<p>This paper proposes a multi-objective capacitated location-routing problem with stochastic demands and time windows applicable in household waste logistics management. The problem involves two interrelated decisions: locating waste transfer stations and routing vehicles through transfer stations and collection points. A solution approach Query based on a squirrel search algorithm with path-relinking, randomized local search, stochastic simulation and non-dominated sorting is introduced to solve the problem. The effects of a vehicle preference index and trapezoidal time windows over total cost and satisfaction are examined through numerical experiments. The approach is tested on benchmark instances and compared with other methods, showing that our algorithm is effective and efficient in finding satisfactory solutions within a reasonable computational time. A real case study is presented to demonstrate the applicability and usefulness of the proposed model and solution method.</p>