Fuzzy Optimization Techniques for Shortest Path Problems
Summary
Fuzzy optimization for shortest path problems addresses uncertainty in network weights by representing arc costs with fuzzy numbers rather than crisp values. By extending classical algorithms—such as Dijkstra’s and Bellman–Ford—to operate in fuzzy environments, researchers can model the imprecision inherent in travel times, traffic densities, service reliability and other real‐world factors. Techniques range from type-1 fuzzy sets that capture simple vagueness to interval-valued and intuitionistic fuzzy sets that account for higher-order uncertainty and indeterminacy. Metaheuristic approaches, including evolutionary algorithms, swarm intelligence and nature-inspired methods, have been adapted to process fuzzy arithmetic and ranking functions, enabling efficient exploration of complex networks. Applications span urban traffic management, telecommunications routing, logistics planning and emergency response, demonstrating both theoretical advances in fuzzy set theory and practical gains in decision accuracy under ambiguity.
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Recent studies have introduced advanced metaheuristic and multi-objective frameworks to solve fuzzy shortest path problems under complex uncertainty. One work extends fuzzy arithmetic to mixed interval-valued fuzzy numbers and proposes a modified artificial bee colony algorithm that approximates membership functions via α-cuts and custom distance measures; this approach outperforms genetic and particle swarm methods in wireless sensor network routing by reducing convergence time and iteration counts. Another study bridges fuzzy multi-objective shortest path problems and data envelopment analysis, treating each arc as a decision-making unit with fuzzy inputs and outputs; by computing relative fuzzy efficiency scores, the problem is transformed into a single-objective fuzzy shortest path formulation that accommodates conflicting criteria such as cost, time and risk. A further contribution presents a ripple-spreading algorithm inspired by natural wave propagation; capable of handling triangular and trapezoidal fuzzy weights, it identifies all Pareto-optimal paths in a single run while maintaining theoretical guarantees of optimality and demonstrating robustness across benchmark scenarios.
Fuzzy Optimization Techniques for Shortest Path Problems publication trend
The graph below shows the total number of articles in fuzzy optimization techniques for shortest path problems across all publications each year (not limited to Nature Index journals).
Technical terms
Fuzzy set: A mathematical construct in which elements have degrees of membership between zero and one, modelling vagueness rather than binary inclusion.
Membership function: A curve that assigns to each element of a domain a value in [0,1], representing its degree of belonging to a fuzzy set.
Interval-valued fuzzy number: A fuzzy number characterised by an interval of membership grades for each element, capturing uncertainty about the degree of membership.
Triangular fuzzy number: A simple fuzzy number defined by a triplet (l, m, u), representing a linear increase from l to m and a decrease from m to u in membership values.
Multi-objective optimisation: The process of simultaneously optimising two or more conflicting objectives, seeking a set of trade-off or Pareto-optimal solutions.
References
- Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem. Complex & Intelligent Systems (2021).
- Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach. Complex & Intelligent Systems (2021).
- A deterministic and nature-inspired algorithm for the fuzzy multi-objective path optimization problem. Complex & Intelligent Systems (2022).
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