A discrete teaching–learning based optimization algorithm with local search for rescue task allocation and scheduling

doi:10.1016/j.asoc.2022.109980

Applied Soft Computing

Volume 134, February 2023, 109980

https://doi.org/10.1016/j.asoc.2022.109980 Get rights and content

Highlights

•
A $k$ -means clustering algorithm with constraints is proposed for rescue task allocation.
•
A discrete teaching–learning optimization algorithm is designed to determine the task scheduling sequence for each team.
•
A two-stage local search strategy is presented to perform a deep search for the incumbent solution.

Abstract

The allocation and scheduling of the emergency rescue forces is a fundamental task in emergency management. This paper aims to address the allocation and scheduling problem to minimize the average completion time of all rescue teams by using a discrete teaching–learning based optimization algorithm with local search (DTOLS). First, an improved $k$ -means clustering algorithm with constraints is proposed to assign tasks to rescue teams based on the location of rescue tasks. Second, a hybrid discrete optimization algorithm based on a teaching–learning mechanism is designed to generate the task scheduling sequence for each rescue team as an initial solution. Next, an efficient two-phase local search strategy is presented to improve the current solution. For three neighborhood task moves based on problem characteristics, which contains insert task within a team, swap tasks within a team, insert task between teams, the speed-up techniques are introduced to reduce the computational complexity of calculating completion time of a rescue team. Finally, the parameters of DTOLS are calibrated by Taguchi method to determine appropriate values. DTOLS is compared with the state-of-the-art algorithms, and the experimental results demonstrate the effectiveness of DTOLS in solving a set of test instances.

Introduction

In recent years, an increasing number of severe disasters have been observed, such as the 2010 Yushu earthquake, 2011 Yingjiang earthquake, 2013 Yaan earthquake, 2019 novel coronavirus, and 2021 Zhengzhou flood. Catastrophes and secondary geological events pose a significant threat to infrastructure systems and result in significant human casualties. Consequently, for mitigating losses, timely and efficient rescue work is important. Previous experience demonstrated that rescue team forces are limited in the majority of practical emergency scenarios, particularly for early relief operations [1]. Therefore, to reduce casualties and economic losses, rationalized rescue team allocation and scheduling is important for an emergency response.

We present herein a small-size instance for illustration where eight tasks are assigned to two rescue teams. As shown in Fig. 1(a), the position of the two rescue teams is marked by a green circle, whereas yellow circles mark tasks distributed in the affected areas. Our aim is to determine the task sequence by minimizing the average completion time of two rescue teams. It is possible to work out a solution by classical methods such as branch-and-bound and greedy search for this simplified instance. Fig. 1(b) shows a solution adopted for the case. However, most real-world rescue task scheduling problems involve a relatively large number of tasks spread out in the affected area and the response time for working out the scheduling scheme is limited. Moreover, the rescuers’ physical conditions change along with the high-intensity rescue work, which affects the processing time of follow-up tasks. Consequently, it necessitates extensive research for the considered problem in practice.

In this paper, we present a discrete teaching–learning based optimization algorithm with local search to solve the considered problem. The main contributions are summarized as follows:

(1) An improved $k$ -means clustering algorithm is designed to assign tasks to rescue teams.

(2) A discrete teaching–learning optimization algorithm is proposed to determine the task scheduling sequence for each team.

(3) A two-stage local search strategy is presented to perform a deep search for incumbent solution.

(4) Three speed-up techniques based on problem characteristics are utilized to reduce the computational complexity of calculating the completion time of a rescue team after a task movement.

The remainder of this paper is organized as follows. Section 2 provides the related work. Section 3 illustrates the mathematical model. Section 4 briefly introduces the original teaching–learning-based optimization algorithm. The proposed algorithm is described in detail in Section 5. Section 6 presents the simulation experiments and results. Finally, conclusions and future work are reviewed in Section 7.

Section snippets

Related work

As mentioned above, the proposed problem involves large scale permutations to be scheduled and is proved to be NP-hard [2]. The deterministic approaches easily become infeasible in computing time when solving large-scale instances, therefore, many researchers have focused on the problem in developing efficient evolutionary algorithm which provides acceptable solutions in a reasonable time during recent years.

In this paper, we investigate the relevant work from the following two aspects: the

The rescue task allocation and scheduling problem

As shown in Ref. [2], the problem is to assign rescue tasks to rescue teams distributed in the disaster area, and determine the processing sequence of tasks for each team to minimize the average completion time of rescue teams. The notations of the proposed mathematical model are listed in Table 2.

Generally speaking, rescue teams must make certain preparations before performing rescue tasks. After necessary preparations, each team starts from rescue operations center and travels to the disaster

Teaching–learning-based optimization algorithm

The teaching–learning-based optimization (TLBO) algorithm is a population-based heuristic stochastic swarm intelligent algorithm inspired by simulating the process of imparting knowledge from teacher to students and mutual interaction between learners in a traditional classroom [29]. In TLBO algorithm, learners are regarded as the search points that correspond to individuals in evolutionary algorithms. The learner with the best fitness value is defined as teacher. Different from traditional

Proposed method

Our proposed method involves two stages: initialization and local search. To be specific, the initialization includes two phases: In the first phase, rescue tasks are clustered based on their geographical location to ensure that tasks processed by a rescue team are adjacent, which can be regarded as initialization of task allocation. In the second phase, a discrete teaching–learning-based optimization algorithm is designed to provide an initial task scheduling sequence for each team. The local

Experiment and numerical results

Based on the public statistical data from China Earthquake Administration, and National Disaster Reduction Center of China during five years, we construct a set of 18 test instances with size $n \times m$ ( $n$ denotes the number of rescue teams and $m$ denotes the number of rescue tasks) ranging from 10 × 50 to 50 × 1000, which are in accordance with the range of actual disaster relief data. The test suite is constructed based on the given disaster areas and task distribution which are approximately in

Conclusions

In this study, a rescue task allocation and scheduling problem in emergency is presented. This problem is a necessary task in rescue planning work due to its large amount of rescue tasks and quite limited response time. Our research will help decision-makers improve the efficiency of multiple rescue operations.

This article is innovative in a number of ways. Firstly, earlier studies applied evolutionary algorithms to solve task allocation and scheduling simultaneously and the algorithm does not

CRediT authorship contribution statement

Ying Xu: Conceptualization, Software, Formal analysis, Writing – original draft. Xiaobo Li: Supervision, Resources, Methodology, Project administration, Writing – review & editing. Qian Li: Methodology, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

This research was supported in part by the National Natural Science Foundation of China [grant number 61373057]; Zhejiang Natural Science Foundation [grant number LQ20F020025]; Ningbo Natural Science Foundation [grant number 202003N4073]; Public Welfare project of Ningbo City [grant numbers 202002N3139, 2019C10051].

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View full text

A discrete teaching–learning based optimization algorithm with local search for rescue task allocation and scheduling

Highlights

Abstract

Introduction

Section snippets

Related work

The rescue task allocation and scheduling problem

Teaching–learning-based optimization algorithm

Proposed method

Experiment and numerical results

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Funding

Int. J. Disaster Risk Reduct.

Int. J. Electr. Power

Transp. Res. E

Appl. Math. Model.

Appl. Soft Comput.

Appl. Soft Comput.

Appl. Soft Comput.

European J. Oper. Res.

European J. Oper. Res.

Comput. Ind. Eng.

Appl. Soft Comput.

European J. Oper. Res.

Comput. Aided Des.

Knowl.-Based Syst.

Inform. Sci.

Knowl.-Based Syst.

Int. J. Electr. Power Energy Syst.

Int. J. Electr. Power Energy Syst.

Eng. Sci. Technol. Int. J.

Knowl.-Based Syst.

Procedia Comput. Sci.

Neurocomputing

Neurocomputing

Knowl. Based Syst.

Appl. Soft Comput.

Comput. Ind. Eng.

Neurocomputing

Omega

Swarm Evol. Comput.

Omega

Comput. Oper. Res.

Comput. Oper. Res.

Comput. Oper. Res.

Swarm Evol. Comput.

Eng. Appl. Artif. Intell.

Int. J. Prod. Econ.

Swarm Evol. Comput.