In tourism management, incorporating both economic benefits and environmental protection into optimization frameworks has become a growing trend. Pitakaso et al. (2024) proposed a multi-objective model for sustainable tourist trip design, integrating visitor preferences, site capacities, and environmental constraints to generate Pareto-optimal solutions [5] . Similarly, Aliahmadi et al. (2025) introduced a multi-objective optimization approach for personalized trip planning that balances visitor experience with resource efficiency [6] . These studies highlight the effectiveness of multi-objective modeling in reconciling tourism development with ecological sustainability.

NSGA-II [7] is one of the most widely adopted evolutionary algorithms for solving multi-objective optimization problems, and it has been successfully applied to transportation, scheduling, and resource allocation [8] . In the tourism domain, Zhu et al. (2025) applied NSGA-II to sustainable tourism management, showing how the algorithm can balance economic revenue with ecological constraints [9] . Yang and Bian (2023) developed a multi-objective optimization model to evaluate sustainable tourism capacity, further validating the suitability of NSGA-II for tourism-related optimization problems [10] . These studies provide methodological support for employing NSGA-II in this paper.

In comparative experiments, greedy heuristics, randomized strategies, and local search methods are commonly employed as baselines in tourism optimization and scheduling problems. For instance, greedy insertion and nearest-neighbor heuristics are often used to construct initial solutions for tourist routes, while randomized allocation and simple local search operators (e.g., 2-opt, 3-opt) provide quick but less optimal benchmarks [11] . Although these methods are limited in quality, they serve as practical references to demonstrate the advantages of advanced evolutionary algorithms in solution quality and objective balance.

In summary, existing studies on sustainable tourism and multi-objective optimization have made progress in integrating economic and ecological dimensions, but most focus on either single attractions or high-level management issues. Research on multi-attraction coordination that explicitly addresses both economic-experiential maximization and congestion-ecological minimization remains scarce. By formulating this problem as a dual-objective optimization model, employing NSGA-II for solution generation, and benchmarking against greedy and randomized methods, this study contributes to bridging this research gap and offers a systematic approach to sustainable tourism planning.

In this section, we formulate the Qujing multi-attraction tourism optimization as a multi-objective optimization problem (MOP). The model simultaneously considers (i) maximizing the economic-experiential value of tourist routes, and (ii) minimizing congestion and ecological stress caused by excessive visitor concentration. For the convenience of reading, we have summarized the symbols that appear in the text in Table 1 .

The specific problem modeling is as follows.

The total number of tourists visiting site 𝑖 during period t is:

$N_{i,t}=\underset{r=1}{\overset{R}{{\displaystyle \sum }}}\underset{k\in K}{{\displaystyle \sum }}{q}_t^{r,k}{y}_i^r$ (1)

Objective 1: Economic-Experiential Value Maximization (EEV)

We define the unit value of assigning one tourist from group k to route r as:

$V_{r,k}=\underset{i\in V}{{\displaystyle \sum }}{y}_i^r\left(r_i+\alpha u_i{w}_{ik}\right)-\frac{1}{Q_{scale}}\underset{\left(i,j\right)\in E}{{\displaystyle \sum }}{x}_{ij}^r{c}_{ij}^{travel}$ (2)

The first objective is then formulated as:

$\max F_1=\underset{r=1}{\overset{R}{{\displaystyle \sum }}}\underset{k\in K}{{\displaystyle \sum }}\underset{t\in T}{{\displaystyle \sum }}{q}_t^{r,k}{V}_{r,k}-\underset{r=1}{\overset{R}{{\displaystyle \sum }}}{f}_i{z}_r$ (3)

This objective captures both direct economic revenue and enhanced visitor experience, while accounting for route operation and travel costs.

Objective 2: Congestion-Ecological Stress Minimization (CES) We define the load ratio of site $i$ at time $t$ as:

$z_{i,t}=\frac{N_{i,t}}{ca{p}_i}$ (4)

To penalize congestion, we adopt a convex penalty function:

$\Phi \left(z\right)=\{\begin{array}{l}0,z\le \theta \\ {\beta }_1{\left(z-\theta \right)}^2,\theta <z\le 1\\ {\beta }_1{\left(z-\theta \right)}^2,z>1\end{array}$ (5)

The second objective is then:

$\min F_2=\underset{i\in V}{{\displaystyle \sum }}\underset{t\in T}{{\displaystyle \sum }}\Phi \left(z_{i,t}\right)+{\lambda }_{time}\underset{i\in V}{{\displaystyle \sum }}\underset{t=2}{\overset{H}{{\displaystyle \sum }}}{\left(z_{i,t}-z_{i,t-1}\right)}^2+{\lambda }_{space}\underset{t\in T}{{\displaystyle \sum }}Va{r}_i\left(z_{i,t}\right)$ (6)

where the second and third terms encourage temporal smoothing and spatial balancing, reducing sharp peaks and uneven distribution of visitors.

The Qujing tourism optimization problem can thus be summarized as the following multi-objective optimization problem:

$\max F_1,\min F_2$ (7)

subject to route feasibility, time windows, demand allocation, and capacity constraints.

To adapt NSGA-II to the specific characteristics of the Qujing tourism optimization problem, we designed tailored genetic operators that directly manipulate route structures and visitor allocations. Unlike conventional operators that act on continuous variables, our operators are problem-aware, ensuring feasibility and improving search efficiency. The proposed algorithm flowchart is shown in Figure 1 .

Given two parent solutions, each represented by a set of routes and corresponding visitor allocations, the crossover operator is designed to exchange both structural and allocation information:

1) Route-level exchange: A subset of routes from Parent A is combined with the complementary subset from Parent B. Overlapping routes are merged, and feasibility (capacity and time windows) is checked.

2) Visitor reallocation: For routes that appear in both parents, the offspring inherits a weighted average of their visitor allocations. The weights are biased towards the parent with higher fitness, promoting exploitation of good solutions.

3) Feasibility repair: If the offspring violates site capacity or budget constraints, a greedy repair step redistributes excess visitors to underutilized routes or adjusts timing to avoid congestion.

This operator allows the offspring to inherit diverse route structures while maintaining feasible visitor flows.

To avoid premature convergence and to explore underutilized parts of the solution space, we employ a mutation operator that adaptively perturbs visitor allocations:

1) Local redistribution: A fraction of visitors assigned to congested sites is shifted to alternative sites within the same route or to parallel routes serving similar attractions.

2) Temporal adjustment: Visitors are shifted across adjacent time periods to reduce peak congestion while preserving demand satisfaction.

3) Adaptive intensity: The mutation probability is increased for individuals with higher congestion penalties $F_2$, encouraging stronger exploration when ecological stress is high, and reduced otherwise.

1) Feasibility preservation: Operators are designed to directly handle capacity and time constraints, reducing the need for excessive repair.

2) Problem awareness: By incorporating route structure and visitor flows, the search process explicitly targets the trade-off between economic-experiential value and congestion-ecological stress.

3) Diversity and exploitation balance: Route-level crossover provides structural diversity, while adaptive mutation fine-tunes allocations, together enabling efficient convergence towards a well-distributed Pareto front.

The experiments are conducted in the context of multi-attraction tourism planning in Qujing City, Yunnan Province. We select 5 - 11 representative attractions (e.g., Pearl River Source, Jiulong Waterfalls, Luoping Rapeseed Flower Fields, Huize Ancient City, Shengjingguan, etc.) together with one central depot (downtown or high-speed railway station) as the starting and ending point.

1) Time discretization: A day is divided into H = 6 time periods (e.g., morning/afternoon/evening across weekdays and weekends).

2) Tourist groups: We consider K = 3 groups (family tourists, hiking/photography, leisure sightseeing). Each group is associated with demand volume $D_k$ and preference weights $w_{ik}$ for different attractions.

3) Capacities: Each attraction $i$ has a maximum ecological/operational capacity $ca{p}_i$, with seasonal adjustments for peak seasons.

4) Economic and experiential values: Revenue $r_i$ is derived from ticket prices, while satisfaction scores $u_i$ are estimated based on historical survey and rating data.

5) Transportation network: Travel time $t_{ij}$ and travel cost $c_{ij}^{travel}$ between sites are estimated using real-world road distances.

The experimental data are constructed by integrating publicly available information (attraction lists and ticket prices from official tourism sources, travel distances from online maps, satisfaction scores from survey/rating platforms) with modeled assumptions on tourist group preferences and ecological capacities, following common practices in tourism optimization studies.

In our implementation, the population size is set to 100, and the algorithm runs for 300 generations. The crossover probability is fixed at 0.9, while the mutation probability is set as the reciprocal of the number of decision variables $1/d$. For the congestion penalty function, the threshold is set to $\theta =0.8$, with penalty coefficients ${\beta }_1=1$, ${\beta }_2=20$, and $\gamma =10$. The weights for the temporal smoothing term and the spatial balancing term are both assigned the value of 0.5.

To ensure the stability of the experiments, each algorithm was independently executed 30 times, and the quality of the obtained Pareto fronts was evaluated using the hypervolume (HV) indicator. All objective values were normalized prior to evaluation, and the reference point for HV calculation was set to (1.1, 1.1). The detailed results are reported in Table 2 . A larger HV indicates a better Pareto front—i.e., broader coverage of the objective space and closer convergence toward the ideal point.

We designed experiments with different scales of sightseeing scenarios by varying the number of attractions, specifically N = 5, 7, 9, and 11. As shown in Table 2 , our proposed method consistently outperforms all baseline approaches. This improvement can be attributed to the problem-specific crossover and mutation operators carefully designed for this study. To provide a more intuitive comparison, the detailed numerical analysis is presented in Figure 2 .

Despite the encouraging results, several limitations of this study should be acknowledged. First, the current framework relies on static demand assumptions and fixed parameter settings, which may not fully capture the temporal variability of tourist flows and ecological sensitivities in real-world contexts. Second, while the customized evolutionary operators enhance solution quality, their effectiveness may be sensitive to specific tuning choices and problem instances. These factors suggest that further validation under dynamic, large-scale, and heterogeneous conditions will be necessary to consolidate the generalizability of our findings.