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Genetic-based algorithms for cash-in-transit multi depot vehicle routing problems: economic and environmental optimization

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Abstract

With the gradual increase of commercial banks and the expansion of their branches, the demand for cash transportation inflates sharply, bringing opportunities to the business development of Cash-In-Transit (CIT) sectors. However, the branches are often distributed in densely populated areas where traffic jams occur from time to time, which poses a severe challenge to the route planning of CIT vehicles. In addition, risk factors need to be considered during the optimization process because the goods transported belong to valuables. In order to effectively deal with the routing problem of CIT sectors, this paper established a bi-objective model and a goal programming model of Risk-Constrained Multi Depot Vehicle Routing Problems (RCMDVRPs) using real-time traffic data. Based on the traditional genetic algorithm, a Hybrid Genetic Algorithm with Intensification procedures (HGAI) is proposed to solve the goal programming model by using a three-level linked list structure to express chromosomes visually. Then, a new Self-constrained Hybrid Genetic Algorithm (SHGA) is designed for the bi-objective model. Besides, an online path updating strategy is developed to guide remote vehicles against time-dependent traffic flows. Finally, the HGAI is performed on benchmark instances to verify its accuracy. Experimental results of performance test show that the algorithm can achieve a gap of about 3% compared with the Best Known Result (BKR). The results of a case study also show that the two models and the corresponding algorithms are feasible and can be used to solve large-scale problems according to the special preferences and goals of decision-makers.

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Abbreviations

CIT:

Cash-in-transit

RCMDVRP:

Risk-constrained multi depot vehicle routing problem

HGAI:

Hybrid genetic algorithm with intensification procedures

SHGA:

Self-constrained hybrid genetic algorithm

BKR:

Best known result

VRP:

Vehicle routing problem

MDVRP:

Multi depot vehicle routing problem

CTVRP:

Cash-in-transit vehicle routing problem

GA:

Genetic algorithm

ACO:

Ant colony optimization

NP:

Nondeterministic polynomial-time

RCTVRP:

Risk-constrained cash-in-transit vehicle routing problem

NSGA:

Nondominated sorting genetic algorithm

ALNS:

Adaptive large neighborhood search

CO2 :

Carbon dioxide

FGVRP:

Fuel-efficient green vehicle routing problem

GCVRP:

Green capacitated vehicle routing problem

GP:

Goal programming

VRPTW:

Vehicle routing problem with time windows

CVRP:

Capacitated vehicle routing problem

EC:

Energy consumption

CO:

Carbon monoxide

NOx :

Nitrogen oxide

VOC:

Volatile organic compounds

PM:

Particulate matter

COPERT:

Computer program to calculate emissions from road transport

LDV:

Light-duty diesel vehicle

FC:

Fuel consumption

EF:

Emission factor

MCDM:

Multi-criteria decision making

MOP:

Multi-objective optimization problem

PFIH:

Push-forward insertion heuristic

BCRC:

Best cost route crossover

IM:

Intensification method

DC:

Distribution center

ETA:

Estimated time of arrival

TSP:

Traveling salesman problem

i :

Customers, nodes, depots, goals

j :

Customers, nodes, depots

k:

Vehicles

\(N = \left\{ {1, \ldots ,n} \right\}\) :

The set of customers

\(S = \left\{ {{\text{DC}}1,{\text{DC}}2,...} \right\}\) :

The set of depots

\(V = S \cup N\) :

The set of nodes

\(A = {\text{arc}}(i,j),i,j \in V,i \ne j\) :

The set of arcs

\(K = \left\{ {1, \ldots ,m} \right\}\) :

The set of vehicles

\(q_{i}\) :

The demand of customer i

\({\text{st}}_{i}\) :

The service time of customer i

\(d_{ij}\) :

The travel distance on arc(i, j)

\(t_{ij}\) :

The travel time on arc(i, j)

\(T\) :

The efficient working time (the length of time windows)

\(Q\) :

The capacity of vehicles

\(D_{ik}\) :

The onboard cash when the vehicle k departs from customer i

\(R_{i}^{k}\) :

The risk index when the vehicle k departs from customer i

\(\theta\) :

The threshold for global risk index

\(M,M^{{\prime }}\) :

Two big enough numbers

\(b = [b_{1} ,b_{2} , \ldots ]\) :

Goal vector

\(w = \left[ {\left( {w_{{b_{1} }}^{ - } ,w_{{b_{1} }}^{ + } } \right),\left( {w_{{b_{2} }}^{ - } ,w_{{b_{2} }}^{ + } } \right), \ldots } \right]\) :

Weight vector

\(\overline{n}_{i} ,\overline{p}_{i}\) :

Unwanted deviational variables of the i-th goal

\(x_{ijk}\) :

Equals 1 if the arc (i, j) is traversed by vehicle k; 0 otherwise

\(y_{ik}\) :

Equals 1 if node i,\(i \in V\) is served by vehicle k; 0 otherwise

\(u_{ik}\) :

Auxiliary variable for sub-tour elimination constraints in route k

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Acknowledgements

This research was funded by the Chongqing graduate Scientific research innovation Projects [grant numbers CYB20178 and CYB19172]. The authors are grateful to the support of the General Project of Chongqing Natural Science Foundation [grant number cstc2020jcyj-msxmX0108], and the Key scientific and technological innovation project of “Construction of Chengdu-Chongqing Economic Circle” [grant number KJCXZD2020031].

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  1. School of Economics and Management, Chongqing Jiaotong University, Chongqing, 400074, China

    Xianlong Ge & Yuanzhi Jin

  2. Department of Computer Technology and Information Engineering, Sanmenxia Polytechnic, Sanmenxia, 472000, China

    Yuanzhi Jin

  3. School of Business, Xinyang Normal University, Xinyang, 464000, China

    Long Zhang

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Ge, X., Jin, Y. & Zhang, L. Genetic-based algorithms for cash-in-transit multi depot vehicle routing problems: economic and environmental optimization. Environ Dev Sustain 25, 557–586 (2023). https://doi.org/10.1007/s10668-021-02066-9

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