Multi-robot routing with linear decreasing rewards over time

2013

In this paper, we study Multiple Agents Maximum Collection Problem with Time Dependent Rewards (MAM-CP-TDR) which is a variant of Multiple Tour Maximum Collection Problem (MTMCP) (Butt & Cavalier, 1994). In MAMCP-TDR, there are multiple agents to collect linearly decreasing rewards over time. The objective is to maximize total surplus (total reward collected minus total travel cost) by routing multiple agents from a central depot. We propose a mathematical formulation for the problem. Since the problem is strongly NP-hard, we develop a heuristic algorithm, called Cluster-and-Route Algorithm (CRA), to find near-optimal solutions. In CRA, first we cluster the targets/rewards using the well-known k-means clustering algorithm. Then, we find tours by solving a single agent problem for each cluster. To solve the single agent problem, we propose several routing algorithms. Finally, we implement several improvement ideas to improve the final solution. We conduct computational experiments on randomly generated instances and instances of a related problem in the literature to test the performance of routing algorithms for single agent case and the CRA for MAMCP-TDR in terms of solution time and solution quality. Compared to the mathematical formulation, we conclude that CRA provides solutions with similar quality for small instances and performs significantly better both in terms of solution time and solution quality on medium and large instances.

Proceedings of the AAAI Conference on Artificial Intelligence

We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of con...

Proceedings of the AAAI Conference on Artificial Intelligence

We propose an auction algorithm to allocate tasks that have temporal constraints to cooperative robots. Temporal constraints are expressed as time windows, within which a task must be executed. There are no restrictions on the time windows, which are allowed to overlap. Robots model their temporal constraints using a simple temporal network, enabling them to maintain consistent schedules. When bidding on a task, a robot takes into account its own current commitments and an optimization objective, which is to minimize the time of completion of the last task alone or in combination with minimizing the distance traveled. The algorithm works both when all the tasks are known upfront and when tasks arrive dynamically. We show the performance of the algorithm in simulation with different numbers of tasks and robots, and compare it with a baseline greedy algorithm and a state-of-the-art auction algorithm. Our algorithm is computationally frugal and consistently allocates more tasks than th...

2005

Single auction-based methods are known to be efficient for multi-robot problem solving. In this work, we investigate performance of our general multi robot coordination framework for multi robot multi target exploration problem under uncertainties in dynamic environments. Our framework offers a real time single item allocation method featuring different mechanisms for failure recovery. In multi robot exploration problem, a different version of well known NP-hard MTSP (Multiple Traveling Salesman Problem), each target is visited by at least one robot in its open tour. Overall objective function for cost optimization while visiting targets varies by different exploration domains. In this work, we present performance results for total cost minimization objective. There are many efficient centralized heuristic methods for generating close to optimal solutions. These heuristics may be used to allocate targets to robots. However, when the environment is dynamic and/or unknown, initially assigned targets may need to be reallocated during run time. In our framework, redundant calculations are eliminated by means of incremental assignments based on up-to-date situations of the environment. Offered precautions in the framework maintain the quality of solutions as close to optimal as possible. Experiments are conducted on simulations. The comparison of the proposed method is made with Prim Allocation method.

When multiple robots are supposed to operate together, coordination and communication issues arise. “Which robot should execute which task?” is the key question of the multi-robot task allocation problem. Properly allocating tasks among robots so as to obtain optimality is a primary research problem in the multi-robot coordination domain. Based on a simultaneous consideration of the team cost and computation time, a new approach for integrating path planning into a robot’s bids for tasks is presented. A practical path finding technique is proposed and combined with the Travelling Salesman Problem solution and Dijkstra shortest path solution for calculating bids. This combination produces a good alternative for path planning. By using this model for bid valuation, the cost is calculated without sacrificing the performance. Simulation experiments prove that the approach addressed in this paper has great advantages, including less computation, better real-time performance, a stronger ability to find the optimal result, etc.

European Journal of Operational Research, 2015

In the Team Orienteering Arc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error on all instances for which the optimal solution is available is 0.67%.

HAL (Le Centre pour la Communication Scientifique Directe), 2018

The paper proposes Dynamic Multi Robot-Routing (DMRR), as a continuous adaptation of the multi-robot target allocation process (MRTA) to new discovered targets. There are few works addressing dynamic target allocation. Existing methods are lacking the continuous integration of new targets, handling its progressive effects, but also lacking dynamicity support (e.g. parallel allocations, participation of new robots). The present paper proposes a framework for dynamically adapting the existing robot missions to new discovered targets. Missions accumulate targets continuously, so the case of a saturation bound for the mission costs is also considered. Dynamic saturation-based auctioning (DSAT) is proposed for allocating targets, providing lower time complexities (due to parallelism in allocation). Comparison is made with algorithms ranging from greedy to auction-based methods with provable sub-optimality. The algorithms are tested on exhaustive sets of inputs, with random configurations of targets (for DMRR with and without a mission saturation bound). The results for DSAT show that it outperforms state-of-the-art methods, like standard sequential single-item auctioning (SSI) or SSI with regret clearing.

International journal of engineering research and technology, 2020

Dynamic task allocation for multiple robot network is the fundamental criterion for successful completion of the conquest. Primarily the target task is partitioned into number of sub-tasks thereafter executed by the robots in a distributed manner. Multi-robot task allocation is a combinatorial optimization problem. Most of the prevailing optimization schemes of task allocation considers single objective parameter. This paper presents a bi-objective task allocation scheme for multi-robot network. It establishes the model of task allocation by considering the minimal utilization of time and battery energy resources. It proposes a numerical problem-solving method to obtain the optimal weight values to be used in the objective function. It encompasses the Linear Integer Programming optimization (LIP) technique for task allocation. Time consumption and energy consumption rates are considered as the evaluation parameters for the proposed scheme. The dynamic task allocation scheme is simul...

ArXiv, 2021

We consider the Maximum-Profit Routing Problem (MPRP), a variant of pick-up routing problem introduced in [1, 3], in which the goal is to maximize total profit. The original MPRP restricts vehicles to visit a site at most once. In this paper, we consider extensions of MPRP, in which a site may be visited by a vehicle multiple times. Specifically, we consider two versions: one in which the quantity to be picked up at each site is constant in time (MPRP-M), and one with time-varying supplied quantities, which increase linearly in time (MPRP-VS). For each of these versions, we come up with a constant-factor polynomial-time approximaltion scheme.

Engineering Optimization

The orienteering problem (OP) is a routing problem that has numerous applications in various domains such as logistics and tourism. The objective is to determine a subset of vertices to visit for a vehicle so that the total collected score is maximized and a given time budget is not exceeded. The extensive application of the OP has led to many different variants, including the team orienteering problem (TOP) and the team orienteering problem with time windows. The TOP extends the OP by considering multiple vehicles. In this article, the team orienteering problem with variable profits (TOPVP) is studied. The main characteristic of the TOPVP is that the amount of score collected from a visited vertex depends on the duration of stay on that vertex. A mathematical programming model for the TOPVP is first presented and an algorithm based on iterated local search (ILS) that is able to solve modified benchmark instances is then proposed. It is concluded that ILS produces solutions which are comparable to those obtained by the commercial solver CPLEX for smaller instances. For the larger instances, ILS obtains good-quality solutions that have significantly better objective value than those found by CPLEX under reasonable computational times.