Decomposition-based hyperheuristic approaches for the bi-objective cold chain considering environmental effects

https://doi.org/10.1016/j.cor.2020.105043Get rights and content

Highlights

  • A bi-objective model for the LRPLCCC with environmental, economic and social effects.

  • Practical factors including SPD, HTW, HF, and the mixed transport are considered.

  • A hyper-heuristic method based on MOEA/D are designed to solve the proposed problem.

Abstract

This paper proposed a novel approach for a practical version of the cold chain, namely location-routing problem-based low-carbon cold chain (LRPLCCC). In the proposed bi-objective model, the first objective is the total logistics cost, including the fixed costs of the opened depots and leased vehicles, as well as the cost of fuel consumption and carbon emissions, and the second is to minimize the amount of quality degradation that aims at improving clients’ satisfaction and maintain product freshness. The cargos of clients are classified into three types: general, refrigerated, and frozen cargos. Since the presented problem is NP-hard, a novel multi-objective hyperheuristic (MOHH) was proposed to obtain the Pareto solutions. In this framework, three selection strategies were developed to improve the performance of MOHH, that is, random simple, choice function, and FRR-MAB (fitness rate rank based multi-armed bandit), and three acceptance criteria using the decomposition approaches in MOEA/D were also developed, namely penalty-based boundary intersection, Tchebycheff, and modified Tchebycheff approaches. Extensive experiments were provided to verify the efficiency of the proposed algorithms and assessed the effects of algorithm parameters on the Pareto front. The results showed that the efficiency of the proposed algorithm outperforms several existing well-known multi-objective evolutionary algorithms (MOEA).

Introduction

The cold chain refers to the transportation of temperature-sensitive products along a supply chain through thermal and refrigerated packaging methods and the logistical planning to protect the integrity of these perishable goods (Zheng et al., 2014). To maintain the quality and safety of perishable goods, much more fuel would be used to keep the low-temperature properties compared to non-cold chain transportation. Hence, cold-chain logistics are high-energy consumption and high-emission business in the logistics industry (Wang et al., 2017). Besides, client satisfaction depends on the quality of the shipments. Therefore, how to save energy, reduce carbon emissions, and maintain the quality of goods is an important issue in cold chain logistics. Correspondingly, cold chain logistics should consider triple indicators: economic, environmental, and social effects. This motivated us to define a cold chain model concerning environmental issues and the quality of perishable goods, aimed at reducing the total logistics costs, fuel consumption and carbon emissions (FCCE), and quality decay of perishable goods.

In this paper, we study cold chain design issues and provide a mathematical model to represent its economic, environmental, and social benefits. This problem was developed as a bi-objective mixed integer programming problem. The first objective is to minimize the expected total cost of the supply chain, which includes the fixed cost of the selected depots (i.e., the capacity cost), the fixed cost of the leased vehicle, and the total route cost related to FCCE costs, and the second goal is to minimize the total amount of damages for the quality of perishable products. The first objective involves environmental and economic effects, while the second attempts to improve the social impact in terms of client satisfaction. Besides, our problem is a mixed version of the general and cold supply chains, in other words, the proposed model could be used to serve the client's needs which may be general cargo (GC, room temperature), refrigerated cargo (RC, e.g., 3–10 °C), and frozen goods (FC, e.g., −4 to −24 °C). Several practical demands have also been considered: simultaneous pickup and delivery, hard time windows, and heterogeneous fleets, aiming to provide a diverse range of services to clients.

To solve the model, we propose a novel solution method using a hyper-heuristic framework. Unlike the framework that uses the MOEAs as the low-level heuristics (i.e., MOHH-II (Leng et al., 2019a, Leng et al., 2019b)), our proposed framework (i.e., MOHH-I) is similar to the framework of the single-objective models. The proposed framework comprises two levels: low-level heuristic (LLH) and high-level heuristic (HLH). LLH consists of a large composite neighborhood described by 14 operators. In HLH, three adaptive selection strategies have been developed to improve the performance of MOHH, namely random simple (RS), choice function (CF), and FRR-MAB (FM). Meanwhile, three decomposition methods used in MOEA/D (Zhang and Li, 2007), namely penalty-based boundary crossing (PBI), Tchebycheff (TE) and modified TE (MTE), were used as key components for the proposed acceptance criteria, that is, maximum benefit, random benefit, and roulette selection. In the experiment, we analyzed the effects of parameter configurations used in the proposed algorithm on the Pareto front, and also examined the efficiency of the proposed algorithm by comparing it with several well-known MOEAs.

To the best of our knowledge, the proposed algorithms have not been studied thus far for the presented problem. The rest of this paper is organized: in the next section, we review the recent literature on the models estimating FCCE, the cold chain logistics, and the multi-objective hyperheuristics. Section 3 defines the formulations for the LRPLCCC considering simultaneous pickup and delivery, heterogeneous fleet, and hard time windows; Section 4 provides the solution method, including the solution representation, the low-level heuristics, the high-level heuristics, and a framework; Section 5 describes the computational experiments and simulated results, and Section 6 outlines the study conclusions.

Section snippets

Literature review

This paper proposes solution methods and an optimization model for the cold chain logistics considering the location-routing problem and environmental benefits. Therefore, the following sections provide literature reviews of the model for estimating FCCE, the low carbon LRP (LCLRP), the cold chain considering environmental effects, and MOHH.

Mathematical model

The LRPLCCC is described as a complete and directed graph G = (V, E), where V is a set of nodes (V = N ∪ M) and E is a set of edges. And the variants of the models detailed:

  • (1)

    Each client i ∈ N has di delivery demand, pi pickup demand, sti service time, and a hard time window (ei, li). Moreover, the demands of each client are one of three types: GC, RC, and FC.

  • (2)

    Each depot j ∈ M has CDj capacity, FDj cost, and a closing time DTWj.

  • (3)

    A heterogeneous fleet H={h1, h2, h3} is used to serve clients with an

Proposed methods

The following sections describe the proposed algorithms (i.e., MOHH/D) for the LRPLCCC in terms of the following aspects: (1) framework of MOHH/D; (2) high-level strategies including three selection strategies and three acceptance criteria; (3) the pool of operators used as LLH; (4) solution representation and initial population.

Optimization simulation and analysis of results

The following sections described and discussed the implementation aspects and assessments of the proposed MOHH/D.

Concluding remarks

This paper proposed a bi-objective model for the cold chain considering a location-routing decision and environmental effects. In the proposed problem, the first objective consists of three parts: the fixed cost of the opened depots, the fixed cost of renting vehicles, and the cost of fuel consumption and carbon emission, while the second objective was used to minimize the total quality decay of perishable food, which could improve the client satisfaction. Meanwhile, a mixed delivery strategy

Acknowledgments

The authors would like to thank Professor Ling Wang (Department of Automation, Tsinghua University) for helping to define models and conduct experiments. This work was funded by the National Natural Science Foundation of China grant numbers 51875524 and 61873240, Natural Science Foundation of Zhejiang grant number Y19F030052, and the open fund of the key laboratory for metallurgical equipment and control of the ministry of education in the Wuhan University of Science and Technology 2017B04.

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