This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method.

The primary purpose of this study is to introduce diamond intuitionistic fuzzy sets ( D-IFS s). Although several generalizations of intuitionistic fuzzy sets have been introduced in the literature, the constraints of IFS s limit decision-makers ability to freely choose the degree of membership (validity, etc.) and non-membership (non-validity, etc.). The D-IFS , however, offers this flexibility, which is why these new sets are introduced. By applying a mild restriction on the D-IFS , a novel generalization, known as the lozenge intuitionistic fuzzy set has been acquired. Some properties of these intuitionistic fuzzy sets are characterized geometrically. The main aim of this research is also to establish some basic operations and inclusions for D-IFS s, along with some well-known rules. On the other hand, Szmidt and Kacprzyk’s forms of Hamming distance and, Euclidean distance for D-IFS s are defined. Additionally, new score and accuracy functions are presented to compare newly defined diamond intuitionistic fuzzy relations ( D-IFR s). Moreover, two new max-min operations have been derived to analyze the decomposition of D-IFR s. Finally, a practical assessment of medical diagnosis in patients is conducted to demonstrate the feasibility and value of the proposed approaches.

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

Recently, the rapid advancement and proliferation of drone or unmanned aerial vehicle (UAV) technology have ushered in a new era of possibilities and challenges in various fields

This paper investigates the application of a minimum loss path finding algorithm to determine the maximum flow in generalized networks that are characterized by arc losses or gains. In these generalized network flow problems, each arc has not only a defined capacity but also a loss or gain factor, which must be taken into consideration when calculating the maximum achievable flow. This extension of the traditional maximum flow problem requires a more comprehensive approach, where the maximum amount of flow is determined by accounting for additional factors such as costs, varying arc capacities, and the specific loss or gain associated with each arc. This paper extends the classic Ford–Fulkerson algorithm, adapting it to iteratively identify source-to-sink (s − t) residual directed paths with minimum cumulative loss and generalized augmenting paths (GAPs), thus enabling the efficient computation of maximum flow in such complex networks. Moreover, to enhance the computational performance of the proposed algorithm, we conducted extensive studies on parallelization techniques using graphics processing units (GPUs). Significant improvements in the algorithm’s efficiency and scalability were achieved. The results demonstrate the potential of GPU-accelerated computations in handling real-world applications where generalized network flows with arc losses and gains are prevalent, such as in telecommunications, transportation, or logistics networks.