A two-individual based path-relinking algorithm for the satellite broadcast scheduling problem
Introduction
Satellite-based communications play a vital role in promoting socio-economic and cultural activities globally, including the development of a global network culture, distribution of entertainment products, and promotion of trade [1]. Over the past three decades, the number of satellite communication systems has grown significantly owing to the explosive growth of their basic applications and the associated activities around such applications [2].
A satellite communication system generally consists of satellites operating in high- or low-altitude earth orbits. Since low-altitude satellites are not always visible from terrestrial terminals, switching between satellites assigned to a given terminal (handover operation) is necessary to satisfy communication demands. This handover operation in a low-altitude satellite communication system needs to be optimized to achieve maximum broadcasting timeslots. The satellite broadcast scheduling problem (SBSP) aims to maximize the broadcast time from the satellites to terminals. This is achieved by finding a valid broadcasting schedule that maximizes the number of broadcasting timeslots while satisfying various operational and demand constraints. A wide variety of business enterprises need to broadcast information to their clients via channels housed in the system. Hence, an optimal or a near-optimal broadcast scheduling scheme is vital to the efficacy of the communication system. Moreover, optimal (near-optimal) broadcast schedules significantly improve the utilization of valuable satellite communication resources.
The SBSP received considerable research attention over the past two decades resulting in various mathematical models and solution procedures [3], [4], [5], [6], [7], [8], [9]. Specifically, Funabiki and Nishikawa [10] proposed a simple binary neural model that searches for a globally optimal solution. Shen and Wang [11] described a competitive Hopfield neural network model, using a competitive winner-take-all mechanism, which resulted in algorithms with reduced running times and improved the convergence rate. Li et al. [12] used a genetic algorithm to solve the SBSP using an appropriately designed genetic operator to expedite the convergence rate and improve performance. Chen et al. [13], [14] presented a low complexity algorithmic framework to obtain a broadcasting schedule by reformulating the SBSP into a low-density parity-check-like problem through a factor graph. Xia et al. [15] applied the particle swarm optimization procedure to tackle the SBSP by minimizing the difference between the number of timeslots in the solution and the required number of timeslots. Salman et al. [16] introduced a problem-specific knowledge-based heuristic algorithm for solving the SBSP. Salman et al. [17] applied a binary version of the differential evolution hybridized with ideas extracted from stochastic diffusion search to develop a highly competitive algorithm, in comparison to other existing algorithms. Sezgin and Omer [7] proposed an ant colony optimization (ACO) algorithm for solving the SBSP. Recently, Mehdi and Hedieh [4] proposed a boosted binary differential evolutionary approach to solve the SBSP, where they used a specially selected (best) method from different alternatives at different stages of the evolution process. The SBSP is known to be an NP-hard problem [3], [11], [12], [18]. Therefore, exact algorithms for solving it are unlikely to run in polynomial time. Thus, our primary focus is also on developing effective heuristic algorithms to tackle the SBSP that are attractive in terms of solution quality as well as running time.
Population-based evolutionary algorithms have been known to perform well in terms of solution quality for a variety of NP-hard optimization problems, such as the flow shop scheduling problem [19], [20], bandwidth coloring problem [21], and job shop scheduling problem [22]. Nevertheless, they often suffer from the drawback that a large number of ‘individuals’ need to be managed by taking into consideration both solution quality and distance between the individuals [23]. Interestingly, two recent algorithmic developments [24], [25] showed that, by managing only two individuals, remarkable performance could be achieved for the graph coloring problem and the flexible job shop scheduling problem. Evolutionary algorithms managing exactly two individuals are called master-apprentice evolutionary algorithms (MEAs) [24], named after their ability to mimic real-life activities where an apprentice gains knowledge from a master. When two apprentices (individuals) evolve over a given number of generations (cycles), they themselves become masters and share many similarities. Therefore, when a cycle ends, one apprentice replaces the master from the previous cycle to continue the evolution and to absorb the essence of the history (the previous cycle). Benefiting from a simple and manageable population of two individuals, an MEA can strike a reasonable balance between solution quality and computational efficiency.
Unlike the traditional population-based algorithms that have been extensively studied over the past two decades, MEA is a recent evolutionary framework with a good record of performance. Thus, to extend and enhance the research contributions on evolutionary algorithms that manage only two individuals, in this paper, we introduce the two-individual based path-relinking (TPR) algorithmic framework and apply it to solve the SBSP.
The main contributions of this paper can be summarized as follows:
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The proposed TPR algorithm is the first adaptation of the master-apprentice evolutionary framework tailored to solve the SBSP. The algorithm introduces several original features, including a powerful solution-based tabu search strategy for identifying a local optimum and a distance-controlled relinking operator with a greedy-repair mechanism to tunnel through infeasible regions of the solution space.
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We evaluate the performance of the proposed algorithm by comparing it with the best-performing algorithms for SBSP using 64 benchmark instances. One set of benchmark instances is standard, publicly available, and of smaller size. We also generated a new set of benchmark instances which are made available to the public. Further, our computational study examined key components and parameters of the algorithm and identified their impacts its performance. The analysis disclosed that our TPR algorithm outperformed the best known algorithms from the literature, in a statistically significant way.
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Some of the central ideas used in the TPR algorithm (such as the two-individual path relinking framework, solution-based tabu strategy, and the distance-controlled relinking operator) are sufficiently simple and general to be adapted to design effective methods for other hard combinatorial optimization problems.
The rest of the paper is organized as follows. In Section 2, we present a formal definition of the SBSP along with a mathematical programming formulation. Section 3 deals with our TPR algorithm. In Section 4, we present the results of extensive computational experiments carried out to assess the performance of the proposed algorithms in comparison to current best-performing approaches. In Section 5, we analyze various components and parameters of the TPR algorithm and study their impacts on its performance. Finally, concluding remarks are given in Section 6.
Section snippets
The satellite broadcast scheduling problem
A satellite broadcast system consists of a set of satellites, a set of ground terminals, and a set of timeslots. Communication links between satellites and terminals are provided in a collection of the timeslots. A timeslot has unit time to broadcast information from a satellite to a ground terminal when they are visible to each other. This visibility information is stored in a binary 3-dimensional array , called the visibility matrix. The th element of is and it
The two-individual based path-relinking algorithm for SBSP
Given an instance of the SBSP composed of satellites, terminals, and timeslots, a solution matrix is a three dimensional array where the th element is denoted by for . Recall that if and only if satellite broadcasts to terminal in timeslot . Thus, the search space for our algorithm is Obviously, . It may be noted that the space is a superset of the feasible solution space for the SBSP,
Computational results
In this section, we present the results of extensive computational experiments carried out to assess the performance of the TPR algorithm in comparison to the state-of-the-art methods from the literature to solve the SBSP. The test bed contains two sets of instances, set I and set II, for a total of 64 instances having the following characteristics:
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Set I: This set consists of 4 instances (i.e., BM4-BM71
Analysis and discussion
In this section we investigate the sensitivity of various parameters and the role of the vital components of the TPR algorithm in accomplishing its superior performance. We are interested in examining the contribution of the solution-based tabu search strategy and the two-individual framework to the success of the algorithm. Such a study will also provide additional insight into the inherent properties of these components.
Conclusion
Single solution based search methods (such as local search and tabu search) usually yield a strong intensity of search with faster convergence but easily fall into a local optimum (as presented in Section 5.2). Population-based path relinking is a popular evolutionary algorithm. As in the case of most population-based algorithms, its main goal is to preserve a large number of individuals to explore the search space. Despite its capability of achieving good diversification outcomes, the price
CRediT authorship contribution statement
Bo Peng: Methodology, Software, Writing - original draft. Yuan Zhang: Supervision, Writing - review & editing. T.C.E. Cheng: Funding acquisition, Writing - review & editing. Zhipeng Lü: Supervision, Project administration, Writing - review & editing. Abraham P. Punnen: Formal analysis, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank the anonymous reviewers for their constructive and important comments which led to major improvements of this article. This research was supported by the Fundamental Research Funds, China under grant numbers JBK2001013 and JBK190504 for the Central Universities of China and the National Natural Science Foundation of China under grant number 71320107001. The work of Abraham P. Punnen was supported by an NSERC discovery grant, Canada.
References (37)
- et al.
A metaheuristic algorithm to solve satellite broadcast scheduling problem
Inform. Sci.
(2015) - et al.
A learning-based path relinking algorithm for the bandwidth coloring problem
Eng. Appl. Artif. Intell.
(2016) - et al.
A tabu search/path relinking algorithm to solve the job shop scheduling problem
Comput. Oper. Res.
(2015) - et al.
A tabu search/path relinking algorithm to solve the job shop scheduling problem
Comput. Oper. Res.
(2015) - et al.
Two-stage solution-based tabu search for the multidemand multidimensional knapsack problem
European J. Oper. Res.
(2019) - et al.
Solution-based tabu search for the maximum min-sum dispersion problem
Inform. Sci.
(2018) - et al.
The irace package: iterated racing for automatic algorithm configuration
Oper. Res. Perspect.
(2016) Communications satellites
(2013)Introduction to Satellite Communications
(2014)- et al.
A new method to optimize the satellite broadcasting schedules using the mean field annealing of a hopfield neural network
IEEE Trans. Neural Netw.
(1995)
Satellite broadcast scheduling based on a boosted binary differential evolution
New Gener. Comput.
Optimal scheduling by competitive activation: application to the satellite antennae scheduling problem
Ant colony optimization approach for satellite broadcast scheduling problem
Communications Satellites: Global Change Agents
A binary hopfield neural-network approach for satellite broadcast scheduling problems
IEEE Trans. Neural Netw.
Optimizing satellite broadcast scheduling problem using the competitive hopfield neural network
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