Dynamic Team Orienteering in Spatial Crowdsourcing

• The paper presents anticipatory algorithms combining scenario sampling and rolling-horizon optimization to address the dynamic team orienteering problem in spatial crowdsourcing.
• It models heterogeneous worker constraints and real-time task arrivals using ALNS and MIP benchmarks, focusing on both profitability and computational tractability.
• Results demonstrate that the Scen-RH-ALNS policy achieves near-optimal profit with significantly lower runtime compared to traditional myopic and exact methods.

The Dynamic Team Orienteering Problem in Spatial Crowdsourcing (DTOP-SC) formalizes the online assignment and routing of mobile workers to spatially distributed, time-constrained micro-tasks, where workers operate under personal origin-destination trajectories and hard time budgets, and platform decisions seek to maximize total collected profit. The complexity arises due to dynamic task arrivals, heterogeneous worker constraints, spatial-temporal dependencies, and real-time operational requirements. DTOP-SC generalizes classical Team Orienteering Problems (TOP), integrating dimensions essential for realistic spatial crowdsourcing systems and is addressed by anticipatory algorithms that combine scenario sampling with rolling-horizon optimization for computational tractability and solution quality (Wu et al., 16 Jan 2026).

1. Formal Definition and Modeling

Let $\mathcal{W} = \{1,\ldots,W\}$ denote the set of workers and $\mathcal{T} = \{1,\ldots,N\}$ the (potentially dynamic) set of tasks. Each worker $w$ travels between personal origin $s_w$ and destination $d_w$ within window $[T^{w}_{\mathrm{start}}, T^{w}_{\mathrm{end}}]$. Task $i$ has profit $p_i \geq 0$, service duration $\tau_i \geq 0$, release time $r_i$, and service time window $[b_i, e_i]$. Let $t_{ij}^w$ denote (worker-specific) travel time from $i$ to $j$.

Decision Variables (static snapshot):

• $x_{ij}^w$: 1 if worker $w$ travels from $i$ to $j$;
• $y_i^w$: 1 if $w$ serves $i$;
• $a_i^w$: Service start time at $i$ on $w$'s route.

Objective:

$$\max\;\sum_{i\in \mathcal T}p_i\left(\sum_{w\in\mathcal W}y_i^w\right)$$

subject to routing, assignment, time window, and feasibility constraints as formalized in [(Wu et al., 16 Jan 2026), eqs. (1)--(8)].

Dynamic arrivals are accommodated by restricting decisions at time $t$ to tasks with $r_i \le t$; newly arriving tasks or workers becoming idle trigger asynchronous event-driven reoptimization epochs.

2. Scenario-Sampling Rolling-Horizon Framework

The DTOP-SC is solved via the Scenario-Sampling Rolling-Horizon (Scen-RH-ALNS) policy:

• Planning epochs: The horizon $[0, H]$ is divided at events (task arrivals, worker idleness).
• At each epoch $t$: Let $A(t)$ be the current set of available, yet-unserved tasks; $\mathcal{W}_{\mathrm{idle}}(t)$ is the set of idle workers.
• Scenario generation: For $S$ independent scenarios, generate $N^{\mathrm{vir}}$ virtual tasks per scenario, the properties of which are sampled non-parametrically to reflect plausible future arrivals.
• Augmentation and solution: Each scenario yields an augmented static problem, solved heuristically.
• Candidate extraction and aggregation: Assignments are filtered by occurrence frequency across scenarios and greedily selected to ensure conflict-free routing (no two workers assigned to the same task or vice versa).

This anticipates potential future events to mitigate myopic decision errors inherent in greedy or short-term policies. The inclusion of sampled virtual tasks helps the optimization account for uncertain future arrivals without requiring explicit stochastic programming (Wu et al., 16 Jan 2026).

3. Static Subproblem and ALNS Solution

At each epoch, the inherently dynamic problem collapses to a heterogeneous time-windowed team orienteering problem (HT-TOPTW) snapshot, constrained to the subset of idle workers and feasible tasks. The adopted heuristic subsolver is an Adaptive Large Neighborhood Search (ALNS) procedure:

• Initialization: Greedy insertion.
• Destroy/repair cycles: Removal of visited tasks (Shaw, random, worst-cost); reinsertion by regret-$k$ or greedy methods.
• Metaheuristics: Simulated annealing for move acceptance, adaptive operator weighting, local 2-opt and inter-route exchanges.

ALNS balances computational efficiency and solution quality, scaling to realistic crowdsourcing problem sizes infeasible for exact methods (Wu et al., 16 Jan 2026).

4. Mixed-Integer Programming Benchmarking

The reference offline solution uses a Mixed-Integer Programming (MIP) model encoding the full problem structure (see Section 1) and solved by commercial solvers (e.g., Gurobi, 600s time limit per instance). The MIP formulation incorporates release-time, routing, assignment, time, and flow conservation constraints. No advanced cuts or valid inequalities are utilized; performance is measured relative to time-limited incumbent solutions ($Z_{\mathrm{MIP}}$). Relaxations and offline MIP bounds serve as benchmarks for evaluating dynamic policies (Wu et al., 16 Jan 2026).

5. Computational Experiments and Results

Two main instance families are used:

• DTOP benchmark (cf. Kirac et al. 2025): 2–4 vehicles, 30–100 requests, varying dynamism levels.
• Map-based DTOP-SC: Tasks/workers sampled from real-world road-map coordinates, 5–15 workers, 50–300 tasks, with strongly heterogeneous instances to test scalability and realism.

The Scen-RH-ALNS decisively outperforms myopic baselines and achieves profit within 1–3% of state-of-the-art dynamic planners at 2–3 orders of magnitude lower runtime (mean instance time: 0.14 s; cf. 192–198 s for MPAc/MPAd). On map-based instances, average gap to time-limited MIP is 0–6% for sizes up to 150 tasks, with smooth computational scaling (mean time 19 s at 100 tasks/10 workers) and robustness to wide parameter regimes. Increasing scenario lookahead reduces optimality gap by a statistically significant margin (0.36 percentage points, $p\approx0.009$ over 31 sets) (Wu et al., 16 Jan 2026).

6. Relation to Uncertain and Time-Growing Rewards

Dynamic orienteering in spatial crowdsourcing has strong conceptual overlap with the Team Orienteering Coverage Planning with Uncertain Reward (TOCPUR) model (Liu et al., 2021). In TOCPUR, each spatial task accrues reward (cost) linearly with unknown rate $\lambda_v$ until serviced, mapping naturally to micro-task urgency or value in DTOP-SC. TOCPUR employs per-iteration reward estimation and MIP-based routing, with extensions to match DTOP-SC requirements including:

• Dynamic arrival of new tasks,
• Worker-task matching constraints ($\sum_m y_{i,m}\le 1$),
• Heterogeneous agent budgets and travel times,
• Time windows via explicit time variables.

The TOCPUR solution approach models an iterative estimation–optimization loop, with proven efficacy for moderate-sized problems; it provides rigorous foundations for DTOP-SC under uncertain and time-evolving rewards (Liu et al., 2021).

7. Insights, Limitations, and Research Directions

Strengths:

• Explicit integration of worker heterogeneity (origins, destinations, time budgets) aligns with actual crowd systems.
• Rolling-horizon scenario sampling mitigates short-sightedness while retaining real-time tractability (sub-second to sub-minute runtimes for up to 150 tasks).
• ALNS solver is robust for multi-period, hard-temporal, and spatial constraints.

Limitations:

• Deterministic, time-independent travel times; does not accommodate stochastic traffic or real-time disturbances.
• Scenario generation is uniform, lacking data-driven predictive models.
• No formal optimality guarantees for the rolling-horizon policy, with benchmark performance tied to scenario and ALNS quality.

Open Research Questions:

• Incorporation of data-driven or machine learning forecasts into scenario generation.
• Robustification for stochastic or time-dependent travel times.
• Integration with deep reinforcement learning for dispatch policy synthesis.
• Meta-control for adaptive tuning of scenario pool sizes or sample characteristics.
• Development of valid inequalities or decomposition frameworks to strengthen large-scale MIP relaxations, thus tightening performance benchmarks.

The DTOP-SC formalism and algorithmic toolkit represent a significant advance in addressing the core computational and operational challenges of large-scale, dynamic, and realistic spatial crowdsourcing platforms (Wu et al., 16 Jan 2026, Liu et al., 2021).