A nondominated sorting genetic algorithm for bi-objective network coding based multicast routing problems

Network coding is a new communication technique that generalizes routing, where, instead of simply forwarding the packets they receive, intermediate nodes are allowed to recombine (code) together some of the data packets received from different incoming links if necessary. By doing so, the maximum information flow in a network can always be achieved. However, performing coding operations (i.e. recombining data packets) incur computational overhead and delay of data processing at the corresponding nodes. In this paper, we investigate the optimization of the network coding based multicast routing problem with respect to two widely considered objectives, i.e. the cost and the delay. In general, reducing cost can result into a cheaper multicast solution for network service providers, while decreasing delay improves the service quality for users. Hence we model the problem as a bi-objective optimization problem to minimize the total cost and the maximum transmission delay of a multicast. This bi-objective optimization problem has not been considered in the literature. We adapt the Elitist Nondominated Sorting Genetic Algorithm (NSGA-II) for the new problem by introducing two adjustments. As there are many infeasible solutions in the search space, the first adjustment is an initialization scheme to generate a population of feasible and diversified solutions. These initial solutions help to guide the search towards the Pareto-optimal front. In addition, the original NSGA-II is very likely to produce a number of solutions with identical objective values at each generation, which may seriously deteriorate the level of diversity and the optimization performance. The second adjustment is an individual delegate scheme where, among those solutions with identical objective values, only one of them is retained in the population while the others are deleted. Experimental results reveal that each adopted adjustment contributes to the adaptation of NSGA-II for the problem concerned. Moreover, the adjusted NSGA-II outperforms a number of state-of-the-art multiobjective evolutionary algorithms with respect to the quality of the obtained nondominated solutions in the conducted experiments

A quantum inspired evolutionary algorithm for dynamic multicast routing with network coding

This paper studies and models the multicast routing problem with network coding in dynamic network environment, where computational and bandwidth resources are to be jointly optimized. A quantum inspired evolutionary algorithm (QEA) is developed to address the problem above, where a restart scheme is devised for well adapting QEA for tracing the ever-changing optima in dynamic environment. Experimental results show that the proposed QEA outperforms a number of existing evolutionary algorithms in terms of the best solution obtained

Rethinking Attention Mechanism in Time Series Classification

Attention-based models have been widely used in many areas, such as computer vision and natural language processing. However, relevant applications in time series classification (TSC) have not been explored deeply yet, causing a significant number of TSC algorithms still suffer from general problems of attention mechanism, like quadratic complexity. In this paper, we promote the efficiency and performance of the attention mechanism by proposing our flexible multi-head linear attention (FMLA), which enhances locality awareness by layer-wise interactions with deformable convolutional blocks and online knowledge distillation. What's more, we propose a simple but effective mask mechanism that helps reduce the noise influence in time series and decrease the redundancy of the proposed FMLA by masking some positions of each given series proportionally. To stabilize this mechanism, samples are forwarded through the model with random mask layers several times and their outputs are aggregated to teach the same model with regular mask layers. We conduct extensive experiments on 85 UCR2018 datasets to compare our algorithm with 11 well-known ones and the results show that our algorithm has comparable performance in terms of top-1 accuracy. We also compare our model with three Transformer-based models with respect to the floating-point operations per second and number of parameters and find that our algorithm achieves significantly better efficiency with lower complexity

An improved MOEA/D algorithm for multi-objective multicast routing with network coding

Network coding enables higher network throughput, more balanced traffic, and securer data transmission. However, complicated mathematical operations incur when packets are combined at intermediate nodes, which, if not operated properly, lead to very high network resource consumption and unacceptable delay. Therefore, it is of vital importance to minimize various network resources and end-to-end delays while exploiting promising benefits of network coding. Multicast has been used in increasingly more applications, such as video conferencing and remote education. In this paper the multicast routing problem with network coding is formulated as a multi-objective optimization problem (MOP), where the total coding cost, the total link cost and the end-to-end delay are minimized simultaneously. We adapt the multi-objective evolutionary algorithm based on decomposition (MOEA/D) for this MOP by hybridizing it with a population-based incremental learning technique which makes use of the global and historical information collected to provide additional guidance to the evolutionary search. Three new schemes are devised to facilitate the performance improvement, including a probability-based initialization scheme, a problem-specific population updating rule, and a hybridized reproduction operator. Experimental results clearly demonstrate that the proposed algorithm outperforms a number of state-of-the-art MOEAs regarding the solution quality and computational time

A Multiobjective Computation Offloading Algorithm for Mobile Edge Computing

In mobile edge computing (MEC), smart mobile devices (SMDs) with limited computation resources and battery lifetime can offload their computing-intensive tasks to MEC servers, thus to enhance the computing capability and reduce the energy consumption of SMDs. Nevertheless, offloading tasks to the edge incurs additional transmission time and thus higher execution delay. This paper studies the trade-off between the completion time of applications and the energy consumption of SMDs in MEC networks. The problem is formulated as a multiobjective computation offloading problem (MCOP), where the task precedence, i.e. ordering of tasks in SMD applications, is introduced as a new constraint in the MCOP. An improved multiobjective evolutionary algorithm based on decomposition (MOEA/D) with two performance enhancing schemes is proposed.1) The problem-specific population initialization scheme uses a latency-based execution location initialization method to initialize the execution location (i.e. either local SMD or MEC server) for each task. 2) The dynamic voltage and frequency scaling based energy conservation scheme helps to decrease the energy consumption without increasing the completion time of applications. The simulation results clearly demonstrate that the proposed algorithm outperforms a number of state-of-the-art heuristics and meta-heuristics in terms of the convergence and diversity of the obtained nondominated solutions

A modified ant colony optimization algorithm for network coding resource minimization

The paper presents a modified ant colony optimization approach for the network coding resource minimization problem. It is featured with several attractive mechanisms specially devised for solving the network coding resource minimization problem: 1) a multi-dimensional pheromone maintenance mechanism is put forward to address the issue of pheromone overlapping; 2) problem-specific heuristic information is employed to enhance the heuristic search (neighboring area search) capability; 3) a tabu-table based path construction method is devised to facilitate the construction of feasible (link-disjoint) paths from the source to each receiver; 4) a local pheromone updating rule is developed to guide ants to construct appropriate promising paths; 5) a solution reconstruction method is presented, with the aim of avoiding prematurity and improving the global search efficiency of proposed algorithm. Due to the way it works, the ant colony optimization can well exploit the global and local information of routing related problems during the solution construction phase. The simulation results on benchmark instances demonstrate that with the five extended mechanisms integrated, our algorithm outperforms a number of existing algorithms with respect to the best solutions obtained and the computational time

A hybrid EDA for load balancing in multicast with network coding

Load balancing is one of the most important issues in the practical deployment of multicast with network coding. However, this issue has received little research attention. This paper studies how traffic load of network coding based multicast (NCM) is disseminated in a communications network, with load balancing considered as an important factor. To this end, a hybridized estimation of distribution algorithm (EDA) is proposed, where two novel schemes are integrated into the population based incremental learning (PBIL) framework to strike a balance between exploration and exploitation, thus enhance the efficiency of the stochastic search. The first scheme is a bi-probability-vector coevolution scheme, where two probability vectors (PVs) evolve independently with periodical individual migration. This scheme can diversify the population and improve the global exploration in the search. The second scheme is a local search heuristic. It is based on the problem-specific domain knowledge and improves the NCM transmission plan at the expense of additional computational time. The heuristic can be utilized either as a local search operator to enhance the local exploitation during the evolutionary process, or as a follow-up operator to improve the best-so-far solutions found after the evolution. Experimental results show the effectiveness of the proposed algorithms against a number of existing evolutionary algorithms