Preference-Agile Multi-Objective Optimization for Real-time Vehicle Dispatching

Jiahuan Jin; Wenhao Zhao; Rong Qu; Jianfeng Ren; Xinan Chen; Qingfu Zhang; Ruibin Bai

cs.AIApr 12, 2026

Preference-Agile Multi-Objective Optimization for Real-time Vehicle Dispatching

Authors: Jiahuan Jin, Wenhao Zhao, Rong Qu, Jianfeng Ren, Xinan Chen, Qingfu Zhang, Ruibin Bai

Organizations: School of Computer Science, University of Nottingham Ningbo China, Ningbo, China. · School of Computer Science, University of Nottingham, Nottingham, UK. · Department of Computer Science, City University of Hong Kong, Hong Kong

Abstract

Multi-objective optimization (MOO) has been widely studied in literature because of its versatility in human-centered decision making in real-life applications. Recently, demand for dynamic MOO is fast-emerging due to tough market dynamics that require real-time re-adjustments of priorities for different objectives. However, most existing studies focus either on deterministic MOO problems which are not practical, or non-sequential dynamic MOO decision problems that cannot deal with some real-life complexities. To address these challenges, a preference-agile multi-objective optimization (PAMOO) is proposed in this paper to permit users to dynamically adjust and interactively assign the preferences on the fly. To achieve this, a novel uniform model within a deep reinforcement learning (DRL) framework is proposed that can take as inputs users' dynamic preference vectors explicitly. Additionally, a calibration function is fitted to ensure high quality alignment between the preference vector inputs and the output DRL decision policy. Extensive experiments on challenging real-life vehicle dispatching problems at a container terminal showed that PAMOO obtains superior performance and generalization ability when compared with two most popular MOO methods. Our method presents the first dynamic MOO method for challenging \rev{dynamic sequential MOO decision problems

Figures & tables

Figure 1: A simple scenario example to illustrate the proposed PAMOO algorithm for online truck dispatching in a container terminal. At time

t

, one idle truck needs to be dispatched for a new task (dedicated to different QCs). Among three choices QC1, QC2 and QC3 with incremental queue lengths and decremental empty travel distances (indicated by three red lines on the left side of figure). Dispatching decisions are made by jointly considering a dynamic preference (based on expert experience on macro-level situational judgments) and fine-grained data reflecting real-time state features.

Figure 2: A route example for a single task. An idle truck receives the dispatching task at yard A. The first and second operation nodes are QC1 and crane at yard B, respectively. The truck route in red represents empty mileage and the route in blue is the loaded travel distance. The objectives are to minimize both aggregated idle time of all QCs and total empty mileages by all trucks.

Panel of Figure 3 — Figure 3: An illustrative example where truck with task $w^{q}_{i}$ arrives too late at $q$ -th QC, causing a QC idle duration (a) and arrives at QC before the prior task’s completion, resulting in truck queuing (b).

Figure 4: An illustration of learning based interactive adjustments of user preferences in PAMOO. It employs a multi-policy inner loop RL with policies $\pi^{*}(a|s,\theta)$ . Once trained, PAMOO makes decisions for any combinations of state $s$ and preference vector $\bm{p}$ in a single run.

Index	Description
1	The remain task number of each QC
2	The total working truck number of each QC
3	The distance for the truck to complete each tasks
4	The necessary distance before the truck arrive at
	each QC
5	The queue lengths at each QC

Table 1: Items of agent’s observation at each time step.

Figure 5: The network structure of the proposed PAMOO for online truck dispatching.

Figure 6: Interpretation of the preference calibration method.

Parameters	Values
batch size $B$	32
clipping rate $\epsilon$	0.2
discount rate $\gamma$	1
epochs per iteration $M$	10
number of iteration $K$	5000
episodes per iteration $N$	10

Table 2: Hyper-parameters used in PAMOO.

Figure 7: The relationship between the hypervolume indicator and the reference policy.

Method	80 Trucks			100 Trucks			120 Trucks
Method	HV	Sparsity	Gap(%)	HV	Sparsity	Gap(%)	HV	Sparsity	Gap(%)
NSGA-II (500)	0.669	91.86	25.0%	0.674	31.68	23.5%	0.708	21.73	20.45%
NSGA-II (1000)	0.729	19.44	18.27%	0.728	20.1	17.37%	0.759	16.1	14.72%
NSGA-II (2000)	0.807	4.01	9.53%	0.784	23.8	11.01%	0.798	9.31	10.34%
MOEA/D (500)	0.682	31.94	23.54%	0.675	75.3	23.38%	0.693	19.75	22.13%
MOEA/D (1000)	0.72	35.1	19.28%	0.746	56.85	15.32%	0.751	53.66	15.62%

Table 3: Comparison Result to NSGA-II and MOEA/D.

Panel of Figure 8 — Figure 8: Approximate Pareto front obtained by our method and benchmarks on instances of different number of trucks.

Figure 9: Pareto frontiers generated by proposed method that trained by a small number of preferences.

Figure 10: Pareto frontiers generated by PAMOO and outer loop method on instance of 120 trucks.

Preferences	PAMOO		Outer Loop Method
Preferences	QC Idle Time (min/QC)	Empty Travel Distance (m/task)	QC Idle Time (min/QC)	Empty Travel Distance (m/task)
[1.0, 0.0]	13.04	799.11	12.16	876.9
[0.9, 0.1]	13.21	759.0	12.49	842.33
[0.8, 0.2]	13.26	703.38	12.36	813.71
[0.7, 0.3]	13.69	657.03	12.39	755.92
[0.6, 0.4]	14.6	612.71	12.68	722.04

Table 4: Numerical Result of Comparison to Outer Loop Method.

Figure 11: Sample efficiency of inner-loop (ours) and outer-loop methods compared with NSGA-II and MOEA-D.

Figure 12: Ablation study results on adopting various RL algorithms and network architectures.

Method	80 Trucks			100 Trucks			120 Trucks
Method	HV	Sparsity	Gap(%)	HV	Sparsity	Gap(%)	HV	Sparsity	Gap(%)
Evenly Preferences (11 Pref.)	0.684	253.03	5.79%	0.676	260.71	7.02%	0.679	267.98	7.24%
Evenly Preferences (21 Pref.)	0.709	64.48	2.34%	0.705	66.14	3.03%	0.709	68.91	3.14%
Evenly Preferences (51 Pref.)	0.723	11.42	0.41%	0.721	11.8	0.83%	0.724	11.06	1.09%
Adjusted Preferences (11 Pref.)	0.694	240.93	4.41%	0.683	240.13	6.05%	0.685	241.41	6.42%
Adjusted Preferences (21 Pref.)	0.716	58.29	1.38%	0.718	60.55	1.24%	0.719	60.9	1.78%

Table 5: Comparison Result between Even and Adjusted Preferences.

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Multi-Objective Optimization Multi-Objective Evolutionary Optimization

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Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.

Abstract

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