There are several intelligent algorithms that are continually being improved for better performance when solving the flexible job-shop scheduling problem (FJSP); hence, there are many improvement strategies in the literature. To know how to properly choose an improvement strategy, how different improvement strategies affect different algorithms and how different algorithms respond to the same strategy are critical questions that have not yet been addressed. To address them, improvement strategies are first classified into five basic improvement strategies (five structures) used to improve invasive weed optimization (IWO) and genetic algorithm (GA) and then seven algorithms (S1–S7) used to solve five FJSP instances are proposed. For the purpose of comparing these algorithms fairly, we consider the total individual number (TIN) of an algorithm and propose several evaluation indexes based on TIN. In the process of decoding, a novel decoding algorithm is also proposed. The simulation results show that different structures significantly affect the performances of different algorithms and different algorithms respond to the same structure differently. The results of this paper may shed light on how to properly choose an improvement strategy to improve an algorithm for solving the FJSP.

Populations of multipopulation genetic algorithms (MPGAs) parallely evolve with some interaction mechanisms. Previous studies have shown that the interaction structures can impact on the performance of MPGAs to some extent. This paper introduces the concept of complex networks such as ring-shaped networks and small-world networks to study how interaction structures and their parameters influence the MPGAs, where subpopulations are regarded as nodes and their interaction or migration of elites between subpopulations as edges. After solving the flexible job-shop scheduling problem (FJSP) by MPGAs with different parameters of interaction structures, simulation results were measured by criteria, such as success rate and average optimal value. The analysis reveals that (1) the smaller the average path length (APL) of the network is, the higher the propagation rate will be; (2) the performance of MPGAs increased first and then decreased along with the decrease of APL, indicating that, for better performance, the networks should have a proper APL, which can be adjusted by changing the structural parameters of networks; and (3) because the edge number of small-world networks remains unchanged with different rewiring possibilities of edges, the change in performance indicates that the MPGA can be improved by a more proper interaction structure of subpopulations as other conditions remain unchanged.

With recent industrial upgrades, it is essential to transform the current forward supply networks (FSNs) into closed-loop supply networks (CLSNs), which are formed by the integration of forward and reverse logistics. The method chosen in this paper for building reverse logistics is to add additional functions to the existing forward logistics. This process can be regarded as adding reverse edges to the original directed edges in an FSN. Due to the limitation of funds and the demand for reverse flow, we suppose that a limited number of reverse edges can be built in a CLSN. To determine the transformation schemes with excellent robustness against malicious attacks, this paper proposes a multi-population evolutionary algorithm with novel operators to optimize the robustness of the CLSN, and this algorithm is abbreviated as MPEA-RSN. Then, both the generated and realistic SNs are taken as examples to validate the effectiveness of MPEA-RSN. The simulation results show that the index R, introduced to evaluate the robustness of CLSNs, can be improved by more than 95%, and this indicates that (1) the different schemes for adding reverse routes to an FSN can lead to different robustness values, and (2) the robustness of the transformed CLSN to malicious attacks can be significantly improved after optimization by MPEA-RSN. When an FSN is to be transformed into a CLSN, this paper can provide a frame of reference for building a CLSN that is robust to malicious attacks from a network structural perspective.