The capacitated dispersion problem, which is a variant of the maximum diversity problem, aims to determine a set of elements within a network. These elements could symbolize, for instance, facilities in a supply chain or transmission nodes in a telecommunication network. While each element typically has a bounded service capacity, in this research, we introduce a twist. The capacity of each node might be influenced by a random Bernoulli component, thereby rendering the possibility of a node having zero capacity, which is contingent upon a black box mechanism that accounts for environmental variables. Recognizing the inherent complexity and the NP-hard nature of the capacitated dispersion problem, heuristic algorithms have become indispensable for handling larger instances. In this paper, we introduce a novel approach by hybridizing a heuristic algorithm with reinforcement learning to address this intricate problem variant.

The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to $25\%$ better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems.

This paper introduces a sim-exact methodology for stochastic combinatorial optimization problems. The approach combines exact optimization models with Monte Carlo or discrete-event simulation to evaluate candidate solutions under uncertainty. The method iteratively adjusts a control parameter based on simulation feedback and solves a sequence of deterministic optimization problems. Unlike scenario-based stochastic programming, the approach does not rely on explicit scenario enumeration, and unlike simheuristics, it preserves optimality with respect to each deterministic subproblem. The methodology is tested on the vehicle routing problem with stochastic demands under different levels of demand variability. Results are compared with a simheuristic approach and a sample average approximation (SAA) method. The results show that sim-exact performance is comparable to simheuristics, with no statistically significant differences in most cases, while SAA shows weaker performance under medium and high variability.

The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer’s frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications.

This paper presents a sim-exact algorithm for solving a stochastic capacitated dispersion problem under uncertainty. The method extends previous simheuristic approaches by replacing metaheuristic search with an iterative sequence of mixed-integer programming models, combined with simulation to evaluate stochastic feasibility and solution quality. Capacity uncertainty is modeled using a scaled Beta distribution. A chance constraint ensures that total effective capacity meets a required threshold with a given reliability level. To handle the nonlinearity of the dispersion objective, a mixed-integer linear programming formulation based on a telescopic representation of pairwise distances is used. The sim-exact procedure solves a sequence of increasingly conservative models controlled by a safety stock parameter. An incumbent solution pool is maintained across iterations. This pool is used to generate warm starts, improve bounds, reuse feasible solutions, and define stopping criteria. These mechanisms allow information to be transferred between iterations and reduce computational effort. Computational experiments are conducted on standard benchmark instances and compared against a simheuristic algorithm and a sample average approximation framework. Results show that the sim-exact method consistently produces higher-quality solutions than the simheuristic approach, with an average improvement of around 9.8% in objective value. It also yields stronger solutions than sample average approximation, which shows limited reliability in producing feasible solutions even for a large number of scenarios.