Deep soft-rock tunnels are prone to large deformations and structural damage. This study used the Guanyinping Tunnel as a prototype and conducted 1/50-scale progressive loading model tests under three support configurations: rock-bolt-free, equal-length rock bolts, and mixed long–short rock bolts. Rock stress, radial rock displacement (u), and rock bolt axial force (F_N) at the vault, arch shoulders, sidewalls, and wall feet were monitored to reveal reinforcement mechanisms and mechanical response. The results indicated that stress evolution in the bolt-free case exhibited significant spatial heterogeneity. The vault experienced horizontal stress concentration, while the arch shoulder underwent vertical stress concentration. u underwent a three-stage nonlinear progression: elastic linear growth, plastic linear growth, and plastic-accelerated growth. Displacement at the vault was markedly larger than that at other locations. Equal-length rock bolts substantially improved the rock mass stability by delaying stress concentration and fracture propagation. This reinforcement raised the elastic response threshold to 96 kPa and substantially reduced u. F_N at the vault and shoulder followed linear growth, accelerated growth, and then gradual decline, whereas F_N at the sidewalls and wall feet exhibited a steady linear trend. Combined long and short rock bolts produced a multi-level anchoring effect. Short bolts induced a shallow arching action, while long bolts provided deep suspension. This synergy raised the elastic response threshold to a maximum of 120 kPa and moderated the stress reduction process. Deep residual stresses increased to 74.3–88.4% of peak values. The displacement gradient between shallow and deep rock masses was significantly reduced. The coordinated deformation capacity within the anchoring zone was markedly enhanced. F_N distribution exhibited spatial differentiation: short bolts carried the load initially, followed by the activation of long bolts. Both anchoring schemes increased residual stress and mitigated rock mass deformation. The deformation control effect was stronger in shallow rock mass than in deep rock mass. Improvements at the vault and arch shoulders exceeded those at the sidewalls and wall feet. The mixed short–long bolt configuration was superior because it maximized the self-bearing capacity of the deep rock mass. The findings provide experimental data and theoretical guidance for the design and optimization of rock-bolt support in deep soft-rock tunnels.

Aiming at the problem that existing intuitionistic fuzzy entropy measures fail to fully balance the interaction between intuition (determined by hesitation degree) and fuzziness (characterized by the difference between membership degree and non-membership degree), this paper proposes the concept of isentropic arc, reveals the mutual offset effect of the two in entropy composition, and provides a new theoretical perspective for the planar analysis of entropy measures. Further research finds that there are maximum and minimum entropy points in the intuitionistic fuzzy entropy plane. Based on this, two different types of isentropic arcs can be constructed. Combining this feature with the core logic of approaching the ideal solution, this paper constructs a new intuitionistic fuzzy entropy measure formula based on the TOPSIS method. This formula can characterize the synergistic influence of intuition and fuzziness at the same time, meets all the constraints of the axiomatic definition, and is more suitable for the needs of actual decision-making scenarios. Comparative analysis of numerical examples shows that the proposed new entropy measure has significantly better discrimination than existing methods for six groups of samples with a high hesitation degree and high fuzziness, and the entropy value ranking is consistent with the ranking of the uncertainty information contained in the samples. Finally, the weight decision-making model based on this entropy measure is applied to the evaluation of coal mine emergency rescue capability, verifying its practical value in solving complex uncertainty problems.

Effective constrained multiobjective optimization requires a search process to coordinate feasibility attainment, objective-space progress, and population distribution under a limited evaluation budget. This coordination becomes more difficult in dual-population frameworks when auxiliary search loses objective-direction information, applies unsuitable constraint tolerance, or consumes resources that no longer match its current contribution. Motivated by these limitations, we develop the Multi-Morphogen Field-Guided Constrained Multiobjective Evolutionary Algorithm (MFGCMOEA). Its main population is responsible for feasibility-oriented convergence, whereas the auxiliary population encodes each objective through a separate morphogen channel. Signals are propagated according to relative geometry in objective-rank space, allowing local search information to modify the developmental state of each candidate. These channel-wise states are then used to construct individual constraint buffers and multidimensional phenotypes, so promising infeasible directions can remain competitive without collapsing multiple objectives into a single scalar evaluation. Diversity regulation is applied only when truncation is required on the critical developmental front. For computational coordination, MFGCMOEA derives resource evidence from offspring developmental quality and realized auxiliary recruitment and combines it with a symmetric basal-growth term to prevent overly polarized offspring allocation. The method was evaluated on 47 benchmark problems from four suites using 30 independent runs. Among nine algorithms, MFGCMOEA obtained the best overall mean ranks, approximately 1.66 for IGD and 1.74 for HV. On the 26 problems with complete valid results for all methods, the Friedman test detected significant overall differences, while Holm-adjusted pairwise comparisons favored MFGCMOEA against all eight competitors with large rank-biserial effect sizes. Additional convergence, distribution, ablation, and diagnostic results further confirm the roles of the developmental-field representation and homeostatic resource regulation.

Solving constrained multiobjective optimization problems (CMOPs) is highly challenging due to the presence of complicated feasible regions, intense conflicts among objectives, and unevenly distributed constraints. As a result, conventional methods relying on a single constraint-handling mechanism frequently fail to maintain a stable equilibrium among solution feasibility, diversity, and convergence. To overcome these bottlenecks, this article introduces AFFCMO, a novel adaptive feasibility-guided framework tailored for constrained multiobjective optimization. At its core, the proposed approach utilizes a coevolutionary dual-population architecture that divides the search process into two distinct tasks. Specifically, an auxiliary population is tasked with global exploration, while a primary population focuses on the intensive exploitation of discovered feasible areas. To achieve this, the primary population leverages a DE/current-to-pbest/1 differential evolution strategy to closely approximate the constrained Pareto front. Simultaneously, the auxiliary population expands the search space using a mutation operator that adapts to the current evolutionary stage. Furthermore, exploration is bolstered by a multicriterion environmental selection scheme designed for the auxiliary group. By combining Euclidean geometric distributions, constraint relaxation, and value modeling inspired by epidemic dynamics, this strategy successfully preserves valuable infeasible solutions that can guide the search. Additionally, a dynamic resource allocation strategy based on historical search feedback and Thompson sampling is incorporated. This mechanism continuously evaluates the recent search contributions of both populations and adaptively adjusts their offspring sizes, thereby reducing the bias introduced by static allocation schemes. This mechanism continuously assesses the actual search contributions of both populations, allowing for the adaptive resizing of offspring generations and thereby eliminating the inherent biases of static allocation methods. Comprehensive empirical evaluations are conducted on 47 benchmark problems from four distinct test suites. The results indicate that AFFCMO significantly outperforms seven contemporary multiobjective evolutionary algorithms in terms of exploring complex feasible regions, preserving solution diversity, and achieving high convergence accuracy.

Constrained multiobjective optimization seeks Pareto optimal tradeoffs among conflicting objectives subject to prescribed constraints. Although the final solutions must be feasible, evolutionary variation can generate infeasible intermediate decision vectors during the search. One difficulty in this process is identifying mildly infeasible candidates that still provide valuable search directions, while another is distributing a fixed evaluation budget between cooperative populations whose contributions vary during evolution. To address these issues, this paper proposes IRCMO, a biologically inspired dual population constrained multiobjective evolutionary algorithm. The main population focuses on approximating the Pareto front formed by feasible solutions, while the auxiliary population preserves complementary search directions near constraint boundaries in the decision space. An Immune Tolerance and Niche Exclusion Selection strategy (ITNES) adaptively determines a tolerance boundary from the current feasibility status. It applies a squared response only to excess constraint violation and preserves sparse search directions in both the objective and decision spaces. This enables the auxiliary population to exploit mildly infeasible candidates without losing feasibility pressure, thereby improving convergence and front coverage under restrictive constraint structures. A Replicator Complementarity Homeostatic Resource Allocation strategy (RCHRA) evaluates offspring improvement and cross population complementarity. It assigns more offspring evaluations to the population making a stronger current contribution while maintaining a minimum resource share for both populations. This improves the utilization of the fixed evaluation budget and reduces persistent search imbalance between the two populations. Experiments on 47 benchmark problems and 12 real world CMOPs against seven representative algorithms show that IRCMO obtains the lowest overall average ranks for both IGD and HV. All pairwise Wilcoxon tests are significant at the 0.05 level.

In this work, we further investigate the surface wave attenuation performance of elastic metasurfaces composed of in-filled pipes in a layered half-space, focusing on the dispersion relations and transmission properties. Particularly, both Rayleigh waves and Love waves are considered. The introduction of soil layers will reduce the width of attenuation zones. Additionally, transmission simulations reveal complex propagation patterns for elastic metasurfaces in a layered half-space, including wave reflection, wave resonance, and higher-order wave modes, which will hinder the penetration of converted shear waves into the half-space. In contrast, in reference cases, only surface-shear wave mode conversion is observed. Moreover, the attenuation performance of elastic metasurfaces is also diminished in layered soils in the frequency domain, and a nonuniform displacement distribution behind the elastic metasurface is also found. Last but not least, the feasibility of elastic metasurfaces to train-induced ground-borne vibration mitigation is numerically verified in the time domain. Although the performance of elastic metasurfaces in layered soils is inferior to that in homogeneous soils, they are better than traditional trenches within the main frequency range. Snapshots from the transient simulation clearly show the evolution of wave fields, reinforcing the observed key findings. Due to excellent surface-wave-attenuation performance and ease of realization, these novel elastic metasurfaces hold great potential in ambient vibration mitigation.