On the truck dispatching problem

Decomposition is a well-known strategy in traditional multiobjective optimization. However, the decomposition strategy was not widely employed in evolutionary multiobjective optimization until Zhang and Li proposed multiobjective evolutionary algorithm based on decomposition (MOEA/D) in 2007. MOEA/D proposed by Zhang and Li decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them in a collaborative manner using an evolutionary algorithm (EA). Each subproblem is optimized by utilizing the information mainly from its several neighboring subproblems. Since the proposition of MOEA/D in 2007, decomposition-based MOEAs have attracted significant attention from the researchers. Investigations have been undertaken in several directions, including development of novel weight vector generation methods, use of new decomposition approaches, efficient allocation of computational resources, modifications in the reproduction operation, mating selection and replacement mechanism, hybridizing decomposition- and dominance-based approaches, etc. Furthermore, several attempts have been made at extending the decomposition-based framework to constrained multiobjective optimization, many-objective optimization, and incorporate the preference of decision makers. Additionally, there have been many attempts at application of decomposition-based MOEAs to solve complex real-world optimization problems. This paper presents a comprehensive survey of the decomposition-based MOEAs proposed in the last decade.

A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition

Chapter headings: Introduction. Modelling city logistics. City logistics with ITS. Demand and supply models. Impact models. Vehicle routing and scheduling. Vehicle routing and scheduling with ITS. Location of logistics terminals. Future perspectives. References. Index.

City logistics : network modelling and intelligent transport systems

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS Editor-In-Chief

Online vehicle routing is an important task of the modern transportation service provider. Contributed by the ever-increasing real-time demand on the transportation system, especially small-parcel last-mile delivery requests, vehicle route generation is becoming more computationally complex than before. The existing routing algorithms are mostly based on mathematical programming, which requires huge computation time in city-size transportation networks. To develop routes with minimal time, in this paper, we propose a novel deep reinforcement learning-based neural combinatorial optimization strategy. Specifically, we transform the online routing problem to a vehicle tour generation problem, and propose a structural graph embedded pointer network to develop these tours iteratively. Furthermore, since constructing supervised training data for the neural network is impractical due to the high computation complexity, we propose a deep reinforcement learning mechanism with an unsupervised auxiliary network to train the model parameters. A multisampling scheme is also devised to further improve the system performance. Since the parameter training process is offline, the proposed strategy can achieve a superior online route generation speed. To assess the proposed strategy, we conduct comprehensive case studies with a real-world transportation network. The simulation results show that the proposed strategy can significantly outperform conventional strategies with limited computation time in both static and dynamic logistic systems. In addition, the influence of control parameters on the system performance is investigated.

Online Vehicle Routing With Neural Combinatorial Optimization and Deep Reinforcement Learning

Lately, the Vehicle Routing Problem (VRP) in the city, known as City VRP, has gained popularity with its importance in city logistics. Similar to city logistics, City VRP mainly differs from conventional VRP in terms of the stakeholders involved, namely the shipper, carrier, resident, and administrator. Accordingly, this paper surveys the City VRP literature categorized by stakeholders and summarizes the constraints, models, and solution methods for VRP in urban cities. City VRPs are also analyzed based on the problem of interest considered by the stakeholders and the corresponding models that have been proposed in response. Through this review, we identify the state of the art of City VRP, highlight the core challenging issues, and suggest some potential research area in this field that have remained underexplored.

City Vehicle Routing Problem (City VRP): A Review

The decomposition method in multiobjective evolutionary algorithms (MOEA/D) is an effective approach to evolve solutions along predefined weight vectors for solving multiobjective optimization problems (MOPs). However, obtaining evenly distributed weight vectors for different types of MOPs is a challenge problem especially when the true Pareto fronts (PFs) are unknown before a MOEA/D starts. In this paper, a new MOEA/D with a fast hypervolume archive (called FV-MOEA/D) is proposed to adaptively adjust the weight vectors for various shapes of PFs. The core idea of FV-MOEA/D is to periodically adjust weight vectors based on solutions in the proposed archive, in which convergence and diversity are maintained by maximizing hypervolume. Experimental studies on 58 benchmark MOPs in jMetal demonstrate that the proposed FV-MOEA/D not only reached higher hypervolumes when compare to five classical MOEAs i.e., NSGAII, SPEA2, IBEA, FV-MOEA and MOEA/D, but also obtained well distributed weight vectors on PFs with different geometrical characteristics.

Towards adaptive weight vectors for multiobjective evolutionary algorithm based on decomposition

The Urban Last Mile Logistics (LML) is known to be the most expensive, least efficient and most polluting section of the supply chain. To that extent, a multi-objective heterogeneous capacitated vehicle routing problem with time windows and simultaneous pickup and delivery (MoHCVRPTWSPD) is formulated and solved to cater to this section of the supply chain. The proposed model is solved through two proposed methods that are based on exact methods. A small benchmark was adopted from the current literature to test the proposed methods and computational results are reported. Based on the computational results, a number of insights into the MoHCVRP-TWSPD problem are provided.

Multi-objective Heterogeneous Capacitated Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery for Urban Last Mile Logistics

Indicator-based evolutionary algorithm (IBEA1) is a fast and effective approach for solving multiobjective optimization problems (MOPs). In the classical IBEA1, the parameter κ is predefined to amplify or shrink the indicator differences on pairwise solutions. However, the value of κ in IBEA1 needs to be carefully calibrated based on the selected indicator (e.g., hypervolume or additive e-indicator) and the encountered MOPs. In this paper, a new version of IBEA1 (labeled as IBEA2 hereafter) is proposed to adaptively adjust parameter κ for solving various MOPs. The core idea of IBEA2 is to adapt parameter κ for the purpose of selecting the subset of offspring solutions with the maximum hypervolume into the next population. Experimental studies on 44 benchmark MOPs with 2–5 objectives in jMetal verified that IBEA2 is able to find higher hypervolumes against the four classical MOEAs, which are NSGAII, SPEA2, MOEA/D and IBEA1, in the literature.

Adaptive indicator-based evolutionary algorithm for multiobjective optimization problems

The Robust Vehicle Routing Problem with Time Windows has been gaining popularity over the past few years due to its focus on tackling uncertainty inherent to real world problems. Most of the current approaches in generating robust solutions require prior knowledge on the uncertainties, such as uncertainties in travel time. Hence, they are less than favorable to use in the absence of data, i.e., in the case of data starvation. In this paper, we present an evolutionary algorithm that in the absence of data on travel time uncertainty, provides a decision maker with a collection of solutions, each with a corresponding level of trade-off between total travel distance and solution robustness. In particular, we present a novel realization of route flexibility and its relation to solution robustness. Furthermore, we propose a bi-objective evolutionary algorithm for the vehicle routing problem with time windows where the objectives are (a) total travel distance and (b) solution flexibility. The proposed algorithm is tested on the well-known Solomon benchmarks and a trade-off analysis between total distance and solution flexibility is provided based on the obtained test results. Based on observations from the trade-off analysis, a number of suggestions to improve the current logistics system are provided.

Chen Kim Heng

Papers

City Vehicle Routing Problem (City VRP): A Review

Towards adaptive weight vectors for multiobjective evolutionary algorithm based on decomposition

Multi-objective Heterogeneous Capacitated Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery for Urban Last Mile Logistics

Adaptive indicator-based evolutionary algorithm for multiobjective optimization problems

Application of route flexibility in data-starved vehicle routing problem with time windows