The Multiagent Planning Problem

Abstract

The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given a set ofngoals/targets andmagents, the objective is to findmround trips, such that each target is visited only once and by only one agent, and the total distance of these round trips is minimal. In this paper we describe the Multiagent Planning Problem, a variant of the classical Multiple Traveling Salesmen Problem: given a set ofngoals/targets and a team ofmagents,msubtours (simple paths) are sought such that each target is visited only once and by only one agent. We optimize for minimum time rather than minimum total distance; therefore the objective is to find the Team Plan in which the longest subtour is as short as possible (a min–max problem). We propose an easy to implement Genetic Algorithm Inspired Descent (GAID) method which evolves a set of subtours using genetic operators. We benchmarked GAID against other evolutionary algorithms and heuristics. GAID outperformed the Ant Colony Optimization and the Modified Genetic Algorithm. Even though the heuristics specifically developed for Multiple Traveling Salesmen Problem (e.g.,k-split, bisection) outperformed GAID, these methods cannot solve the Multiagent Planning Problem. GAID proved to be much better than an open-source Matlab Multiple Traveling Salesmen Problem solver.

Decentralized Task Allocation in Multi-Robot Systems via Bipartite Graph Matching Augmented With Fuzzy Clustering

“…This is partly due to increasing concerns regarding the scalability of purely centralized approaches and their vulnerability to communication disruptions, and partly driven by accelerated advancements in system/agent autonomy and Artificial Intelligence (AI) capabilities. In this paper, we consider task allocation for a team of robots in 2D space, and formulate the MATA problem as finding a set of optimal routes that minimize the overall costs incurred by the team [4]. Both a baseline centralized solution approach (based on multitraveling salesman or mTSP problem) and a new decentralized framework (that combines bipartite graph theory and clustering concepts) are developed in this paper, and compared over a set of case studies involving varying numbers of robots and tasks.…”

“…There are also heuristic-based methods to solve the mTSP, such as by Zhang et al [11] and Ryan et al [12], who respectively use Genetic Algorithms (GA) and Tabu search. Recently, Kalmar et al [4] proposed a modified GA method to solve the mTSP. These methods are slow to converge to optimal solutions, and often not suited for near-real-time applications (such as multirobot real-time task-planning).…”

Product Service Scheduling Problem with Service Matching Based on Tabu Search Method

“…Shabanpour et al [19] proposed a new combinatorial algorithm named CGA-MTSP for solving MTSP problem, which is a combination of genetic algorithm and clustering technique. Kalmár-Nagy et al [20] described a variant of the classical multiple traveling salesmen problem. Xinye et al [21] proposed a biobjective ant colony optimization based memetic algorithm to solve MTSP.…”

Decentralized Informative Path Planning With Balanced Exploration-Exploitation for Swarm Robotic Search

“…a source localization problem) using a swarm of robots in 2D space. The online planning problem solved by the robots is then posed as finding a set of waypoints that maximize some measure of collective search efficiency [11]. For this purpose, we formulate, implement and test a novel decentralized algorithm, founded on the batch Bayesian search formalism, that not only tackles the balance between exploration and exploitation, but also allows asynchronous decision-making within the swarm.…”