This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.

Research related to vehicle routing and its applications reveals the interest in supporting the authorities in solving society’s problems. In this way, a bi-objective model of mixed integer linear programming and metaheuristics based on genetic algorithm and local search, applied to reverse logistics by green open vehicle routing, is presented. The process consists of collecting solid urban waste at collection points, contributing to urban sustainability through the route plan determined by the proposal, optimizing distances and costs as well; it also measures the fuel consumption of the vehicles from their departure from the depot to the last collection point, as well as the CO2 emissions during routing. The proposals, implemented in GLPK and Python, obtain results in various scenarios. The model generates solutions quickly in scenarios between 5 and 25 collection points. For larger scenarios it does not find solutions within the time limit of 7200 seconds. The metaheuristics have greater potential as for 31 collection points, the processing time was 2.3 seconds which is a good indication for larger scenarios. Three Sectors of Trujillo city are tested to evaluate our proposal.

Edge detection remains challenging under the strong noise and low-contrast conditions typical of scanning electron microscopy (SEM) images. While fractional-order operators improve robustness over classical derivatives, selecting the fractional order is critical, and existing adaptive strategies either rely on noise-sensitive local variance or require heavily tuned noise-suppression pipelines. This work introduces ABC-AED, an adaptive edge detection method based on the Atangana–Baleanu fractional operator in the Caputo sense, which exploits its smoothing and fading-memory properties to build a fractional edge mask whose order is adaptively determined from a bilateral-filter-based local intensity map, without training data or per-image calibration. The method is evaluated on natural images, noise-corrupted natural images, and SEM images of nanoparticles, and compared against a local-variance-based fractional operator (2D-AFCD) and an adaptive anisotropic diffusion scheme combined with Canny (AAPDE-Canny) using Jaccard index, F1-score, Precision, and Recall. ABC-AED achieves accuracy comparable to, and in several SEM cases slightly better than, AAPDE-Canny, while being more than eight times faster than AAPDE-Canny, offering a favorable accuracy–efficiency trade-off for SEM-based nanoparticle characterization.