The Orienteering Problem (OP) is a well-studied routing problem that has been extended to incorporate uncertainties, reflecting stochastic or dynamic travel costs, prize-collection costs, and prizes. Existing approaches may, however, be inefficient in real-world applications due to insufficient modeling knowledge and initially unknowable parameters in online scenarios. Thus, we propose the Uncertain and Dynamic Orienteering Problem (UDOP), modeling travel costs as distributions with unknown and time-variant parameters. UDOP also associates uncertain travel costs with dynamic prizes and prize-collection costs for its objective and budget constraints. To address UDOP, we develop an ADaptive Approach for Probabilistic paThs - ADAPT, that iteratively performs 'execution' and 'online planning' based on an initial 'offline' solution. The execution phase updates system status and records online cost observations. The online planner employs a Bayesian approach to adaptively estimate power consumption and optimize path sequence based on safety beliefs. We evaluate ADAPT in a practical Unmanned Aerial Vehicle (UAV) charging scheduling problem for Wireless Rechargeable Sensor Networks. The UAV must optimize its path to recharge sensor nodes efficiently while managing its energy under uncertain conditions. ADAPT maintains comparable solution quality and computation time while offering superior robustness. Extensive simulations show that ADAPT achieves a 100% Mission Success Rate (MSR) across all tested scenarios, outperforming comparable heuristic-based and frequentist approaches that fail up to 70% (under challenging conditions) and averaging 67% MSR, respectively. This work advances the field of OP with uncertainties, offering a reliable and efficient approach for real-world applications in uncertain and dynamic environments.

This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is associated with each subgroup and is gained only if all of its nodes are visited; however, at most one subgroup can be visited per cluster. The objective is to maximize the total collected reward while attaining a travel budget. We show that our new formulation has the ability to model and solve two previous well-known variants, the Clustered Orienteering Problem (COP) and the Set Orienteering Problem (SOP), in addition to other scenarios introduced here. An Integer Linear Programming (ILP) formulation and a Tabu Search-based heuristic are proposed to solve the problem. Experimental results indicate that the ILP method can yield optimal solutions at the cost of time, whereas the metaheuristic produces comparable solutions within a more reasonable computational cost.

The Orienteering Problem (OP) presents a unique challenge in combinatorial optimization, emphasized by its widespread use in logistics, delivery, and transportation planning. Given the NP-hard nature of OP, obtaining optimal solutions is inherently complex. While Pointer Networks (Ptr-Nets) have exhibited prowess in various combinatorial tasks, their performance in the context of OP leaves room for improvement. Recognizing the potency of Q-learning, especially when paired with deep neural structures, this research unveils the Pointer Q-Network (PQN). This innovative method combines Ptr-Nets and Q-learning, effectively addressing the specific challenges presented by OP. We deeply explore the architecture and efficiency of PQN, showcasing its superior capability in managing OP situations.

Repeated exploration of a water surface to detect objects of interest and their subsequent monitoring is important in search-and-rescue or ocean clean-up operations. Since the location of any detected object is dynamic, we propose to address the combined surface exploration and monitoring of the detected objects by modeling spatio-temporal reward states and coordinating a team of vehicles to collect the rewards. The model characterizes the dynamics of the water surface and enables the planner to predict future system states. The state reward value relevant to the particular water surface cell increases over time and is nullified by being in a sensor range of a vehicle. Thus, the proposed multi-vehicle planning approach is to minimize the collective value of the dynamic model reward states. The purpose is to address vehicles' motion constraints by using model predictive control on receding horizon, thus fully exploiting the utilized vehicles' motion capabilities. Based on the evaluation results, the approach indicates improvement in a solution to the kinematic orienteering problem and the team orienteering problem in the monitoring task compared to the existing solutions. The proposed approach has been experimentally verified, supporting its feasibility in real-world monitoring tasks.

This paper introduces a wall construction planner for Unmanned Aerial Vehicles (UAVs), which uses a Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic to generate near-time-optimal building plans for even large walls within seconds. This approach addresses one of the most time-consuming and labor-intensive tasks, while also minimizing workers' safety risks. To achieve this, the wall-building problem is modeled as a variant of the Team Orienteering Problem and is formulated as Mixed-Integer Linear Programming (MILP), with added precedence and concurrence constraints that ensure bricks are built in the correct order and without collision between cooperating agents. The GRASP planner is validated in a realistic simulation and demonstrated to find solutions with similar quality as the optimal MILP, but much faster. Moreover, it outperforms all other state-of-the-art planning approaches in the majority of test cases. This paper presents a significant advancement in the field of automated wall construction, demonstrating the potential of UAVs and optimization algorithms in improving the efficiency and safety of construction projects.

In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due to the given maximum flight time. Hence, the requested locations must be prioritized and the problem of selecting the most important locations is modeled as an Orienteering Problem (OP). To fully exploit the kinematic properties of the UAV in such scenarios, we combine the OP with the generation of time-optimal trajectories with bounds on velocity and acceleration. We define the resulting problem as the Kinematic Orienteering Problem (KOP) and propose an exact mixed-integer formulation together with a Large Neighborhood Search (LNS) as a heuristic solution method. We demonstrate the effectiveness of our approach based on Orienteering instances from the literature and benchmark against optimal solutions of the Dubins Orienteering Problem (DOP) as the state-of-the-art. Additionally, we show by simulation \color{black} that the resulting solutions can be tracked precisely by a modern MPC-based flight controller. Since we demonstrate that the state-of-the-art in generating time-optimal trajectories in multiple dimensions is not generally correct, we further present an improved analytical method for time-optimal trajectory generation.

Abstract: Gradual pattern extraction is a field in (KDD) Knowledge Discovery in Databases that maps correlations between attributes of a data set as gradual dependencies. A gradual dependency may take a form of "the more Attribute K, the less Attribute L". In this paper, we propose an ant colony optimization technique that uses a probabilistic approach to learn and extract frequent gradual patterns. Through computational experiments on real-world data sets, we compared the performance of our ant-based algorithm to an existing gradual item set extraction algorithm and we found out that our algorithm outperforms the later especially when dealing with large data sets. Abstract: Ant Colony Optimization algorithm is a magnificent heuristics technique based on the behavior of ants.

This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be one-dimensional or points in the environment, and can have spatial correlation, i.e., visiting a feature in the environment may provide a portion of the reward associated with a correlated feature. A robot incurs costs as it traverses the environment, and the total cost for its route is limited by a resource constraint such as battery life or operation time. As environments are often large, we permit multiple depots where the robots must start and end their routes. The CAOP generalizes the correlated orienteering problem (COP), where the rewards are only associated with point features, and the arc orienteering problem (AOP), where the rewards are not spatially correlated. We formulate a mixed integer quadratic program (MIQP) that formalizes the problem and gives optimal solutions. However, the problem is NP-hard, and therefore we develop an efficient greedy constructive algorithm. We illustrate the problem with two different applications: informative path planning for methane gas leak detection and coverage of road networks.

Multicomponent problems are hard to solve as each component has the potential to influence the feasibility as well as the quality of the other components [4]. Among the studied multi-component problems, vehicle routing problems with loading constraints [15] appear to be very frequently investigated. In these problems, tour are to be created for vehicles while constraints and aims of specific loading policies must be taken into account. One of these problems is the Traveling Thief Problem (TTP), which combines two classic well-known and well-studied problems: the Knapsack Problem (KP) and the Traveling Salesman Problem (TSP). The TTP was proposed in 2013 by Bonyadi et al. [3] in order to provide an academic abstraction of multi-component problems for the scientific community. In the TTP, a thief travels across all cities (TSP component) and steals items along the way (KP component).

We propose a novel non-randomized anytime orienteering algorithm for finding k-optimal goals that maximize reward on a specialized graph with budget constraints. This specialized graph represents a real-world scenario which is analogous to an orienteering problem of finding k-most optimal goal states.