In a multihop wireless network, wireless interference is a crucial factor in the maximum multiflow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks with a link schedule to support it. In this paper, we observe that network coding could help to decrease the impact of wireless interference, and thus propose a framework to study the MMF problem for multihop wireless networks with network coding. Firstly, a network model is established to describe the new conflict relations and schedulability modified by network coding. Next, we formulate the MMF problem to compute the maximum throughput of multiple unicast flows supported by the multihop wireless network with network coding, and show that its capacity region could be enlarged by performing network coding. Finally, we show that determining the capacity region of a multihop wireless network with network coding is an NP-hard problem, and thus propose a greedy heuristic algorithm, called coding-first collecting (CFC), to determine a capacity subregion of the network. We also show that finding an optimal hyperarc schedule to meet a given link demand function is NP-hard, and propose a polynomial algorithm, called coding-first scheduling (CFS), to find an approximate fractional hyperarc schedule in the multihop wireless network with network coding. A numerical analysis of a grid wireless network and a random wireless network is presented to demonstrate the efficiencies of the CFC algorithm and the CFS algorithm based on the framework.

The equilibrium optimizer (EO) is a novel physics-based meta-heuristic optimization algorithm that is inspired by estimating dynamics and equilibrium states in controlled volume mass balance models. As a stochastic optimization algorithm, EO inevitably produces duplicated solutions, which is wasteful of valuable evaluation opportunities. In addition, an excessive number of duplicated solutions can increase the risk of the algorithm getting trapped in local optima. In this paper, an improved EO algorithm with a bis-population-based non-revisiting (BNR) mechanism is proposed, namely BEO. It aims to eliminate duplicate solutions generated by the population during iterations, thus avoiding wasted evaluation opportunities. Furthermore, when a revisited solution is detected, the BNR mechanism activates its unique archive population learning mechanism to assist the algorithm in generating a high-quality solution using the excellent genes in the historical information, which not only improves the algorithm's population diversity but also helps the algorithm get out of the local optimum dilemma. Experimental findings with the IEEE CEC2017 benchmark demonstrate that the proposed BEO algorithm outperforms other seven representative meta-heuristic optimization techniques, including the original EO algorithm.

Many optimisation algorithms improve the algorithm from the perspective of population structure. However, most improvement methods simply add hierarchical structure to the original population structure, which fails to fundamentally change its structure. In this paper, we propose an umbrellalike hierarchical artificial bee colony algorithm (UHABC). For the first time, a historical information layer is added to the artificial bee colony algorithm (ABC), and this information layer is allowed to interact with other layers to generate information. To verify the effectiveness of the proposed algorithm, we compare it with the original artificial bee colony algorithm and five representative meta-heuristic algorithms on the IEEE CEC2017. The experimental results and statistical analysis show that the umbrellalike mechanism effectively improves the performance of ABC.