CN112862269A - Efficient optimal scheduling algorithm for shore bridge - Google Patents

Efficient optimal scheduling algorithm for shore bridge Download PDF

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CN112862269A
CN112862269A CN202110078142.XA CN202110078142A CN112862269A CN 112862269 A CN112862269 A CN 112862269A CN 202110078142 A CN202110078142 A CN 202110078142A CN 112862269 A CN112862269 A CN 112862269A
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孙未未
高�熙
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Abstract

The invention belongs to the technical field of port container scheduling, and particularly relates to an efficient optimal scheduling algorithm for a shore bridge. The algorithm of the invention specifically comprises two stages: a pretreatment stage: counting the container amount to be loaded and unloaded of each berth of the ship, solving the lower bound of the average workload and the lower bound of the workload of the key operation path of the problem, and taking a larger value as the completion time; a scheduling scheme calculation stage: and obtaining a scheduling scheme within linear time complexity by using the calculated completion time. Other existing algorithms cannot calculate optimal scheduling for large-scale traffic within a feasible time and have to find near-optimal scheduling instead. The invention can calculate the optimal scheduling in the linear time complexity, and is obviously superior to the prior method in the quality and the efficiency of the solution.

Description

Efficient optimal scheduling algorithm for shore bridge
Technical Field
The invention belongs to the technical field of port container scheduling, and particularly relates to an optimal scheduling algorithm for a shore bridge.
Background
Quayside container bridge cranes (Quay cranes, called quayside bridges, bridge cranes or bridge cranes for short) are specialized equipment which are arranged on the shore of a container terminal and used for loading and unloading container ships, are the most important container loading and unloading equipment on the container terminal, and the operation capacity of the quayside container bridge cranes determines the container handling capacity of the terminal. Therefore, the Quay bridge Scheduling Problem (QCSP: Quay bridge Scheduling Problem) is one of the most core Scheduling problems in a container terminal. After the ship is landed, each Bay (Bay) is provided with a plurality of containers to be unloaded, and a plurality of shore bridges are required to be distributed to the Bay for operation. The shore bridge is large in size, the requirement of the minimum safety distance is met between two shore bridges, and the scheduling problem of the shore bridge refers to scheduling of the shore bridge, so that all the shore bridges can efficiently operate while the safety distance is kept. Although the shore bridge scheduling problem is significant, it has not been well solved due to its complexity and large scale. If the distance is far enough to ensure the safety when the shore bridge works, the utilization rate of the shore bridge is low, so that the overall working efficiency is low; if the shore bridge is operated as close as possible, the operation of one shore bridge is not completed, which may cause a series of shore bridges to be unable to move due to the limitation of safety distance, and the shore bridge is idle.
Disclosure of Invention
The invention aims to provide an efficient optimal scheduling algorithm for a shore bridge.
The invention provides an efficient optimal scheduling algorithm for a shore bridge, which can schedule the shore bridge within linear time complexity, and provides a shore bridge scheduling algorithm which meets the requirements of minimum completion time and 0 idle time and realizes optimal scheduling.
In the present invention, two lower bounds of completion time are set: the lower bound of the average workload and the lower bound of the workload of the key operation path are as follows:
the lower bound of the average workload is defined as the total container volume divided by the number of shore bridges:
Figure BDA0002908275430000011
the lower bound of the workload of the key operation path is defined as the workload of the key operation path, and the key operation path is defined as: d continuous shellfishes with the largest sum of the workload of the d continuous shellfishes, namely the lower bound of the workload of the key operation path:
Figure BDA0002908275430000012
Figure BDA0002908275430000013
t0the time required for loading and unloading a single container for a single shore bridge, b is the number of berths, q is the number of shore bridges, d is the lower bound of the distance between the shore bridges, p1,p2,…,pbThe total number of containers that need to be handled for each bay.
Any scheduled completion time is not lower than these two lower bounds, i.e., there is a lower bound max (δ, ε) for the completion time.
The invention constructs the completion time equal to the lower bound t in the linear timesThe scheduling scheme of (1); the specific steps are divided into two steps.
A pretreatment stage: solving the lower bound of the average workload and the lower bound of the workload of the key operation path, and taking a larger value as the completion time; wherein:
(1) generally, before a ship is stopped, the following data can be derived from its berthing plan: the number b of the shellfishes, the number q of the shore bridges, the lower limit d of the distance between the shore bridges, and the total amount p of containers to be loaded and unloaded by each shellfishes1,p2,…,pbTime t required for loading and unloading single container by single shore bridge0；
(2) In order to facilitate the efficient calculation of the lower bound of the average workload and the lower bound of the workload of the key operation path, the prefix sum is calculated first
Figure BDA0002908275430000021
Initializing sigma00 and using recursive sigmak＝σk-1+pkCalculating sigmak(ii) a After the prefix sum is obtained, according to the lower bound of the average workload and the lower bound of the workload of the key operation path, the following definitions can be obtained:
Figure BDA0002908275430000022
ε＝t0·max{(σk+d-σk) I 0 is less than or equal to k is less than or equal to b-d, and the larger value t issMax (δ, ε) is the completion time of the final schedule; according to the analysis, when the completion time is tsThen, the scheduling completion time obtains the minimum value and the shore bridge idle time is 0;
(II) a scheduling scheme calculation stage: and constructing the scheduling scheme within linear time complexity by using the calculated completion time. The specific scheduling scheme is as follows: numbering the containers from small to large according to the belonged shellfish positions, and recording
Figure BDA0002908275430000023
Allocating the 1 st to s th containers to the 1 st shore bridge, allocating the s +1 st to 2s th containers to the 2 nd shore bridge, allocating the 2s +1 st to 3s th containers to the 3 rd shore bridge, … …, and repeating the steps until the containers are allocated, and operating according to the sequence of the belonged positions of the containers from small to large after each shore bridge is allocated with tasks.
The time complexity of constructing the scheduling scheme according to the above method is
Figure BDA0002908275430000024
The time complexity can be optimized to o (b) using the following method: definition of
Figure BDA0002908275430000025
To pair
Figure BDA0002908275430000026
Assign g (σ) thi) The shore bridge goes to the berth i to finish sigmaiAfter the loading and unloading tasks of the% s containers, the system continues to operate at the berths i +1, i +2 and … until no containers are subsequently loaded or loaded by other shore bridges.
Here, the symbols:
Figure BDA0002908275430000027
denotes a rounding up operation,% denotes a modulo operation.
The invention has the positive effects that:
(1) the scheduling scheme obtained by the invention enables the completion time to be minimum: the completion time of the shore bridge scheduling scheme obtained through calculation reaches the lower theoretical limit, and the completion time cannot be lower. When the container is loaded and unloaded, the loading and unloading can be finished most quickly by using the shore bridge scheduling scheme obtained by the invention, so that the wharf throughput is improved;
(2) the invention has the highest calculation efficiency: the theoretical time complexity of the algorithm is O (b), the scale of the input data is O (b), and theoretically, an algorithm with lower time complexity cannot be obtained. On a common PC, the time for calculating the optimal shore bridge scheduling for the current largest container ship by using the method provided by the invention is about 8 multiplied by 10-8And second. If the wharf software system adopts the method, the time overhead of the quay crane scheduling problem can be ignored, and the usability of the wharf software system is improved.
Drawings
Fig. 1 is a plan view of a ship when it is landed.
Fig. 2 is a specific example of the scheduling of a ship using the present algorithm.
Detailed Description
Fig. 1 is a plan view of a ship when it is landed. Wherein, each berth of the ship has a plurality of containers to be unloaded, and the berth b and the number p of the containers to be unloaded of each berth can be counted through a schedule1,p2,…,pbAnd setting a safe distance lower bound d and the number q of the shore bridges according to the requirements of the wharf. The shore bridge is not operated at all times and can be in an idle state.
Fig. 2 is a specific example of the scheduling of a ship using the present algorithm. Wherein the abscissa represents the shelve, and the numerical value on the abscissa is the number of the containers to be loaded and unloaded corresponding to the shelve. The ordinate represents time, a continuous rectangle with the same color represents a shore bridge operation process, the longitudinal range of the rectangle is an operation time interval, the abscissa represents the working decibel, and the numerical value in the rectangle represents the container quantity of the operation.
The algorithm flow of the present invention is further described below in conjunction with fig. 2.
A pretreatment stage:
(1) the number b of the shellfishes is 29, the number q of the shore bridges is 9, the lower boundary d of the distance between the shore bridges is 2, the total amount of containers to be loaded and unloaded by each shellfishes is 410,34,377,331,107,459,395,44,148,213,252,201,54,336,233,114,495,236,113,302,193,440,404,53,95,516,104,395 and 95 in sequence, and the time t required by a single shore bridge to load and unload a single container03 (min).
(2) Initializing sigma00 and using recursive sigmak＝σk-1+pkCalculating sigmak0,410,444,821,1152,1259,1718,2113,2157,2305,2518,2770,2971,3025,3361,3594,3708,4203,4439,4552,4854,5047,5487,5891,5944,6039,6555,6659,7054,7149 (numbered starting from 0) was obtained. According toThe lower bound of the average workload and the lower bound of the workload of the key operation path are defined, and can be obtained as follows:
Figure BDA0002908275430000031
ε＝t0·max{(σk+d-σk) L 0 ≦ k ≦ b-d ═ 2562 (minutes);
make it greater by tsMax (δ, ε) 2562 (minutes) 42.7 (hours) is the final scheduled completion time.
(II) a scheduling scheme calculation stage:
(1)s＝ts/t0＝864；
(2) firstly, intuitively know the dispatching scheme, the 1 st to s th containers are allocated to the 1 st shore bridge, the s +1 st to 2s containers are allocated to the 2 nd shore bridge, the 2s +1 st to 3s containers are allocated to the 3 rd shore bridge, … … and the like. As shown in fig. 2, 410 containers of the 1 st bunk, 34 containers of the 2 nd bunk, 377 containers of the 3 rd bunk, and 33 containers of the 4 th bunk are allocated to the first shore bridge, and the following shore bridges are analogized in sequence.
(3) In the actual calculation, g (σ)i) 0,1,1,1,2,2,3,3,3,3, 4,4,4,5,5,5,6,6,6,6,7,7,7,8,8,8,9,9 (numbering starting from 0). g (sigma)0)+1＝g(σ1) Therefore, the 1 st quay crane is assigned to the 1 st berth and needs to complete g (σ)1) % s is 410 containers; g (sigma)3)+1＝g(σ4) Therefore, the 2 nd quay crane is assigned to the 4 th berth and needs to complete g (σ)4) 298 containers; … …, the following shore bridge, and so on. Finally, exactly 9 landbridges are allocated. And (4) each shore bridge finishes the distribution of the shore bridges in sequence and then records the containers of the subsequent shore bridges.
The resulting protocol is shown in FIG. 2. In the figure, the front 8 quay bridges finish all work just at 42.7 hours from the beginning of the work, the 9 th quay bridge finishes in advance, and the completion time of the scheduling scheme achieves the lower bound of 42.7 hours. The above calculation process is implemented in a computer by a plurality of loop statements with time complexity of O (b),the theoretical minimum value is obtained, and the actual running time is 2 multiplied by 10-8And second. This example demonstrates the optimality and efficiency of the invention.

Claims (1)

1. An efficient optimal scheduling algorithm for a shore bridge sets two lower bounds of completion time: the lower bound of the average workload and the lower bound of the workload of the key operation path are as follows:
the lower bound of the average workload is defined as the total container volume divided by the number of shore bridges:
Figure FDA0002908275420000011
the lower bound of the workload of the key operation path is defined as the workload of the key operation path, and the key operation path is defined as: d continuous shellfishes with the largest sum of the workload of the d continuous shellfishes, namely the lower bound of the workload of the key operation path:
Figure FDA0002908275420000012
Figure FDA0002908275420000013
t0the time required for loading and unloading a single container for a single shore bridge, b is the number of berths, q is the number of shore bridges, d is the lower bound of the distance between the shore bridges, p1,p2,…,pbThe total amount of containers to be loaded and unloaded for each bay;
the completion time of any scheduling is not lower than the two lower bounds, namely the completion time has a lower bound max (delta, epsilon);
characterised in that the completion time is constructed in linear time to be equal to the lower bound tsThe scheduling scheme of (1); the method is specifically divided into two stages:
a pretreatment stage: solving the lower bound of the average workload and the lower bound of the workload of the key operation path, and taking a larger value as the completion time; wherein:
(1) before the vessel stops, the following data are obtained from its berthing plan: the number b of the shellfishes, the number q of the shore bridges, the lower limit d of the distance between the shore bridges, and the total amount p of containers to be loaded and unloaded by each shellfishes1,p2,…,pbTime t required for loading and unloading single container by single shore bridge0；
(2) In order to facilitate the efficient calculation of the lower bound of the average workload and the lower bound of the workload of the key operation path, the prefix sum is calculated first
Figure FDA0002908275420000014
Initializing sigma00 and using recursive sigmak＝σk-1+pkCalculating sigmak(ii) a After the prefix sum is obtained, according to the definition of the lower bound of the average workload and the lower bound of the workload of the key operation path, obtaining:
Figure FDA0002908275420000015
ε＝t0·max{(σk+d-σk) I 0 is less than or equal to k is less than or equal to b-d, and the larger value t issMax (δ, ε) is the completion time of the final schedule; when the completion time is tsThen, the scheduling completion time obtains the minimum value and the shore bridge idle time is 0;
(II) a scheduling scheme calculation stage: constructing a scheduling scheme within linear time complexity by using the calculated completion time; the specific process is as follows: numbering the containers from small to large according to the belonged shellfish positions, and recording
Figure FDA0002908275420000016
Allocating 1-s containers to a 1 st shore bridge, allocating s + 1-2 s containers to a 2 nd shore bridge, allocating 2s + 1-3 s containers to a 3 rd shore bridge, … …, and repeating until the containers are allocated, and operating according to the sequence of the belonged positions of the containers from small to large after each shore bridge is allocated with tasks;
definition of
Figure FDA0002908275420000021
To pair
Figure FDA0002908275420000022
st.g(σi-1)+1＝g(σi) Assign g (σ) thi) The shore bridge goes to the berth i to finish sigmaiAfter the loading and unloading tasks of the% s containers, the containers continue to go to the berths i +1, i +2 and … for operation until no container task is subsequently performed or the containers are completed by other shore bridges;
symbol:
Figure FDA0002908275420000023
denotes a rounding up operation,% denotes a modulo operation.
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