One of the advances made in the management of human resources for the effective implementation of service delivery is the creation of personnel schedules. In this context, especially in terms of the majority of health-care systems, creating nurse schedules comes to the fore. Nurse scheduling problem (NSP) is a complex optimization problem that allows for the preparation of an appropriate schedule for nurses and, in doing so, considers the system constraints such as legal regulations, nurses’ preferences, and hospital policies and requirements. There are many studies in the literature that use exact solution algorithms, heuristics, and meta-heuristics approaches. Especially in large-scale problems, for which deterministic methods may require too much time and cost to reach a solution, heuristics and meta-heuristic approaches come to the fore instead of exact methods. In the first phase of the study, harmony search algorithm (HSA), which has shown progress recently and can be adapted to many problems is applied for a dataset in the literature, and the algorithm’s performance is evaluated by comparing the results with other heuristics which is applied to the same dataset. As a result of the evaluation, the performance of the classical HSA is inadequate when compared to other heuristics. In the second phase of our study, by considering new approaches proposed by the literature for HSA, the effects on the algorithm’s performance of these approaches are investigated and we tried to improve the performance of the algorithm. With the results, it has been determined that the improved algorithm, which is called opposition-based parallel HSA, can be used effectively for NSPs.

The traveling salesman problem (TSP) is a well‐known NP‐hard combinatorial optimization problem. In TSP, the objective is to find the shortest distance to the most appropriate route to the starting city. Finding an optimal solution in a reasonable time becomes difficult as the number of cities increases. In recent years, metaheuristic methods obtained optimal or near‐optimal solutions in TSP in an acceptable time. This paper proposes a new hybrid metaheuristic method for solving the TSP. The proposed method is developed by combining the 3‐Opt method and the improved discrete cuckoo search algorithm. The performance of the proposed method is tested on 39 different benchmark problems in the TSPLIB library. For the 39 different benchmark problems with a size of less than 150 cities, the proposed hybrid method found optimal solutions. In addition, it was observed that as the problem size increases, the results obtained are closer to the optimum compared to other methods. When compared to studies in the literature using the same problem, similar or better results were obtained. For 500 iterations, the average best solution of the proposed method differed from the average optimal solution by 0.07%. In the results of the improved discrete cuckoo search algorithm (CSA), this rate was calculated to be 0.08%. In terms of processing time, the average time of the proposed algorithm was 11.46 seconds, while the average time of the improved discrete CSA was 92.86 seconds. For 1000 iterations, the deviation of the proposed method from the average optimal solution is 0.05%, and the average processing time is 23.72 seconds. The experimental results showed that the proposed new hybrid‐improved discrete CSA is effective for solving TSP.

Selecting the right energy storage system (ESS) for grid integration is a high-stakes decision involving conflicting technical, economic, environmental, and risk criteria under deep uncertainty. The existing fuzzy multi-criteria decision-making (MCDM) methods either fail to capture neutral or abstaining expert judgments or treat evaluation criteria as independent, which is an unrealistic assumption in complex engineering decisions. To address both limitations simultaneously, this study develops four new aggregation operators by extending the Bonferroni mean (BM) into the q-rung picture fuzzy sets (q-RPFSs) framework: the q-RPFBM-based, q-RPFWBM-based, q-RPFGBM-based, and q-RPFWGBM-based operators. Unlike the existing q-RPFS operator families (Dombi, Frank, Fermatean, Yager, Maclaurin), which aggregate criteria independently, BM-based operators explicitly model pairwise interactions among criteria with a structurally distinct aggregation logic that is especially critical when criteria such as cost, risk, reliability, and environmental impact are mutually correlated. The theoretical validity of the operators is confirmed through proofs of idempotency, monotonicity, and boundedness. Applied to a comprehensive ESS selection problem for Türkiye (covering nine alternatives across nineteen sub-criteria and five main criteria, including an explicit risk dimension), the framework consistently identifies pumped hydro storage as the optimal choice. Sensitivity analyses under varying q, s, and t parameters, as well as perturbed criterion weights, confirm the robustness of this ranking. The proposed framework offers energy planners and decision-makers a principled and transparent tool for evaluating ESS under high uncertainty and criterion interdependence.