In this study, we have explained a constrained travelling salesman problem (TSP) where total travelling cost must maintain a maximum level. The objective of this proposed TSP is to minimise the total travel time. In this proposed TSP we have considered a time interval dependent constraint as well. There is a time interval in which a traveller must visit a predetermined set of cities (city-set). Here, a city-set consists of a set of cities and the time interval is a time slot in his/her total time to complete the tour. The problem is solved in fuzzy random environment. The travel cost, time, and total travelling cost limit are considered as fuzzy random in nature. The proposed TSP is solved by an ant colony optimisation (ACO)-based approach. The basic ACO algorithm is improved by adopting a filtering operation. Finally, experimental results are given to illustrate the proposed approach; the computed results obtained are also highly encouraging. Copyright © 2021 Inderscience Enterprises Ltd.