**4. Experiments and results**

This section presents the methodology for the experiments and results from the experiments. Section 4.1 presents the methodology. Section 4.2 presents the parameters used in the MS-*MM*AS algorithm. Section 4.3 presents the results.

#### **4.1 Methodology**

The experiments were executed on a computer with an Intel Core i5, 2.6 GHz processor, Windows 10, 64-bit, and 6GB RAM memory. The algorithms were implemented in C ++ lan and compiled with GNU g++ version 4.8.4. The benchmark set proposed in [5] was used to test the effectiveness of the MS-*MM*AS. The sizes of those instances range from 10 to 500 vertices. Small instances have up to 40 vertices, medium up to 100, and large more than 100 vertices. The instances are available for download at https://github.com/brunocastrohs/QTSP-PIC.

The best, average results, and average processing times (in seconds) are reported from 20 independent executions of the MS-*MM*AS. Experiments are conducted to report the distance between the best-known solutions and the best results provided by the MS-*MM*AS. The variability in which the MS-*MM*AS achieved the best-known solutions stated in the benchmark set is also calculated. With these experiments, it is possible to conclude if the MS-*MM*AS algorithm was able to find the best-known solution of each instance and with what variability this happens.

The Friedman test [23] with the Nemenyi post-hoc procedure [24] are applied, with a significance level 0.05, to conclude about significant differences among the results of the MS-*MM*AS and the other three ACO variants proposed in this [5]. The instances were grouped according to their sizes (number of vertices) for the Friedman test. There are eight groups of symmetric (asymmetric) instances, each of them contains nine instances, called *g* <*n*> , where <*n* > stands for the size.

#### **4.2 Parameter tuning**

The IRACE software was used, presented by [22], to tune the parameters of the MS-*MM*AS algorithm. 20 symmetric and 20 asymmetric instances were submitted

*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman… DOI: http://dx.doi.org/10.5772/intechopen.93860*

to adjust the parameters. Those instances were selected at random. The IRACE uses the *maxExperiments* and *maxTime* parameters as stopping criteria. This parameters were set as follows: *maxExperiments* <sup>¼</sup> <sup>10</sup><sup>3</sup> ; and, *maxTime* ¼ ∞.

For the asymmetric instance set, the parameters were defined as follows: *maxIter* ¼ 31; *m* ¼ 51; *α* ¼ 3*:*08; *β* ¼ 10*:*31; *ρ* ¼ 0*:*52; *τmax* ¼ 0*:*8; and *τmin* ¼ 0*:*2. For the symmetric instance set, the parameters were: *maxIter* ¼ 29; *m* ¼ 57; *α* ¼ 2*:*92; *β* ¼ 9*:*53; *ρ* ¼ 0*:*67; *τmax* ¼ 0*:*7; and *τmin* ¼ 0*:*2.

#### **4.3 Results**

The algorithm sets *τmax* as the initial value of pheromone trails (step 2). Since ants begin at vertex *s*, the second vertex is selected randomly with uniform distribution (steps 3 and 4). The *k*-th ant decides which heuristic information, *ξ*, to use (step 7) and builds a route (step 8). The algorithm uses the *RMH* heuristic to assign

(step 10). The MnLS algorithm is applied to *S<sup>i</sup>* (step 12) if the solution *S<sup>i</sup>* ∉ Π. After the local search, the algorithm stores *S<sup>i</sup>* in the hash table Π. At the next iteration, the current *Si* is the starting solution of the local search if it is not in Π. This procedure prevents redundant work. The algorithm updates the best route and the best solution found so far, *W* <sup>∗</sup> and *S* <sup>∗</sup> (step 14). Similar to the original design of *MM*AS, *W<sup>i</sup>* is assigned to *Wbest* at the first 25% iterations or if *i* ranges from [50%,75%] of *maxIter*. *W* <sup>∗</sup> is assigned to *Wbest* if *i* ranges from [25%,50%] of *maxIter* or if it is greater than or equal to 75% of *maxIter* (step 15). This procedure improves diversification by shifting the emphasis over the search space. *Wbest* is used to update

This section presents the methodology for the experiments and results from the

The experiments were executed on a computer with an Intel Core i5, 2.6 GHz processor, Windows 10, 64-bit, and 6GB RAM memory. The algorithms were implemented in C ++ lan and compiled with GNU g++ version 4.8.4. The benchmark set proposed in [5] was used to test the effectiveness of the MS-*MM*AS. The sizes of those instances range from 10 to 500 vertices. Small instances have up to 40 vertices, medium up to 100, and large more than 100 vertices. The instances are

The Friedman test [23] with the Nemenyi post-hoc procedure [24] are applied, with a significance level 0.05, to conclude about significant differences among the results of the MS-*MM*AS and the other three ACO variants proposed in this [5]. The instances were grouped according to their sizes (number of vertices) for the Friedman test. There are eight groups of symmetric (asymmetric) instances, each of them contains nine instances, called *g* <*n*> , where <*n* > stands for the size.

The IRACE software was used, presented by [22], to tune the parameters of the MS-*MM*AS algorithm. 20 symmetric and 20 asymmetric instances were submitted

experiments. Section 4.1 presents the methodology. Section 4.2 presents the parameters used in the MS-*MM*AS algorithm. Section 4.3 presents the results.

available for download at https://github.com/brunocastrohs/QTSP-PIC. The best, average results, and average processing times (in seconds) are reported from 20 independent executions of the MS-*MM*AS. Experiments are conducted to report the distance between the best-known solutions and the best results provided by the MS-*MM*AS. The variability in which the MS-*MM*AS achieved the best-known solutions stated in the benchmark set is also calculated. With these experiments, it is possible to conclude if the MS-*MM*AS algorithm was able to find the best-known solution of each instance and with what variability this

pheromones (step 16). Finally, the algorithm returns *S* <sup>∗</sup> .

*Operations Management - Emerging Trend in the Digital Era*

**4. Experiments and results**

**4.1 Methodology**

happens.

**84**

**4.2 Parameter tuning**

, completing a solution (step 9). The algorithm updates *W<sup>i</sup>* and *S<sup>i</sup>*

passengers to *W<sup>k</sup>*

In this section, the results of the MS-*MM*AS are tested and compared to those produced by the other three ACO variants proposed in [5]: AS, ACS, and MS-ACS.

**Table 1** presents the comparison between the ant algorithms. The best results obtained by MS-*MM*AS were compared with those achieved by each ant algorithm proposed in [5]. The results are in the *X* � *Y* format, where *X* and *Y* stand for the number of instances in which the ant algorithm *X* found the best solution and the number of instances in which the ant algorithm *Y* found the best solution, respectively.

**Table 1** shows that the MS-*MM*AS was the algorithm that reported the best solution for most instances. This algorithm performed best than other ACO variants due to its enhanced pheromone update procedures. The MS implementation with roulette wheel selection proved to be effective at finding the best heuristic information used by the ants during the run. **Table 1** also shows that the MS-*MM*AS provides results with better quality than the MS-ACS in the most symmetric cases. The MS-ACS was superior to the MS-*MM*AS in seventeen asymmetric cases and fourteen symmetric instances. Was observed that the pseudo-random action choice rule of MS-ACS [20], which allows for a greedier solution construction, proved to be a good algorithmic strategy for solving large instances.

**Tables 2** and **3** shows the ranks of the ant algorithms based on the Friedman test [23] with the Nemenyi [24] post-hoc test. The first column of this Tables presents the subsets of instances grouped according to their sizes. The other columns of this Tables present the p-values of the Friedman test and the ranks from the Nemenyi post-hoc test. In the post-hoc test, the order ranks from *a* to *c*. The *c* rank indicates that the algorithm achieved the worst performance in comparison to the others. The *a* rank indicates the opposite. If the performances of two or more algorithms are similar, the test assigns the same rank for them. In this experiment, the significance level was assigned with 0.05.

The p-values presented in **Tables 2** and **3** show that the performance of the ant algorithms was not similar, i.e., the null hypothesis [24] is rejected in all cases. In these Tables, can be observed that MS-*MM*AS ranks higher than AS and ACS for all subsets. The ranks of MS-ACS and MS-*MM*AS were the same in the most cases. This implies that the performance of only these two algorithms where similar, i. e., the relative distance between the results achieved by these two algorithms are short.

To analyze the variability of the results provided by each ant algorithm compared to the best results so far for the benchmark set, three metrics regarding the


#### **Table 1.**

*Comparison between the ant algorithms.*


**Asymmetric Symmetric**

**Instance Best Average Time Percentage Best Average Time Percentage** A-10-3 478.42 863.13 0.15 100% 545.92 996.34 0.15 25% A-10-4 523.57 1069.33 0.14 80% 460.00 838.84 0.18 20% A-10-5 482.60 690.08 0.14 5% 371.93 658.97 0.19 10% A-20-3 519.67 936.47 0.35 5% 679.75 1363.59 0.32 20% A-20-4 458.10 1145.88 0.38 0% 346.30 661.82 0.43 35% A-20-5 398.75 669.82 0.35 10% 351.50 1006.24 0.48 5% A-30-3 618.33 1180.70 0.48 10% 574.33 1469.68 0.50 5% A-30-4 401.20 805.32 1.28 5% 654.80 1202.15 0.40 5% A-30-5 475.83 1033.91 0.58 10% 464.05 911.56 0.66 5% A-40-3 692.00 1060.67 2.83 5% 718.25 1399.04 0.72 10% A-40-4 658.95 1088.41 2.52 5% 570.98 961.13 2.95 5% A-40-5 460.90 900.51 3.11 5% 441.22 836.52 2.89 5% B-10-3 729.50 925.35 0.13 5% 834.67 1485.47 0.20 20% B-10-4 306.90 421.35 0.13 15% 493.58 757.45 0.16 10% B-10-5 434.75 835.01 0.18 55% 726.35 1160.97 0.23 5% B-20-3 805.42 1251.39 0.28 10% 950.00 1666.22 0.45 5% B-20-4 848.62 1366.69 0.35 5% 822.82 1386.67 0.49 5% B-20-5 895.17 1275.78 0.28 70% 660.22 1215.12 0.35 5% B-30-3 747.75 1316.96 1.31 5% 718.67 1358.11 0.93 5% B-30-4 723.27 1301.57 1.51 5% 650.35 1272.86 0.69 5% B-30-5 700.75 1205.96 1.39 5% 504.68 1091.11 0.89 5% B-40-3 964.42 1574.00 2.02 0% 889.83 1682.76 1.97 5% B-40-4 1195.62 2134.73 1.20 5% 743.82 1508.16 2.09 0% B-40-5 819.28 1537.71 1.11 10% 749.82 1351.64 0.85 5% C-10-3 359.25 604.70 0.17 55% 597.83 697.51 0.05 0% C-10-4 307.10 514.66 0.20 5% 408.45 514.65 0.15 85% C-10-5 566.58 783.35 0.17 10% 409.60 846.51 0.23 10% C-20-3 650.25 978.84 0.46 10% 629.92 1063.99 0.36 0% C-20-4 563.78 938.50 0.72 5% 441.65 1019.96 1.06 10% C-20-5 739.22 1056.77 1.02 0% 711.87 1095.84 0.63 5% C-30-3 837.58 1198.09 1.05 5% 830.17 1221.65 0.61 10% C-30-4 754.10 1144.99 2.47 5% 745.92 1096.55 1.16 5% C-30-5 560.18 998.28 2.29 10% 490.80 931.81 2.21 5% C-40-3 1008.00 1541.54 2.59 5% 607.00 946.57 3.45 10% C-40-4 695.30 1172.76 2.06 10% 699.80 1136.17 2.25 0% C-40-5 623.33 1097.22 3.24 10% 475.67 898.80 7.82 0%

*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman…*

*DOI: http://dx.doi.org/10.5772/intechopen.93860*

**Table 6.**

**87**

*Results of the MS-MMAS executions for small instances.*

#### **Table 2.**

*Results of Friedman's test and Nemenyi post-hoc test over asymmetric instances set.*


#### **Table 3.**

*Results of Friedman's test and Nemenyi post-hoc test over symmetric instances set.*


#### **Table 4.**

*Variability of the ants algorithms for asymmetric instances.*


#### **Table 5.**

*Variability of the ants algorithms for symmetric instances.*


*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman… DOI: http://dx.doi.org/10.5772/intechopen.93860*

#### **Table 6.**

*Results of the MS-MMAS executions for small instances.*

**Asymmetric**

**Symmetric**

**Asymmetric**

**Symmetric**

**Metric AS ACS MS-ACS MS-***MM***AS** *ν* 4.30% 2.56% 6.8% 11.84% Φ 0.2075333 0.2773624 0.0541799 0.0054741 Ω 0.2835401 0.4023659 0.1754952 0.5854892

**Metric AS ACS MS-ACS MS-***MM***AS** *ν* 2.01% 0.69% 8.75% 9.05% Φ 0.2169756 0.2285948 0.0547890 0.0113889 Ω 0.3017957 0.3620682 0.1656022 0.6432748

**Subset p-value AS ACS MS-ACS MS-***MM***AS** *g*10 0.003543 b b a a *g*20 0.000205 b c a a *g*30 0.000045 c c b a *g*40 0.000059 b c a a *g*50 0.000035 b b a a *g*100 0.000024 b b a a *g*200 0.000045 c b a a *g*500 0.000098 c b a a

**Subset p-value AS ACS MS-ACS MS-***MM***AS** *g*10 0.003159 b b a a *g*20 0.000040 b c a a *g*30 0.000017 c c a a *g*40 0.000024 b c a a *g*50 0.000048 c c b a *g*100 0.000045 b c a a *g*200 0.000031 b c a a *g*500 0.000037 c b a a

*Results of Friedman's test and Nemenyi post-hoc test over asymmetric instances set.*

*Operations Management - Emerging Trend in the Digital Era*

*Results of Friedman's test and Nemenyi post-hoc test over symmetric instances set.*

*Variability of the ants algorithms for asymmetric instances.*

*Variability of the ants algorithms for symmetric instances.*

**Table 2.**

**Table 3.**

**Table 4.**

**Table 5.**

**86**


results produced by the experiments were adopted. The first metric, *ν*, shows the percentages relative to the number of times an ant algorithm found the best-known solution along 20 independent executions. The second metric, Φ, is the relative distance between the cost of the best-known solution *χ* <sup>∗</sup> and the best solution *χmin* of each ant algorithm. The third metric, Ω, is the relative distance between *χ* <sup>∗</sup> and the average solution *χ<sup>a</sup>* of each ant algorithm. To calculate Φ, the Eq. (9) was used. Ω is calculated using the formula (10). The average values of *ν*, Φ and Ω are

*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman…*

<sup>Φ</sup> <sup>¼</sup> *<sup>χ</sup>min*

<sup>Ω</sup> <sup>¼</sup> *<sup>χ</sup><sup>a</sup>*

It can be observed from **Tables 4** and **5** that the MS-*MM*AS is the best one concerning the *ν* and Φ metrics. The MS-ACS is the best algorithm concerning the Ω metric. **Tables 6** and **7** show the data regarding the results of MS-*MM*AS reported in **Tables 4** and **5**. The results of the other ACO variants can be seen in [5].

**Tables 8** and **9** present the average processing time (in seconds) spent by each heuristic. Instances are grouped by the number of vertices. From these tables, it can be conclude that the MS-*MM*AS was the ant algorithm that demanded more

**n AS ACS MS-ACS MS-***MM***AS** 0.05 0.06 0.12 0.15 0.10 0.13 0.26 0.46 0.20 0.30 1.92 1.37 0.34 0.48 2.29 2.29 0.41 2.20 5.77 5.92 6.68 28.85 32.69 50.75 31.81 270.94 409.72 640.89 41.72 3477.13 3545.20 9940.87

**n AS ACS MS-ACS MS-***MM***AS** 0.05 0.06 0.12 0.17 0.10 0.13 0.27 0.51 0.18 0.24 0.49 0.89 0.28 0.38 0.73 2.78 0.40 0.56 5.41 4.02 8.13 13.51 29.17 34.93 22.94 51.92 112.58 97.43 40.53 75.72 127.83 309.46

*Average time spent by the ant algorithms for the set of asymmetric instances.*

*Average time spent by the ant algorithms for the set of symmetric instances.*

*<sup>χ</sup>* <sup>∗</sup> � <sup>1</sup> (9)

*<sup>χ</sup>* <sup>∗</sup> � <sup>1</sup> (10)

reported in **Tables 4** and **5**.

*DOI: http://dx.doi.org/10.5772/intechopen.93860*

**Table 8.**

**Table 9.**

**89**

#### **Table 7.**

*Results of the MS-MMAS executions for medium and large instances.*

*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman… DOI: http://dx.doi.org/10.5772/intechopen.93860*

results produced by the experiments were adopted. The first metric, *ν*, shows the percentages relative to the number of times an ant algorithm found the best-known solution along 20 independent executions. The second metric, Φ, is the relative distance between the cost of the best-known solution *χ* <sup>∗</sup> and the best solution *χmin* of each ant algorithm. The third metric, Ω, is the relative distance between *χ* <sup>∗</sup> and the average solution *χ<sup>a</sup>* of each ant algorithm. To calculate Φ, the Eq. (9) was used. Ω is calculated using the formula (10). The average values of *ν*, Φ and Ω are reported in **Tables 4** and **5**.

$$
\Phi = \frac{\chi^{\min}}{\chi^\*} - \mathbf{1} \tag{9}
$$

$$
\mathfrak{Q} = \frac{\chi^{\mu}}{\chi^{\*}} - \mathbf{1} \tag{10}
$$

It can be observed from **Tables 4** and **5** that the MS-*MM*AS is the best one concerning the *ν* and Φ metrics. The MS-ACS is the best algorithm concerning the Ω metric. **Tables 6** and **7** show the data regarding the results of MS-*MM*AS reported in **Tables 4** and **5**. The results of the other ACO variants can be seen in [5].

**Tables 8** and **9** present the average processing time (in seconds) spent by each heuristic. Instances are grouped by the number of vertices. From these tables, it can be conclude that the MS-*MM*AS was the ant algorithm that demanded more


**Table 8.**

**Asymmetric Symmetric**

**Instance Best Average Time Percentage Best Average Time Percentage** A-50-3 1058.33 2128.68 2.31 5% 1000.33 1943.13 2.91 5% A-50-4 774.93 1473.57 4.48 5% 783.40 1345.19 3.53 5% A-50-5 673.42 1314.54 4.16 5% 583.08 1008.33 2.59 0% A-100-3 1431.42 2046.96 53.44 5% 1514.08 2292.08 15.66 20% A-100-4 1456.47 2705.07 23.12 5% 1165.90 1595.91 37.11 5% A-100-5 1106.17 1778.38 40.57 10% 980.28 1366.09 58.20 5% A-200-3 2806.75 3610.22 424.60 0% 2793.33 3272.00 257.42 0% A-200-4 2388.88 3196.15 381.07 0% 2199.45 2807.06 79.32 10% A-200-5 1753.00 2286.08 1380.26 10% 2086.82 3237.85 55.37 10% A-500-3 6878.42 7165.39 1641.92 33% 6331.75 7679.65 732.94 10% A-500-4 5572.42 5637.26 4939.84 0% 5030.48 5080.66 913.82 0% A-500-5 4389.92 4539.44 16990.77 50% 4610.95 4696.91 73.97 33% B-50-3 1338.42 2356.24 5.82 10% 966.42 1770.88 4.60 5% B-50-4 951.87 1757.61 5.00 5% 772.67 1490.01 1.47 5% B-50-5 1083.18 1943.22 3.91 5% 692.42 1342.78 4.74 5% B-100-3 1781.00 3115.78 30.96 5% 1803.33 3258.90 15.11 5% B-100-4 1409.65 2467.02 61.76 5% 1648.58 3360.93 11.00 5% B-100-5 1361.20 2734.24 39.89 5% 1018.37 1536.34 99.02 5% B-200-3 3302.83 4840.94 317.37 0% 3016.67 4267.17 56.62 0% B-200-4 2536.80 3477.13 681.75 0% 2326.97 3139.57 81.34 10% B-200-5 2127.88 2814.24 906.74 0% 1893.67 2506.64 102.33 10% B-500-3 6994.84 7203.61 3857.77 0% 6433.92 6475.67 126.51 0% B-500-4 5419.87 5730.97 24183.87 100% 5191.77 5276.98 267.72 0% B-500-5 4546.28 4643.03 21118.98 0% 4379.43 4494.11 164.08 33% C-50-3 1201.92 1801.68 3.12 5% 829.75 1482.86 2.82 5% C-50-4 937.25 1651.11 7.96 5% 901.40 1605.24 6.16 10% C-50-5 609.60 1127.99 16.58 5% 766.48 1366.58 7.43 5% C-100-3 1496.58 2001.76 47.62 0% 1364.00 1819.03 14.21 10% C-100-4 1352.85 2458.82 32.32 5% 1099.00 1445.29 23.98 0% C-100-5 1022.70 1466.42 127.11 0% 991.12 1472.23 35.21 5% C-200-3 2629.00 3197.13 478.90 10% 2510.50 3171.66 65.07 10% C-200-4 2184.85 2648.38 710.70 10% 2141.40 2741.11 52.59 0% C-200-5 1881.03 2296.53 486.62 0% 1713.17 2127.84 126.85 10% C-500-3 6528.08 6618.16 2484.52 0% 6023.42 6087.14 138.12 33% C-500-4 5139.54 5298.21 8188.46 0% 4942.28 4958.64 65.19 33% C-500-5 4286.45 4278.49 6061.78 0% 4167.67 4178.10 302.79 0%

*Operations Management - Emerging Trend in the Digital Era*

**Table 7.**

**88**

*Results of the MS-MMAS executions for medium and large instances.*

*Average time spent by the ant algorithms for the set of asymmetric instances.*


#### **Table 9.**

*Average time spent by the ant algorithms for the set of symmetric instances.*

processing time. **Tables 6** and **7** (1) present detailed results concerning the average time required by the MS-*MM*AS. Data regarding the time consumption of the other ACO variants can be seen in [5].

**6. Conclusions**

*DOI: http://dx.doi.org/10.5772/intechopen.93860*

and ACS.

for the future research.

MaaS Mobility as a Service

ACO Ant Colony Optimization RMH Ride-Matching Heuristic

*MM*AS *MAX-MIN* Ant System

TSP Traveling Salesman Problem QTSP Quota Traveling Salesman Problem

MS Multi-Strategy

AS Ant System

**91**

ACS Ant Colony System

MnLS Multi-neighborhood Local Search MS-ACS Multi-Strategy Ant Colony System

MS-*MM*AS Multi-Strategy *MAX-MIN* Ant System

Ride and Collection Time

**Abbreviations**

This work dealt with a recently proposed variant of the Traveling Salesman Problem named The Quota Traveling Salesman Problem with Passengers, Incomplete Ride, and Collection Time. In this problem, the salesman uses a flexible ride-sharing system to minimize travel costs while visiting some vertices to satisfy a pre-established quota. He must respect the budget limitations and the maximum travel time of every passenger. Each passenger can be transported directly to the desired destination or an alternate destination. The alternative destination idea suggests that when sharing a ride, pro-environmental or money-saving concerns can induce persons to agree to fulfill their needs at a similar destination. Operational

*Multi-Strategy* MAX-MIN *Ant System for Solving Quota Traveling Salesman…*

constraints regarding vehicle capacity and travel time were also considered. The Multi-Strategy *MAX-MIN* Ant System, a variant from the Ant Colony Optimization (ACO) family of algorithms, was presented. This algorithm uses the MS concept improved with roulette wheel selection and memory-based principles to avoid redundant executions of the local search algorithm. The results of MS-*MM*AS were compared with those produced by the ACO algorithms presented in [5]. To support MS-*MM*AS, the ride-matching heuristic and the local search heuristic based on multiple neighborhood operators proposed by [5] were reused. The computational experiments reported in this study comprised one hundred forty-four instances. The experimental results show that the proposed ant algorithm variant could update the best-known solutions for this benchmark set according to the statistical results. The comparison results with three other ACO variants proposed in [5] showed that MS-*MM*AS improved the best results of MS-ACS for ninety-three instances, and a significant superiority of MS-*MM*AS over AS

The presented work may be extended in multiple directions. First, it would be interesting to investigate if the application of the pseudo-random action choice rule [20] could improve the MS-*MM*AS results. Another further promising idea is the use of pheromone update rule based on ants ranking [25]. Extension of the MS-*MM*AS implementation design with parallel computing techniques [10] and hybridization with other meta-heuristics [26–28] is other interesting opportunity

QTSP-PIC Quota Traveling Salesman Problem with Passengers, Incomplete
