed. These formulations attempt to overcome the limitations of a compact integer programming formulation, the utilization of which is challenging for large-scale problems owing to their complexity. Further, based on a branch-and-price approach to solving pattern-based formulations, effective heuristic algorithms are proposed to provide high-quality solutions for large instances. Moreover, through computational experiments on a wide range of instances, including real-world instances, the superiority of the proposed formulations and heuristic algorithms is demonstrated.

NuSC: An Effective Local Search Algorithm for Solving the Set Covering Problem.

The set covering problem (SCP) is a fundamental NP-hard problem in computer science and has a broad range of important real-world applications. In practice, SCP instances transformed from real-world applications would be of large scale, so it is of significant importance to design effective heuristic algorithms, especially local search ones. However, there exist only few research works on developing local search algorithms for solving SCP. In this article, we propose a new local search algorithm for solving SCP, dubbed NuSC. In particular, NuSC introduces a new combined scoring function for subset selection, which combines different subset properties in an effective way and helps NuSC find more optimized solutions. Besides, NuSC incorporates a dynamic weighting scheme for elements, a tabu search strategy, and a novelty selection mechanism to further enhance its practical performance. In order to study the effectiveness and robustness of our proposed NuSC algorithm, we conduct extensive experiments to compare NuSC against many state-of-the-art competitors on various types of SCP instances. Our experimental results demonstrate that NuSC significantly outperforms its competitors on the majority of instances, indicating the superiority of NuSC. Also, our empirical evaluations confirm the effectiveness of each algorithmic technique underlying NuSC.

DAG-Order: An Order-Based Dynamic DAG Scheduling for Real-Time Networks-on-Chip

With the high-performance requirement of safety-critical real-time tasks, the platforms of many-core processors with high parallelism are widely utilized, where network-on-chip (NoC) is generally employed for inter-core communication due to its scalability and high efficiency. Unfortunately, large uncertainties are suffered on NoCs from both the overly parallel architecture and the distributed scheduling strategy (e.g., wormhole flow control), which complicates the response time upper bounds estimation (i.e., either unsafe or pessimistic). For DAG-based real-time parallel tasks, to solve this problem, we propose DAG-Order, an order-based dynamic DAG scheduling approach, which strictly guarantees NoC real-time services. First, rather than build the new analysis to fit the widely used best-effort wormhole NoC, DAG-Order is built upon a kind of advanced low-latency NoC with SLT ( S ingle-cycle L ong-range T raversal) to avoid the unpredictable parallel transmission on the shared source-destination link of wormhole NoCs. Second, DAG-Order is a non-preemptive dynamic scheduling strategy, which jointly considers communication as well as computation workloads, and fits SLT NoC. With such an order-based dynamic scheduling strategy, the provably bound safety is ensured by enforcing certain order constraints among DAG edges/vertices that eliminate the execution-timing anomaly at runtime. Third, the order constraints are further relaxed for higher average-case runtime performance without compromising bound safety. Finally, an effective heuristic algorithm seeking a proper schedule order is developed to tighten the bounds. Experiments on synthetic and realistic benchmarks demonstrate that DAG-Order performs better than the state-of-the-art related scheduling methods.

Computing Offloading Based on TD3 Algorithm in Cache-Assisted Vehicular NOMA-MEC Networks.

In this paper, in order to reduce the energy consumption and time of data transmission, the non-orthogonal multiple access (NOMA) and mobile edge caching technologies are jointly considered in mobile edge computing (MEC) networks. As for the cache-assisted vehicular NOMA-MEC networks, a problem of minimizing the energy consumed by vehicles (mobile devices, MDs) is formulated under time and resource constraints, which jointly optimize the computing resource allocation, subchannel selection, device association, offloading and caching decisions. To solve the formulated problem, we develop an effective joint computation offloading and task-caching algorithm based on the twin-delayed deep deterministic policy gradient (TD3) algorithm. Such a TD3-based offloading (TD3O) algorithm includes a designed action transformation (AT) algorithm used for transforming continuous action space into a discrete one. In addition, to solve the formulated problem in a non-iterative manner, an effective heuristic algorithm (HA) is also designed. As for the designed algorithms, we provide some detailed analyses of computation complexity and convergence, and give some meaningful insights through simulation. Simulation results show that the TD3O algorithm could achieve lower local energy consumption than several benchmark algorithms, and HA could achieve lower consumption than the completely offloading algorithm and local execution algorithm.

A Cooperative Scatter Search With Reinforcement Learning Mechanism for the Distributed Permutation Flowshop Scheduling Problem With Sequence-Dependent Setup Times

The integration of reinforcement learning technology into meta-heuristic algorithms to address complex combinatorial optimization problems has attracted much attention in recent years. A cooperative scatter search with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning mechanism (QCSS) is proposed for solving the DPFSP-SDST. In the diversification generation method, two effective heuristic algorithms are designed to construct an initial population with high quality and diversity. In the improved method, eight domain knowledge-guided perturbation operators are combined with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning to balance the exploration and exploitation capabilities of the QCSS algorithm. The reference set <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathrm{RefSet})$</tex-math> </inline-formula> is divided into two subpopulations, and adaptive competition is adopted between the subpopulations to enhance search efficiency. In addition, a restart mechanism is proposed in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{RefSet}$</tex-math> </inline-formula> update phase to ensure the diversity of solutions. The performance of the QCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the QCSS algorithm.

Economical revenue maximization in mobile edge caching and blockchain enabled space-air-ground integrated networks

In this paper, we study an edge caching and blockchain enabled space-air-ground integrated networking (SAGIN) network, where a low-earth-orbit (LEO) satellite serves as the content provider, and multiple edge caching enabled unmanned aerial vehicles (UAVs) will cache some contents to provide user equipments (UEs) with satisfactory content access services together with the satellite. Moreover, there’s a blockchain system that is deployed on UAVs, to provide the network with trust mechanism without requiring a centralized authority. From the standpoint of the operator, we intend to maximize the long-term averaged economical revenue by providing UEs with satisfactory and secure content access services. To achieve this purpose, we will jointly optimize the content placement of each UAV, content replacement when each UAV is full, the access control of each UE, and the blockchain deployment strategy about each UAV. the concept of queues in Lyapunov optimization is utilized to represent the backlog of edge equipment, ensuring the stability of virtual queues on UAVs and satellites, while satisfying the caching capacity constraints for content caching and blockchain deployment. Due to the tight coupling of optimization in each time slot and the variables within each time slot, our problem, which involves stochastic optimization and binary integer programming, is challenging to solve. To address this issue, we initially employ Lyapunov optimization theory to transform and decouple the problem into individual time-slot optimization problems. Subsequently, we utilize an effective heuristic algorithm called the fireworks algorithm to solve these individual optimization problems. However, the original fireworks algorithm cannot be directly applied to our problem due to its binary characteristics and inter-coupling constraints. Therefore, we have redesigned the explosion and mutation operations to adapt them to our specific problem. Simulation results demonstrate that our proposed algorithm outperforms other baseline algorithms.

Wart-Treatment Efficacy Prediction Using a CMA-ES-Based Dendritic Neuron Model

Warts are a prevalent condition worldwide, affecting approximately 10% of the global population. In this study, a machine learning method based on a dendritic neuron model is proposed for wart-treatment efficacy prediction. To prevent premature convergence and improve the interpretability of the model training process, an effective heuristic algorithm, i.e., the covariance matrix adaptation evolution strategy (CMA-ES), is incorporated as the training method of the dendritic neuron model. Two common datasets of wart-treatment efficacy, i.e., the cryotherapy dataset and the immunotherapy dataset, are used to verify the effectiveness of the proposed method. The proposed CMA-ES-based dendritic neuron model achieves promising results, with average classification accuracies of 0.9012 and 0.8654 on the two datasets, respectively. The experimental results indicate that the proposed method achieves better or more competitive prediction results than six common machine learning models. In addition, the trained dendritic neuron model can be simplified using a dendritic pruning mechanism. Finally, an effective wart-treatment efficacy prediction method based on a dendritic neuron model, which can provide decision support for physicians, is proposed in this paper.

Novel empty train return strategy and passenger control strategy to satisfy asymmetric passenger demand: A joint optimization with train timetabling

Big cities’ bi-directional metro lines often have unbalanced passenger demand, i.e., up-directional passenger demand is oversaturated but down-directional passenger demand is unsaturated. In recent years, the method to relieve congestion in oversaturated direction has attracted much attention, but many problems in the unsaturated direction have not gotten as much attention, e.g., the waste of transportation resources caused by low loading rate, and the insufficient utilization of platform space resources caused by less waiting passengers. To address these problems, this paper introduces a new collaborative optimization model for the train timetable, passenger control and rolling stock schedule on a bi-directional metro line with unbalanced passenger demand. With consider the real-time state of bi-directional platform passengers, a platform passenger control strategy is designed to promote the utilization of platform resources, and an empty train return strategy is proposed to transfer transportation resources to oversaturated direction. To characterize the problem mathematically, a multi-objective mixed-integer nonlinear programming model (MINLP) is formulated to minimize the passengers’ waiting time, the difference of bi-directional platform passenger density and the use cost of trains. An effective heuristic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) and the adaptive large neighborhood search (ALNS) is designed to find high-quality solutions for the proposed model. Finally, five sets of numerical examples based on the Beijing metro Batong line, are conducted to validate the performance of the proposed method in this paper. The experimental results demonstrate the method can fully utilize the transportation and platform resources of the unsaturated direction, to improve transport efficiency and relieve platform congestion of oversaturated direction.

Multi-Objective Multi-Stage Optimize Scheduling Algorithm for Nonlinear Virtual Work-Flow Based on Pareto

Work-flow scheduling is for finding the allocation method to achieve optimal resource utilization. In the scheduling process, constraints, such as time, cost and quality, need to be considered. How to balance these parameters is a NP-hard problem, and the nonlinear manufacturing process increases the difficulty of scheduling, so it is necessary to provide an effective heuristic algorithm. Aiming at these problems, a multi-objective nonlinear virtual work-flow model was set up, and a multi-objective staged scheduling optimization algorithm with the objectives of minimizing cost and time and maximizing quality was proposed. The algorithm includes three phases: the virtualization phase abstracts tasks and services into virtual nodes to generate a virtual work-flow model; the virtual scheduling phase divides optimized segments and obtains the solution set through reverse iteration; the generation phase obtains the scheduling path according to the Pareto dominance. The proposed algorithm performed 10.5% better in production quality than the minimum critical path algorithm, reduced the time to meet the time constraint by 9.1% and saves 13.7% more of the cost than the production accuracy maximization algorithm.

Traffic-aware efficient consistency update in NFV-enabled software defined networking

In network function virtualization(NFV)-enabled software defined networks, the controller needs to frequently update the flow forwarding rules in the data plane to adapt to dynamic changes in network topologies or service requests. However, inconsistent rule updates may lead to blackholes, loops, transient congestion or policy violations (e.g., packets do not traverse designated network functions in a specific order), resulting in service interruption and throughput degradation. Therefore, this paper proposes an effective rule consistent update mechanism to avoid the above four problems simultaneously, while improving network throughput and satisfying user requests. Specifically, we first build three effective models to avoid blackholes, loops, and policy violations. Then, considering that network function nodes may change the sizes of their processed flows, we build a congestion avoidance model based on traffic changes to avoid congestion, which can reduce unnecessary rule update delays and packet loss. Subsequently, we prove that the consistent update problem constructed above is NP-hard, and then design an effective heuristic rule consistent update algorithm to obtain the rule update sequence that can simultaneously avoid blackholes, loops, congestion, and policy violations. Extensive trace-driven simulation results show that compared with the existing update methods, our proposed method can improve the success rate by up to 20.6% and reduce the maximum link utilization by up to 7.5%.

ILSGVCP: An improved local search algorithm for generalized vertex cover problem

The generalized vertex cover problem (GVCP) is a well-known combinatorial problem of the classic minimum vertex cover problem with rich applications. And local search algorithm is an effective heuristic algorithm to solve GVCP. Therefore, In this paper, we develop an improved local search algorithm for the problem, namely ILSGVCP. Specifically, new choosing small weight rules called CSWR is presented for initialization to acquire a high-quality candidate solution. Furthermore, we propose a dynamic perturbation mechanism called DP with a novel formula which makes local search perturbed dynamically. Moreover, we combine CSWR and DP to propose our algorithm ILSGVCP. Finally, we carry out experiments to evaluate ILSGVCP on random instances with up to 1000 vertices and 400,000 edges and DIMACS instances. A detailed experimental evaluation reveals that ILSGVCP outperforms other state-of-the-art algorithms for the GVCP.

An Effective Heuristic Algorithm for Flexible Flow Shop Scheduling Problems with Parallel Batch Processing

An Effective Heuristic Algorithm for Flexible Flow Shop Scheduling Problems with Parallel Batch Processing

HSLS: An efficient local search algorithm for the hardware and software partitioning problem

Hardware and software partitioning (HW/SW) is a crucial step in the co-design of embedded systems, which is a typical combinatorial optimisation problem. In practice, HW/SW instances would be of large scale, so it is of significant importance to design effective heuristic algorithms to obtain a high-quality partitioning scheme. Different from previous heuristics, the HW/SW problem is treated as the minimum weight dominating set (MWDS) problem in this letter, and the mature local search framework for solving the MWDS problem is introduced to solve the HW/SW problem. In addition, two suitable vertex selection rules based on scoring function and tabu are proposed. Combined with the introduced local search framework, an efficient local search algorithm named HSLS is obtained. 96 classic benchmark instances are used to evaluate the performance of the HSLS algorithm, and the four latest evolutionary algorithms designed for the HW/SW problem are used as comparison algorithms, which are genetic algorithm, binary particle swarm optimisation, differential evolution, and group theory-based optimisation algorithm. The experimental results show that the HSLS algorithm is far superior to the four comparison algorithms in terms of the optimal solution and obtains optimal solution on 78 benchmark instances, the four comparison algorithms obtain 43, 29, 42, and 41 optimal solutions respectively.

An integrated local-search/set-partitioning refinement heuristic for the Capacitated Vehicle Routing Problem

In this paper, an effective heuristic algorithm for large-scale instances of the Capacitated Vehicle Routing Problem is proposed. The technique consists in a local search method entangled with a restricted Set Partitioning problem optimization. Helsgaun’s LKH-3 algorithm has been used for the local search phase, with a number of implementation improvements. The restricted Set Partitioning formulation is solved by means of an exact commercial Integer Liner Programming solver. The resulting algorithm is able to consistently improve the solutions obtained by a state-of-the-art heuristic from the literature, as well as some of the best-know solutions maintained by the CVRPLIB website.

Joint optimization of train scheduling and rolling stock circulation planning with passenger flow control on tidal overcrowded metro lines

This study proposes a joint optimization method for train scheduling and rolling stock circulation planning with the consideration of passenger flow control strategy on a tidal oversaturated metro line, in which different types of rolling stocks with various loading capacities are put into operations to satisfy the uneven passenger demand in different periods (e.g., peak hours and off-peak hours). To characterize the problem mathematically, a mixed-integer nonlinear programming model is formulated to minimize the passenger waiting time and operating costs of the metro system simultaneously. This model is further reformulated equivalently into a mixed-integer linear programming model via the linearization method. An effective heuristic algorithm based on the tabu search and CPLEX solver is designed to find high-quality solutions for the proposed problem. Finally, two sets of numerical examples, including a small-scale example and a large-scale example based on the Beijing metro Batong line, are conducted to validate the performance of the proposed methods. The experimental results demonstrate that scheduling multiple types of rolling stocks can effectively reduce the transportation costs and satisfy passenger demand in different periods.

An effective heuristic clustering algorithm for mining multiple critical nodes in complex networks

Influence maximization is of great significance in complex networks, and many methods have been proposed to solve it. However, they are usually time-consuming or cannot deal with the overlap of spreading. To get over the flaws, an effective heuristic clustering algorithm is proposed in this paper: (1) nodes that have been assigned to clusters are excluded from the network structure to guarantee they do not participate in subsequent clustering. (2) the K-shell (ks) and Neighborhood Coreness (NC) value of nodes in the remaining network are recalculated, which ensures the node influence can be adjusted during the clustering process. (3) a hub node and a routing node are selected for each cluster to jointly determine the initial spreader, which balances the local and global influence. Due to the above contributions, the proposed method preferably guarantees the influence of initial spreaders and the dispersity between them. A series of experiments based on Susceptible–Infected–Recovered (SIR) stochastic model confirm that the proposed method has favorable performance under different initial constraints against known methods, including VoteRank, HC, GCC, HGD, and DLS-AHC.

Joint optimization of antenna selection and beamforming in MIMO SWIPT systems with bidirectional communication

This paper investigates joint optimization of antenna selection and beamforming in multiple-input multiple-output simultaneous wireless information and power transfer systems with bidirectional communication. The downlink–uplink rate region is used as the performance metric. The formulated optimization problem is non-convex mixed integer programming, which is challenging to solve. The problem is first converted into a form of a quadratically constrained quadratic program. Given fixed receive and transmit antenna sets at the energy harvesting device, the authors apply the semidefinite relaxation to obtain a convex problem for optimal beamforming which can be solved efficiently. It is proved that the semidefinite relaxation is tight. The authors solve the relaxed problem for every possible receive and transmit antenna sets and find the optimal solution by search. Moreover, a low-complexity method to alleviate the computational complexity of the optimal solution by deriving effective heuristic algorithms for the beamforming and antenna selection is proposed. Simulation results demonstrate that both the optimal and the low-complexity algorithms outperform the benchmark power splitting, when the circuit power consumption is sufficiently high or the number of receive antennas at the energy harvesting device is sufficiently large. Also, a near-optimal performance can be achieved by the proposed low-complexity method.

Fast and Accurate Algorithms for Mapping and Aligning Long Reads.

For DNA sequence analysis, we are facing challenging tasks such as the identification of structural variants, sequencing repetitive regions, and phasing of alleles. Those challenging tasks suffer from the short length of sequencing reads, where each read may cover less than 2 single nucleotide polymorphism (SNP), or less than two occurrences of a repeated region. It is believed that long reads can help to solve those challenging tasks. In this study, we have designed new algorithms for mapping long reads to reference genomes. We have also designed efficient and effective heuristic algorithms for local alignments of long reads against the corresponding segments of the reference genome. To design the new mapping algorithm, we formulate the problem as the longest common subsequence with distance constraints. The local alignment heuristic algorithm is based on the idea of recursive alignment of k-mers, where the size of k differs in each round. We have implemented all the algorithms in C++ and produce a software package named mapAlign. Experiments on real data sets showed that the newly proposed approach can generate better alignments in terms of both identity and alignment scores for both Nanopore and single molecule real time sequencing (SMRT) data sets. For human individuals of both Nanopore and SMRT data sets, the new method can successfully math/align 91.53% and 85.36% of letters from reads to identical letters on reference genomes, respectively. In comparison, the best known method can only align 88.44% and 79.08% letters of reads for Nanopore and SMRT data sets, respectively. Our method is also faster than the best known method.