Combinatorial Optimization for Multiple Traveling Salesman Problems
Summary
The Multiple Traveling Salesman Problem (MTSP) is a canonical combinatorial optimisation challenge in which a fleet of salespeople must collectively visit a set of locations and return to a common depot while minimising aggregate cost. Extending the classical Travelling Salesman Problem, MTSP introduces additional dimensions of complexity, including workload balance among agents, capacity limits, time‐window constraints and heterogeneous agent capabilities. Exact methods based on integer programming offer guaranteed optimality but scale poorly, becoming infeasible for even modestly sized instances. As a consequence, research has focused on heuristic and metaheuristic frameworks—such as genetic, ant colony, particle swarm and novel population-based algorithms—that trade optimality guarantees for rapid convergence on high-quality solutions. Hybrid strategies that combine global search with local‐search operators or problem‐specific clustering have proven particularly effective at reconciling multi-objective goals. Applications span logistics and distribution, ride-sharing and drone deployment, mission planning for autonomous vehicles, and maintenance scheduling in manufacturing. Recent advances have sought to integrate real-time data streams, accommodate stochastic travel times and embed learnable components, signalling a trend towards adaptive and data-driven combinatorial optimisation in dynamic environments.
Research from Nature Portfolio
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Research from all publishers
Recent studies have introduced nature-inspired metaheuristics to enhance solution quality and operational realism. A discrete penguin search optimisation algorithm modelled on penguin foraging behaviours has been applied to standard benchmark instances, demonstrating rapid convergence and superior workload balance in large-scale MTSP scenarios. In spherical routing contexts—where nodes lie on a curved surface to represent global coordinates—an artificial electric field algorithm augmented by a greedy state transition strategy has improved population diversity and route accuracy, highlighting the value of three-dimensional modelling for air- and sea-borne logistics. Additionally, hybrid ant colony optimisation frameworks have been devised to incorporate minimum-spanning-tree heuristics and refined pheromone-update rules, effectively addressing vehicle capacity and delivery time-window constraints; empirical results show notable reductions in total distance and enhanced adherence to practical operational limits.
Combinatorial Optimization for Multiple Traveling Salesman Problems publication trend
The graph below shows the total number of articles in combinatorial optimization for multiple traveling salesman problems across all publications each year (not limited to Nature Index journals).
Technical terms
Combinatorial optimisation: The process of finding an optimal object from a finite set of discrete configurations.
Multiple Traveling Salesman Problem (MTSP): An extension of the Travelling Salesman Problem in which multiple agents must cover all nodes and return to a depot.
Metaheuristic algorithm: A higher-level procedure designed to guide subordinate heuristics to explore large search spaces efficiently.
Workload balance: The objective of distributing tasks or travel distances equitably among multiple agents.
Capacity constraint: A limitation on the quantity of goods or services an agent can handle on a route.
Time-window constraint: Specified intervals within which visits to particular locations must occur.
References
- Artificial Electric Field Algorithm with Greedy State Transition Strategy for Spherical Multiple Traveling Salesmen Problem. International Journal of Computational Intelligence Systems (2022).
- Efficient routing optimization with discrete penguins search algorithm for MTSP. Decision Making Applications in Management and Engineering (2023).
- Ant Colony Optimization With an Improved Pheromone Model for Solving MTSP With Capacity and Time Window Constraint. IEEE Access (2020).
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