CN114021883A - Dispatching method for subway transfer shared bicycle in peak period - Google Patents
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Abstract
The invention discloses a dispatching method for a subway transfer shared bicycle in a peak period, which comprises the steps of acquiring subway station data and shared bicycle data of a research area in advance, and carrying out data cleaning and data analysis on the shared bicycle data; dividing the research area into areas by using a Geohash algorithm, converting the areas into a coordinate system, and obtaining the distance between the areas through coordinates so as to determine the distance problem during scheduling; classifying the shared bicycle by using a DBSCAN clustering algorithm, wherein a clustering result provides a scheduling object for implementing a greedy algorithm; and selecting the optimal substructure by using a greedy algorithm and combining the prior data to obtain a local optimal scheduling scheme. The invention is not only beneficial to relieving serious traffic pressure, but also has positive reference significance for solving the problem of the tide of the bicycle in other areas, and promotes the development of a rail transit station shared bicycle connection system to a healthier and more reasonable direction.
Description
Technical Field
The invention belongs to the field of traffic, and particularly relates to a dispatching method of a subway transfer shared bicycle in a peak period.
Background
The shared bicycle is an emerging vehicle, has the characteristics of convenience and no pollution, and is rapidly developed after being pushed out. The shared bicycle greatly solves the problem of the last kilometer, and gradually becomes one of the important connection modes for public transport travel.
The subway connection sharing bicycle improves the traveling efficiency of people, however, around some subway stations, the following problems exist in connection of the subway and the sharing bicycle: if the car is returned at a fixed rental location, or the rental location has no car, and the rental location is full, the travel experience of the pedestrians is seriously influenced.
Particularly, in the peak period, the phenomenon that one vehicle is difficult to share is more serious. Meanwhile, the shared bicycle is parked around some stations, so that the phenomenon of parking congestion occurs, and the traffic service capability of corresponding areas is weakened. And management departments lack detailed demand forecasting support, and the refined management of 'one station for one strategy' is difficult to be carried out only by the total quantity of regional trips.
Therefore, a method is needed to alleviate the problems of disordered parking and uneven distribution of the shared bicycle at the subway station entrance and solve the problem of tide of the shared bicycle.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects in the prior art, the invention provides a dispatching method of a subway transfer shared bicycle in a peak period, so as to relieve the disordered parking of the shared bicycle at the current subway station port and solve the problem of uneven distribution of the shared bicycle.
The technical scheme is as follows: the invention provides a dispatching method of a subway transfer shared bicycle in a peak period, which specifically comprises the following steps:
(1) crawling subway station data in the targeted area on a hectogram application program by utilizing a Python crawler;
(2) the method comprises the steps that shared bicycle data in a targeted area are crawled by a Python crawler and a related website, and data cleaning and data analysis are conducted on the shared bicycle data;
(3) dividing the regions into regions by using a Geohash algorithm, establishing a coordinate system, and obtaining the distance between the regions through coordinates in the coordinate system;
(4) the shared bicycle data are classified by using a DBSCAN clustering algorithm, the shared bicycle data can be divided into three types of core points, boundary points and noise points according to a clustering result, the core points are areas with large usage of the shared bicycle, the noise points are areas with small usage, the usage of the shared bicycle of the noise points is between the core points and the noise points, and the clustering result provides a scheduling object for implementing the greedy algorithm;
(5) and selecting an optimal substructure by using a greedy algorithm and combining the regional distance data provided by the Geohash algorithm and the scheduling object data provided by the DBSCAN clustering algorithm to obtain a local optimal scheduling scheme.
Further, the step (1) is realized as follows:
the method comprises the steps of establishing a Baidu map application from a Baidu map open platform by utilizing a Python crawler, applying for a signaling AK, opening a POI module of an API (application program interface), selecting a retrieval mode, setting a retrieval city, retrieving a keyword subway, substituting an obtained URL (uniform resource locator) and the Baidu signaling AK into the Python, and utilizing Python coding to obtain required data.
Further, the step (3) includes the steps of:
(31) obtaining a region Geohash code according to the geographical position information; obtaining a regional Geohash code by utilizing a Geohash six-bit code and setting precision;
(32) according to the Geohash code graph, establishing a plane rectangular coordinate system as a distance coordinate system, making a point line graph, and obtaining the distance of a corresponding area according to the distance between points; converting the longitude and latitude of the shared bicycle order information into a Geohash code, and recording the bicycle stock at each position according to the bicycle lock opening and closing:
wherein, LOCK _ STAUS represents the locking and unlocking record of the bicycle, 0 is unlocking, 1 is locking, and underflow represents the regional stock; inflow-1 represents the regional inventory-1; inflow +1 represents the zone inventory + 1.
Further, the step (4) comprises the steps of:
(41) calculating Euclidean distance between data in the set area:
setting data in the shared bicycle gathering area as two tuples, and calculating the Euclidean distance between the data in the two tuples:
where d is the Euclidean distance between the data in two tuples, x1Longitude, y, for a set of shared bicycle data in the first tuple1For a group of shared numbers of single cars in the first tupleAccording to the latitude; x is the number of2Longitude for a set of shared bicycle data within the second tuple; y is2A latitude for a set of shared bicycle data within the second tuple;
(42) selecting a radius parameter r and a neighborhood density threshold minPts, and utilizing Python coding to realize clustering:
using Python coding to take a data set packaged in sklern as a parameter, setting two lists by combining the number of the obtained Euclidean distance calculation points, putting the accessed points into one list, putting the points which are not accessed into the other list, and selecting a proper radius r and a neighborhood density threshold Eps for traversal processing; if the list for storing the points which are not accessed yet has points, the traversal processing is continued until the list reaches an empty set; if there is no access point, randomly selecting a no access point, if the number of objects in the neighborhood of the point is larger than a specified threshold, indicating that the point is a core object, adding the accessed points to the points in the neighborhood of the point, removing the no access points, finding out the core objects of the points, and placing the core objects in a list, which is called core point; putting the remaining points in the neighborhood into a list, called boundary points; the other points are placed in a list called noise points;
(43) evaluation with reference to the contour coefficients yields the following formula:
wherein a (i) is the average distance from the sample i to other samples in the same cluster, b (i) is the average distance from the sample i to some other cluster CjIf s (i) is close to 1, the average distance of all samples in (1) indicates that the sample i is reasonably clustered; if the clustering is reasonable, ending; and unreasonable, selecting a new radius r and a neighborhood density threshold Eps, and repeating the steps.
Further, the step (5) includes the steps of:
(51) acquiring a shared bicycle gathering area and flow:
substituting the shared bicycle data of each type of clusters of the DBSCAN clustering algorithm into Python, obtaining the area and the central longitude and latitude of each bicycle aggregation area by using the Python, and numbering each shared bicycle aggregation area; time extraction is carried out on order data, and specific regional flow statistics is completed, namely the flow of different times in a certain range is counted;
(52) determining an optimization index:
the optimization index is min (1-global single vehicle utilization rate) + scheduling cost
Min (1-global bicycle utilization) + min (number of dispatching bicycles)
+ min (number of dispatching bicycles) + min (distance dispatching bicycle)
(53) Selecting an optimal substructure, and implementing a greedy algorithm by using Python coding:
comparing the number of the contained bicycles and the bicycle flow of each shared bicycle aggregation area by utilizing Python codes, calculating the value of subtracting the number of the contained shared bicycles from the bicycle flow of each aggregation area, and putting the value into two lists according to the positive and negative of the obtained value, wherein if the value is 0, the value can not be considered; maximizing the optimization index to be used as an optimal substructure of a greedy algorithm; randomly selecting one from the list for storing positive values as an initial target, and selecting data from the list for storing negative values to enable the sum of the positive values and the negative values to be close to 0, wherein the selected number of the negative values can be selected more; and sequentially proceeding downwards until the lists for storing positive values all finish scheduling, and obtaining a local optimal solution.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. according to the invention, a Geohash algorithm is utilized to divide a region to be researched into regions, the regions are converted into a coordinate system, and the distance between the regions is obtained through coordinates, so that the distance problem during dispatching is determined; 2. according to the invention, a DBSCAN clustering algorithm and a greedy algorithm are combined to obtain a more reasonable and effective scheduling scheme, and an unreasonable or less reasonable scheduling scheme obtained by a single algorithm due to error is eliminated; 3. the rationality and effectiveness of the scheduling scheme are verified by using analog simulation, and if the rationality and effectiveness are reasonable, the scheduling scheme is ended; otherwise, returning to the algorithm step; 4. the dispatching method for solving the problem of subway transfer shared bicycle in the peak period can relieve serious traffic pressure, and has positive reference significance in solving the problem of tide of the shared bicycle.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a dispatching method of a subway transfer shared bicycle in a peak period, which specifically comprises the following steps as shown in figure 1:
step 1: the method comprises the steps of establishing a Baidu map application on a Baidu map open platform by utilizing a Python crawler, applying for a signaling AK, opening a POI module of an API (application program interface), selecting a rectangular retrieval mode, setting a retrieval city, retrieving a keyword subway, substituting an obtained URL (uniform resource locator) and the Baidu signaling AK into the Python, and utilizing Python coding to obtain required data.
And in the crawling process, attention is paid to conversion between the Baidu coordinates and the Mars coordinates, and data visualization is realized by using a Gaode map API after data cleaning.
Step 2: and crawling the shared bicycle data in the targeted area by using a Python crawler and a related website, and performing data cleaning and data analysis on the shared bicycle data.
In the embodiment, when cleaning the shared bicycle data, the order data of the shared bicycle is crawled by using Python in a digital Chinese website, if one cycle of unlocking and locking occurs in one order, the order is a group of successful orders, and if the other cycle of continuously unlocking for multiple times or continuously locking for multiple times occurs, the order is defined as a problem order. When a problem order is found, the first unlocking record and the last locking record are stored, and other redundant records are deleted, so that the accuracy of the number of vehicles is ensured.
Then, the shared bicycle data is analyzed, in this embodiment, the shared bicycle data is calculated from 6 in the morning: 00 to night 21: 00 quantitative analysis is carried out every 1 hour, and the analysis determines the peak time of the connection of the sharing single vehicle.
And step 3: dividing the research area into areas by using a Geohash algorithm, establishing a coordinate system, obtaining the distance between the areas through coordinates in the coordinate system, and determining the distance between the areas when scheduling is performed by using a greedy algorithm, wherein the specific process comprises the following steps:
(3.1) aiming at the geographical position information, obtaining a region Geohash code: in this embodiment, the geo-hash six-bit code is used to set the precision, the latitude and longitude information of a region is converted into a string code which can be sorted and compared, i.e., the geo-hash code of the region is obtained, and a geo-hash code map is drawn by using drawing software (such as a high-grade map API).
And (3.2) converting the longitude and latitude of the shared bicycle into a Geohash code, and recording the storage amount of the shared bicycle, wherein the specific process comprises the steps of establishing a plane rectangular coordinate system as a distance coordinate system of the shared bicycle according to a Geohash code diagram, manufacturing a point line diagram, and obtaining the distance between areas according to the distance between points (the distance between the areas can be used in the dispatching distance in the greedy algorithm optimization index). According to the order information of the shared bicycle, the latitude and longitude of each order information is converted into a Geohash code (the Geohash code is that the latitude and longitude information of a region is converted into a character string code which can be sequenced and compared), and the bicycle storage at each position is recorded according to the bicycle lock, namely the bicycle storage at each position is recorded according to the bicycle lock
The LOCK _ STAUS represents a single-vehicle LOCK-unlocking record, 0 is unlocking, 1 is locking, inflow represents area stock, inflow-1 represents that a shared single vehicle leaves the area because of unlocking, the area stock is-1, and inflow +1 represents that the shared single vehicle stays in the area because of locking, and the area stock is + 1.
The division of the area is that the longitude and latitude conversion is based on the dichotomy idea, namely, the earth dimension interval is divided into two intervals, the left interval is 0, the right interval is 1, and the division is continuously carried out according to the precision requirement. Dividing the earth dimension interval of-90, 90 to obtain two intervals of-90, 0 and 0,90, wherein the left interval of-90, 0 is 0 and the right interval of 0,90 is 1, and obtaining table 1.
Table 1 partitioning a region into regions using a Geohash algorithm
| bit | min | mid | max |
| 1 | -90 | 0 | 90 |
| 0 | 0 | 45 | 90 |
| 1 | 0 | 22.5 | 45 |
| 1 | 22.5 | 33.75 | 45 |
| … | … | … | … |
And 4, step 4: the shared bicycle data are classified by using a DBSCAN clustering algorithm, the shared bicycle data can be classified into three types of core points, boundary points and noise points according to clustering results, the core points are areas with large shared bicycle usage, the noise points are areas with small usage, the shared bicycle usage of the noise points is between the core points and the noise points, and the clustering results provide scheduling objects for implementing the greedy algorithm.
The DBSCAN clustering algorithm of the invention utilizes numpy, random and math libraries in Python and refers to data set databases packaged in sklearn to implement the DBSCAN clustering algorithm, and the specific process is as follows:
(4.1) calculating the Euclidean distance between two groups of shared bicycle data in the set area:
setting data in the shared bicycle gathering area as two tuples, and calculating the Euclidean distance between the data in the two tuples:
wherein d is the Euclidean distance between data in two tuples; x is the number of1Longitude, y, for a set of shared bicycle data in the first tuple1Latitude of a group of shared bicycle data in the first tuple; x is the number of2Longitude for a set of shared bicycle data within the second tuple; y is2The latitude of a set of shared bicycle data within the second tuple.
(4.2) selecting a radius parameter r and a neighborhood density threshold minPts of a DBSCAN clustering algorithm, and clustering by utilizing Python coding:
and (2) taking a data set packaged in the sklern as a parameter by utilizing Python coding, combining the number of Euclidean distance calculation points obtained in the step (1), constructing two lists by utilizing Python, putting accessed points into one list, putting points which are not accessed into the other list, and performing traversal processing on a row with the radius r and the neighborhood density threshold value minPts. If there are more points on the list that have not been accessed, the traversal process continues until the list reaches an empty set. If there is no access point, randomly selecting a no access point, if the number of objects in the neighborhood of the point is larger than a specified threshold, indicating that the point is a core object, adding the accessed points to the points in the neighborhood of the point, removing the no access points, finding out the core objects of the points, and placing the core objects in a list, which is called core point; putting the remaining points in the neighborhood into a list, called boundary points; the other points are placed in a list called noise points, i.e. the data is classified into three categories, core points, boundary points and noise points.
(4.3) evaluating the rationality of the DBSCAN clustering algorithm:
the invention refers to the contour coefficient for evaluation, and the evaluation is carried out by using the following formula:
wherein, a (i) is the average distance from the sample i to other samples in the same cluster, b (i) is the average distance from the sample i to all samples in some other cluster, and s (i) is the rationality value of the clustering result, and if s (i) is closer to 1, the more rational the clustering of the sample i is. Generally, it is reasonable to cluster s (i) greater than 0.85.
If the DBSCAN cluster is reasonable, ending; and unreasonable, selecting a new radius r and a neighborhood density threshold value minPts, and repeating the steps. The radius r is typically of the order of ± 10 from the calculated euclidean distance mean.
And 5: the optimal substructure of the greedy algorithm is selected by utilizing the greedy algorithm and combining the prior data to obtain a local optimal scheduling scheme, and the specific process is as follows:
(5.1) acquiring the gathering area and the flow rate of the shared bicycle:
and substituting the shared bicycle data of each type of clusters in the DBSCAN clustering algorithm into Python, obtaining the area and the central longitude and latitude of each shared bicycle aggregation area by using the Python, and numbering each shared bicycle aggregation area. In this embodiment, order data is extracted from order data time, and specific statistics of the flow rate of the shared vehicles in the area is completed, that is, the flow rate of the shared vehicle in the area where the shared vehicles are gathered at different times in a certain range is counted.
(5.2) determining an optimization index when the shared bicycle is dispatched:
when the method for dispatching the shared bicycle is used for solving the connection problem, the cost is considered, and the specific weighing factors of dispatching comprise: the usage rate of the shared bicycle after scheduling; scheduling cost in the scheduling process; scheduling the number of the shared bicycles; and dispatching the number of the shared bicycle. The optimization indexes of the shared bicycle scheduling method are as follows:
the optimization index is min (1-global single vehicle utilization rate) + scheduling cost
Min (1-global bicycle utilization) + min (number of dispatching bicycles)
+ min (number of dispatching bicycles) + min (distance dispatching bicycle)
(5.3) selecting an optimal substructure, and using Python coding to realize a greedy algorithm:
the invention compares the number of the contained single vehicles and the single vehicle flow of each shared single vehicle gathering area by utilizing Python codes, and calculates the difference value of the single vehicle flow of each gathering area minus the number of the contained shared single vehicles. The formula is as follows:
n＝flow-amount
and n is a difference value, flow is the flow of the shared bicycles in one aggregation area, and amount is the number of the shared bicycles in one aggregation area.
And constructing two lists by utilizing Python, and putting the two lists according to the positive and negative properties of the obtained difference value n, namely putting a positive value in the difference value n into one list, putting a negative value in the difference value n into the other list, and if the value is 0, not considering the putting into the list. And maximizing the optimized value of the optimization index to be used as an optimal substructure of the greedy algorithm. Randomly selecting one from the list for storing positive values as an initial target, and selecting data from the list for storing negative values to enable the sum of the positive values and the negative values to be close to 0, wherein the selection number of the negative values can be selected more. And sequentially proceeding downwards until the lists for storing positive values all finish scheduling, and obtaining a local optimal solution, namely an optimal scheduling scheme.
And verifying the effectiveness of the obtained scheduling scheme by using analog modeling, wherein the specific process is as follows:
1) inputting the longitude and latitude of a subway station, and establishing a model according to data:
in this embodiment, two models before and after the optimization of the subway station are constructed, one model is a control group model, and the other model is an experimental group model. Firstly, finding a research area by using an electronic map GIS (geographic information system) of the analog, inputting the longitude and latitude of subway stations of the research area into the electronic map GIS, and setting the number of people flowing out of each station per hour as the average value of the number of people using a sharing bicycle to plug in each station per hour. A shared bicycle gathering area is set up according to the data near each station. At this point, the preliminary model building of the two models is completed. On the basis of the preliminary model, maintaining an original scheduling scheme for shared single vehicles in a research area in a group model; and dispatching the shared single vehicles in the research area in the experimental group model according to the result obtained by the greedy algorithm.
2) And running a control group model and an experimental group model, comparing the number of people staying in the two groups of stations, and verifying the rationality and effectiveness of the scheduling scheme.
TABLE 2 comparison of results after model run
After 24 hours of operation, the amount of retained pedestrians at the station is compared. If the number of detained people at each site of the experimental group model is reduced by more than 15 percent compared with that of the control group model, the scheduling scheme is reasonable and effective, and the process is finished; if the reduction is not realized or the reduction degree is not 15%, the scheduling scheme is unreasonable and ineffective, and the greedy algorithm step 5 is returned. The result of the model operation is shown in table 2, and the rationality and effectiveness of the scheduling scheme of the present invention can be seen from table 2.
Claims (5)
1. A dispatching method for subway transfer shared bicycle in peak period is characterized by comprising the following steps:
(1) crawling subway station data in the targeted area on a hectogram application program by utilizing a Python crawler;
(2) the method comprises the steps that shared bicycle data in a targeted area are crawled by a Python crawler and a related website, and data cleaning and data analysis are conducted on the shared bicycle data;
(3) dividing the regions into regions by using a Geohash algorithm, establishing a coordinate system, and obtaining the distance between the regions through coordinates in the coordinate system;
(4) the shared bicycle data are classified by using a DBSCAN clustering algorithm, the shared bicycle data can be divided into three types of core points, boundary points and noise points according to a clustering result, the core points are areas with large usage of the shared bicycle, the noise points are areas with small usage, the usage of the shared bicycle of the noise points is between the core points and the noise points, and the clustering result provides a scheduling object for implementing the greedy algorithm;
(5) and selecting an optimal substructure by using a greedy algorithm and combining the regional distance data provided by the Geohash algorithm and the scheduling object data provided by the DBSCAN clustering algorithm to obtain a local optimal scheduling scheme.
2. The method for dispatching the subway docking sharing single vehicle in the rush hour according to claim 1, wherein said step (1) is implemented as follows:
the method comprises the steps of establishing a Baidu map application from a Baidu map open platform by utilizing a Python crawler, applying for a signaling AK, opening a POI module of an API (application program interface), selecting a retrieval mode, setting a retrieval city, retrieving a keyword subway, substituting an obtained URL (uniform resource locator) and the Baidu signaling AK into the Python, and utilizing Python coding to obtain required data.
3. The method for dispatching the subway docking sharing single vehicle during the rush hour according to claim 1, wherein said step (3) comprises the steps of:
(31) obtaining a region Geohash code according to the geographical position information; obtaining a regional Geohash code by utilizing a Geohash six-bit code and setting precision;
(32) according to the Geohash code graph, establishing a plane rectangular coordinate system as a distance coordinate system, making a point line graph, and obtaining the distance of a corresponding area according to the distance between points; converting the longitude and latitude of the shared bicycle order information into a Geohash code, and recording the bicycle stock at each position according to the bicycle lock opening and closing:
wherein, LOCK _ STAUS represents the locking and unlocking record of the bicycle, 0 is unlocking, 1 is locking, and underflow represents the regional stock; inflow-1 represents the regional inventory-1; inflow +1 represents the zone inventory + 1.
4. The method for dispatching the subway docking sharing single vehicle during the rush hour according to claim 1, wherein said step (4) comprises the steps of:
(41) calculating Euclidean distance between data in the set area:
setting data in the shared bicycle gathering area as two tuples, and calculating the Euclidean distance between the data in the two tuples:
where d is the Euclidean distance between the data in two tuples, x1Longitude, y, for a set of shared bicycle data in the first tuple1Latitude of a group of shared bicycle data in the first tuple; x is the number of2Longitude for a set of shared bicycle data within the second tuple; y is2A latitude for a set of shared bicycle data within the second tuple;
(42) selecting a radius parameter r and a neighborhood density threshold minPts, and utilizing Python coding to realize clustering:
using Python coding to take a data set packaged in sklern as a parameter, setting two lists by combining the number of the obtained Euclidean distance calculation points, putting the accessed points into one list, putting the points which are not accessed into the other list, and selecting a proper radius r and a neighborhood density threshold Eps for traversal processing; if the list for storing the points which are not accessed yet has points, the traversal processing is continued until the list reaches an empty set; if there is no access point, randomly selecting a no access point, if the number of objects in the neighborhood of the point is larger than a specified threshold, indicating that the point is a core object, adding the accessed points to the points in the neighborhood of the point, removing the no access points, finding out the core objects of the points, and placing the core objects in a list, which is called core point; putting the remaining points in the neighborhood into a list, called boundary points; the other points are placed in a list called noise points;
(43) evaluation with reference to the contour coefficients yields the following formula:
wherein a (i) is the average distance from the sample i to other samples in the same cluster, b (i) is the average distance from the sample i to some other cluster CjIf s (i) is close to 1, the average distance of all samples in (1) indicates that the sample i is reasonably clustered; if the clustering is reasonable, ending; and unreasonable, selecting a new radius r and a neighborhood density threshold Eps, and repeating the steps.
5. The method for dispatching of the rush hour subway docking sharing bicycle according to claim 1, wherein said step (5) comprises the steps of:
(51) acquiring a shared bicycle gathering area and flow:
substituting the shared bicycle data of each type of clusters of the DBSCAN clustering algorithm into Python, obtaining the area and the central longitude and latitude of each bicycle aggregation area by using the Python, and numbering each shared bicycle aggregation area; time extraction is carried out on order data, and specific regional flow statistics is completed, namely the flow of different times in a certain range is counted;
(52) determining an optimization index:
the optimization index is min (1-global single vehicle utilization rate) + scheduling cost
Min (1-global bicycle usage) + min (number of scheduled bicycles) + min (scheduled bicycle distance)
(53) Selecting an optimal substructure, and implementing a greedy algorithm by using Python coding:
comparing the number of the contained bicycles and the bicycle flow of each shared bicycle aggregation area by utilizing Python codes, calculating the value of subtracting the number of the contained shared bicycles from the bicycle flow of each aggregation area, and putting the value into two lists according to the positive and negative of the obtained value, wherein if the value is 0, the value can not be considered; maximizing the optimization index to be used as an optimal substructure of a greedy algorithm; randomly selecting one from the list for storing positive values as an initial target, and selecting data from the list for storing negative values to enable the sum of the positive values and the negative values to be close to 0, wherein the selected number of the negative values can be selected more; and sequentially proceeding downwards until the lists for storing positive values all finish scheduling, and obtaining a local optimal solution.
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