A bi-objective dynamic collaborative task assignment under uncertainty using modified MOEA/D with heuristic initialization
Introduction
The revolution of network-centric warfare has systematically organized the originally separated combat platforms, thereby achieving a high level of information sharing and increasing the chance of more efficient operations. However, the collaborative task assignment of multi-platforms remains an urgent problem that needs to be solved. Generally, in a Command & Control System (CCS), combat platforms can be divided into three categories: sensor platforms (SP), weapon platforms (WP), and Command & Control platforms (CCP). Each part plays an essential role in the completion of the overall combat mission. From the perspective of the classic ‘Observe-Orient-Decide-Act’ (OODA) loop developed by Boyd, SP plays the role of ‘Observe’. It acquires battlefield information to support the decision making of CCP and provide fire guidance for WP. CCP is the controller of the system, and it plays the roles of ‘Orient’ and ‘Decide’ in the OODA loop. WP plays the role of ‘Act’. Under the command of CCP and the guidance information of the target provided by SP, WP performs the task of interception. Information is exchanged continuously between different platforms and forms a complex feedback control chain. Fig. 1 shows a typical informational combat scenario. The platforms are organized in a distributed network, and the information of sub-platforms is shared among the network centers. The platforms can exchange information with a network center to obtain the overall battlefield situation; thus, any platform is capable of forming effective cooperation with others.
Under the background of network-centric warfare, uncertainty is an important characteristic, and it exists throughout the combat process. In general, the uncertainty in CCS is mainly from two layers:
- (1)
Bottom execution layer. In this layer, the SP and WP execute the detection and interception tasks, respectively. The actual performance of the platforms is influenced by many factors, such as ambient noise, target interference, and stability of the platform itself. The effect of execution may be varied as we have predicted, and this causes uncertainty. The uncertainty of the SP is manifested in the capturing probability, tracking accuracy, etc. The WP is uncertain mainly in the interception probability.
- (2)
Situational decision layer. The situational decision layer fuses the information from the bottom execution layer to form a battlefield situation and performs the task assignment based on it. On the one hand, the information from the bottom execution layer is nondeterministic, inconsistent, and incomplete; therefore, uncertainty should be an important feature of fused battlefield situations. On the other hand, when making assignment decisions, the trails and intents of the enemy should be inferred. Due to the intelligence and synergy of the enemy, the accuracy of our inferred results can be affected, thus introducing uncertainty.
The aim of this paper is to solve the dynamic task assignment under uncertainty in a defensive scenario. The main contributions of this paper can be summarized as follows. Firstly, a bi-objective dynamic collaborative task assignment model under uncertainty is formulated, which has considered the cooperation between SPs and WPs. Secondly, a novel multi-objective constructive heuristic based on efficiency cost ratio is proposed. The infeasible quaternions are deleted based on rules, and the crowding-distance-based deleting of heuristic individuals maintains the diversity of population. Thirdly, several modifications are made on MOEA/D to enhance the searching performance during the evolutionary process. Finally, the Taguchi method with a novel response metric is applied to calibrate the parameters.
The outline of the paper is as follows: Section 2 will briefly review previous work. In Section 3, we formulate the problem. Section 4 presents the proposed solution algorithm, MMOEA/D-Heuristic. Some numerical experiment is carried in Section 5. The conclusion and future work are presented in Section 6.
Section snippets
Related work
The problem of multi-platform collaborative task assignment has been studied since the 1950s, and this problem is termed as the classical weapon target assignment (WTA). Lloyd proved that WTA is an NP-hard problem (Lloyd & Witsenhausen, 1986). Recently, Kline, Ahner, and Hill (2018) reviewed the research on WTA. Most of the researchers have neglected the influence of SP on WP. This is applicable when the SP resources are sufficient. However, the scale of the battlefield keeps expanding, and the
Problem formulation
The combat scenario considered in this paper is narrated as follows. The defender has Q sensor platforms and W weapon platforms to defend an asset. They are connected by networks and can combine with each other to finish a task collaboratively. At a certain time, T incoming targets appear and aim at the asset. Before the enemy finishes the attack, the defender has a time interval to intercept these targets, which can be divided into several stages with a fixed length. A stage is the minimum
MOEA/D optimizer
Since the problem is NP-hard, there is no polynomial-time algorithm to obtain the exact solution. MOEA/D (Zhang & Li, 2007), proposed by Zhang et al., has attracted considerable attention recently. This framework aims to decompose a multi-objective problem into a set of scalar subproblems and optimizes them simultaneously. MOEA/D offers a clear and extensible framework that utilizes the neighbor structure. Hence, we mainly focus on studying this framework. It should be noted that the solving
Comparison algorithm
To prove the effectiveness of the modified MOEA/D with heuristic initialization, we take another famous multi-objective optimization framework, NSGA-II (Deb et al., 2000), as the main comparison algorithm. Following six algorithms are designed to compare: NSGA-II with and without heuristic initialization (NSGA-II-Heuristic and NSGA-II), MOEA/D with and without heuristic initialization (MOEA/D-Heuristic and MOEA/D), and modified MOEA/D with and without heuristic initialization (MMOEA/D-Heuristic
Conclusion and future work
In this paper, we focus on modeling the dynamic collaborative task assignment. A bi-objective dynamic assignment model is established. To solve the model efficiently, a modified MOEA/D with heuristic initialization is proposed. The solution representation is designed. A novel constructive heuristic initialization based on efficiency-cost ratio is proposed to generate an initial hybrid population. The nadir-based Tchebycheff approach is employed to obtain a better approximation to the whole
CRediT authorship contribution statement
Wenqin Xu: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. Chen Chen: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Writing - review & editing. Shuxin Ding: Conceptualization, Formal analysis, Investigation, Methodology, Validation, Supervision, Writing - review & editing. Panos M. Pardalos: Conceptualization, Funding acquisition,
Declaration of Competing Interest
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Acknowledgments
We thank the editors and anonymous reviewers for their helpful comments and suggestions on improving the presentation of this paper. This work was supported by the National Natural Science Foundation of China (NSFC) with Grant No. 61773066 and a provincial and ministerial project with Grant No. 61403120401. P. M. Pardalos is partially supported by the Paul and Heidi Brown Preeminent Professorship at ISE (University of Florida, USA) and a Humboldt Research Award (Germany).
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