CN112232587B

CN112232587B - Combination optimization method and system based on improved Skyline algorithm

Info

Publication number: CN112232587B
Application number: CN202011181387.7A
Authority: CN
Inventors: 张楠; 姜鑫; 母瑛; 佘平
Original assignee: CETC 32 Research Institute
Current assignee: CETC 32 Research Institute
Priority date: 2020-10-29
Filing date: 2020-10-29
Publication date: 2023-08-11
Anticipated expiration: 2040-10-29
Also published as: CN112232587A

Abstract

The application provides a combination optimization method and a combination optimization system based on an improved Skyline algorithm, wherein the method comprises the following steps: step M1: selecting the goods with the largest side length, the largest area or the largest perimeter in all the goods to be loaded as first goods respectively; step M2: according to skyline scoring rules, three articles are selected and placed in the box, waste space is calculated respectively, and the selected waste space is minimum; step M3: selecting a lowest-height skyline, judging whether a waste space exists according to a skyline scoring rule, and setting a generating function according to the current waste space when the waste space exists; step M4: selecting the goods with the largest generating function as the next goods and placing the next goods into a box, and repeatedly executing the steps M3 to M4 until any one of the goods cannot be placed; step M5: and (3) lifting the space-wasting astronomical line to a height which is flush with the space-wasting astronomical line with lower heights at the left side and the right side of the space-wasting astronomical line, combining the space-wasting astronomical line with the space-wasting astronomical line, and repeatedly executing the steps M3 to M5 until the boxing is completed. The application can improve the boxing rate.

Description

Combination optimization method and system based on improved Skyline algorithm

Technical Field

The application relates to optimized scheduling, in particular to a combined optimization method and system based on an improved Skyline algorithm, and more particularly relates to an improvement of the Skyline algorithm based on reinforcement learning.

Background

The boxing problem is a typical combinatorial optimization problem, namely how to provide more services with limited resources, achieving more value. Many problems in real life can be abstracted into boxing problems, such as how goods are loaded into trucks in the transportation industry to reduce transportation cost; how to cut cloth in the clothing industry to reduce cloth waste; how to cut glass to reduce glass splinters in the glass manufacturing industry; even in the cloud computing industry, how to configure computers meets the storage and computing requirements of a data center at minimal cost. These problems can be solved by abstracting them into a boxing problem.

The boxing problem is classified into a one-dimensional problem, a two-dimensional problem and a three-dimensional problem, wherein the two-dimensional boxing problem has proven to be an NP-hard problem. Three types of approaches to solving the NP-hard problem exist: exact algorithms, approximate algorithms, and heuristic algorithms. The accurate algorithm aims to find the optimal solution of the problem, and most of the accurate algorithm adopts a technical route of exhaustion and pruning, so that a solution can be found under the condition of small data volume, but very long calculation time is required under the condition of large data volume, and the expansion is difficult. The approximation algorithm does not guarantee that the optimal solution is found, and the time complexity is polynomial-level compared with the precise algorithm, so that the method has a great advantage in calculation time. The heuristic algorithm generally gives a feasible solution under the conditions of acceptable calculation time and calculation resources, and then optimizes the solution continuously through a certain rule, and common heuristic algorithms include genetic algorithm, simulated goods returning algorithm and the like.

The heuristic algorithm skyline mainly aims at the two-dimensional boxing problem, the idea of reinforcement learning is introduced, the scoring mechanism of the skyline is optimized, and meanwhile, the problem that a first article in the skyline algorithm is difficult to determine and is cold to start is solved, so that the boxing efficiency of the skyline algorithm is improved. In the large-scale boxing problem, the algorithm still has a good calculation effect.

Patent document CN109272135a (application number: 201710586358.0) discloses a method for boxing articles, which can determine a boxing algorithm corresponding to the number of articles to be boxed according to the number of articles to be boxed, and if the number of articles is large, the time complexity of the determined boxing algorithm is low, so that the execution efficiency of the boxing algorithm is improved. In addition, the method can obtain the specification information of the pre-stored articles, and the package boxes capable of containing all the articles and the articles contained in each package box can be obtained by inputting the specification information into a boxing algorithm. And the boxing algorithm can meet preset boxing conditions in the solving process, and the boxing conditions can comprise any one or more of the minimum number of parcel boxes, the minimum specification of parcel boxes and the nearest picking path of articles in the same parcel box, so that any one or more of the maximum utilization of the parcel box space, the minimum cost of the parcel boxes and the minimum picking path of articles are achieved.

The patent document CN109272135a mainly adopts a non-passing packing algorithm according to the number of cargoes to be loaded, so as to realize a more efficient algorithm under the condition that the cargoes are many, thereby reducing the running time of the algorithm. The application mainly provides a solution to solve the problem of cold start according to the problem of skyline, introduces the idea of reinforcement learning, and optimizes the original cargo scoring mechanism by using a new generating function to select the next cargo more suitable to be put into a box.

Patent document CN106648834a (application number: 201611205454.8) discloses a virtual machine scheduling method based on a batch packing problem, the method includes the steps that a virtual machine scheduler periodically receives new virtual machine requests submitted by users, and simultaneously collects state information of virtual machines running on each physical machine in a system, wherein the information of the virtual machines running on each physical machine in the system is about to finish running, the virtual machine scheduler adjusts for each new set of virtual machine requests by adopting a batch packing algorithm, a difference between a new virtual machine and a corresponding relation table before and after the virtual machine scheduler is scheduled by the virtual machine scheduler comparison algorithm is obtained, migration instructions are formulated and sent to a designated physical machine, and the related physical machines complete virtual machine migration according to the instructions. Compared with the prior art, the method of the application closes the idle server to reduce the energy consumption, and simultaneously effectively reduces the migration times of the virtual machine and improves the distribution efficiency.

The patent document CN106648834a mainly abstracts the scheduling problem of the virtual machine in the cloud computing environment into the boxing problem for processing, and utilizes the scheduler to more reasonably allocate the resources of the physical server through the analysis of the state of the virtual machine, mainly utilizes the idea of the boxing algorithm to solve the problem in production, and aims at not optimizing the boxing algorithm. The application is mainly an improvement and optimization of the packing idea.

In view of the above-mentioned drawbacks of the prior art, the technical problem to be solved by the present application is embodied in the following points:

1) The problem of cold start in the skyline algorithm is solved;

2) Under the condition of various specifications of the articles, the boxing rate is improved;

3) The speed of the large-scale boxing problem is improved.

Disclosure of Invention

Aiming at the defects in the prior art, the application aims to provide a combination optimization method and a combination optimization system based on an improved Skyline algorithm.

The combination optimization method based on the improved Skyline algorithm provided by the application comprises the following steps:

step M1: three cargoes with the largest side length, the largest area or the largest perimeter in all cargoes to be loaded are selected to be respectively placed into the box as first cargoes;

step M2: according to skyline scoring rules, three articles are selected and placed in the box, waste spaces after four cargoes are placed in the box are calculated respectively, and the placement rule of the first four cargoes with the smallest waste space is selected as the whole boxing strategy;

step M3: selecting a lowest-height skyline, judging whether a waste space exists according to a skyline scoring rule, and setting a generating function according to the current waste space when the waste space exists;

step M4: selecting the goods with the largest generating function as the next selected goods, placing the goods into a box, and repeatedly executing the steps M3 to M4 until the space is wasted and any one of the goods can not be placed;

step M5: and (3) lifting the space-wasting astronomical line to a height which is flush with the astronomical line with lower height on the left side and the right side of the space-wasting astronomical line, combining the space-wasting astronomical line with the space-wasting astronomical line, and repeatedly executing the steps M3 to M5 until the boxing is completed.

Preferably, the step M1 includes:

step M1.1: counting the length and width of all cargoes to be loaded, and calculating the area and perimeter of each cargoes according to the length and width;

step M1.2: and respectively finding out three cargoes with the maximum side length, the maximum area or the maximum circumference, and respectively putting the cargoes into the box as the first cargoes.

Preferably, the skyline scoring rule in the step M2 includes: generic skyline scoring rules and/or refined skyline scoring rules.

Preferably, the wasted space in the step M2 includes:

wasteS＝w1*min(h1,h2) (1)

wherein, the waste S represents wasted space; w1 represents the width of the wasted space, h1 represents the height of one side of the wasted space, and h2 represents the height of the other side of the wasted space.

Preferably, the step M3 includes:

step M3.1: selecting the lowest-height skyline, scoring all cargoes which are not filled into the box according to a skyline scoring rule, and when the score of each cargoes obtained according to the skyline scoring rule is smaller than a preset value, wasting space exists;

step M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS (2)

wherein F (X) represents a generating function; c1 represents the weight of skyline scoring; c2 represents the weight of wasted space; score represents the score obtained according to the skyline scoring rule; the waste of space is denoted by waste of space.

According to the application, a combination optimization system based on an improved Skyline algorithm comprises:

module M1: three cargoes with the largest side length, the largest area or the largest perimeter in all cargoes to be loaded are selected to be respectively placed into the box as first cargoes;

module M2: according to skyline scoring rules, three articles are selected and placed in the box, waste spaces after four cargoes are placed in the box are calculated respectively, and the placement rule of the first four cargoes with the smallest waste space is selected as the whole boxing strategy;

module M3: selecting a lowest-height skyline, judging whether a waste space exists according to a skyline scoring rule, and setting a generating function according to the current waste space when the waste space exists;

module M4: selecting the goods with the largest generating function as the next selected goods, putting the goods into a box, and repeatedly triggering the execution of the modules M3 to M4 until the space is wasted and any one of the goods can not be put into the box;

module M5: and lifting the space-wasting astronomical line to a height which is flush with the astronomical line with lower height on the left side and the right side of the space-wasting astronomical line, combining the space-wasting astronomical line with the space-wasting astronomical line, and repeatedly triggering the modules M3 to M5 to execute until the boxing is completed.

Preferably, the module M1 comprises:

module M1.1: counting the length and width of all cargoes to be loaded, and calculating the area and perimeter of each cargoes according to the length and width;

module M1.2: and respectively finding out three cargoes with the maximum side length, the maximum area or the maximum circumference, and respectively putting the cargoes into the box as the first cargoes.

Preferably, the skyline scoring rule in the module M2 includes: generic skyline scoring rules and/or refined skyline scoring rules.

Preferably, the wasted space in the module M2 includes:

wasteS＝w1*min(h1,h2) (1)

Preferably, the module M3 comprises:

module M3.1: selecting the lowest-height skyline, scoring all cargoes which are not filled into the box according to a skyline scoring rule, and when the score of each cargoes obtained according to the skyline scoring rule is smaller than a preset value, wasting space exists;

module M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS (2)

Compared with the prior art, the application has the following beneficial effects:

1. the application takes the size of the wasted space as the standard for selecting the next article, which is more beneficial to the full utilization of resources;

2. the application uses the idea of reinforcement learning to select the next 'optimal' goods within the time acceptable range, thereby improving the boxing efficiency;

3. according to the application, the first cargo of skyline is selected through multiple indexes, so that the problem of cold start is solved;

4. the application provides a solution for the boxing of large-scale cargoes.

Drawings

Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:

FIG. 1 is a generic skyline scoring rule;

FIG. 2 is a refinement skyline scoring rule;

FIG. 3 shows the boxing effect display based on the combination optimization method of the application, wherein the boxing rate is 98.882%;

FIG. 4 shows the boxing effect display based on the combination optimization method of the application, and the boxing rate is 94.886%;

FIG. 5 is a diagram of cargo placement parameters;

FIG. 6 is a schematic view of the "astronomical line";

fig. 7 is a schematic diagram of a "astronomical line" merge.

Detailed Description

The present application will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present application, but are not intended to limit the application in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present application.

Example 1

The combination optimization method based on the improved Skyline algorithm provided by the application comprises the following steps: as shown in figures 1-7 of the drawings,

Specifically, the step M1 includes:

Specifically, the skyline scoring rule in the step M2 includes: generic skyline scoring rules and/or refined skyline scoring rules.

Specifically, the wasted space in the step M2 includes:

wasteS＝w1*min(h1,h2) (1)

Specifically, the step M3 includes:

step M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS (2)

Specifically, the module M1 includes:

Specifically, the skyline scoring rule in the module M2 includes: generic skyline scoring rules and/or refined skyline scoring rules.

Specifically, the wasted space in the module M2 includes:

wasteS＝w1*min(h1,h2) (1)

Specifically, the module M3 includes:

module M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS (2)

Example 2

Example 2 is a modification of example 1

The design idea of the Skyline algorithm is to treat the upper edge of the cargo as an independent "astronomical line", and select the lowest astronomical line each time to place the cargo. In the aspect of selecting goods, the skyline scores the goods according to a certain scoring rule, and the goods with the highest scores are selected to be placed. When placing the first piece of goods, fewer conditions can be relied upon, and it is common practice to select the goods with the largest area or perimeter. Two problems of the skyline algorithm can be found, 1. The problem of cold start exists in the goods placed on the first block; 2. the scoring rule is formulated according to the current step, and is easy to sink into local optimum.

Aiming at the problems of the kyline algorithm, the application provides an improvement of the kyline algorithm based on reinforcement learning. The concept of wasting space is introduced, and when each goods is put into the container, the weight sum of the wasted space and the score is used instead of the scoring of skyline, so that the space of fragments can be reduced better, and the boxing efficiency is improved. Meanwhile, the idea of pre-judging according to the current environment in reinforcement learning is introduced, and when one cargo is put into each time, whether the wasted space can be used by smaller cargoes or not is considered, so that the cargoes are selected. When the problem of cold start is solved, goods with the largest area and perimeter and the largest side length are selected respectively for placement, three goods are placed again on the basis of the goods by utilizing an optimized skyline algorithm, and the placement of the optimal first goods is selected according to the size of the wasted space after the placement of the first four goods, so that the problem of cold start is avoided to a certain extent.

The application mainly comprises three optimizing points, namely 1. The selection strategy of the first goods; 2. a selection mechanism of the next goods wasting space is added; 3. and strengthening a fragment space filling mechanism of learning judgment. The respective optimization points are described in detail below.

In the initial stage of the skyline algorithm, since the whole box is empty, the score of almost all the goods is 0 according to the scoring rule of skyline, so that it is difficult to select the most suitable first goods. The method comprises the steps of selecting a largest cargo according to the area, the circumference and the largest side length as indexes, putting three cargoes according to a skyline scoring algorithm, and after four cargoes are put, wasting space is the smallest, namely, the first four cargoes are determined by a placement strategy.

The original skyline scoring strategy only compares the width and the height of the goods with the difference value of the selected astronomical line and the heights of two sides, waste space is introduced as an index, a reinforcement learning mechanism is utilized to design a generating function, namely the weighted sum of the original score and the waste space is used as a final judgment basis, and the space waste is reduced.

After a good is placed, if a new wasted space is created, a search is made among the remaining goods to see if a good can be found that can fill the space, to further reduce wasted space.

The detailed process of optimizing the point 1 is as follows:

1.1 assume that the length and width of the box are L and W, respectively;

1.2, counting the length and width of all cargoes to be loaded, storing an array of arrayLength and arrayWidth, calculating the area and perimeter of each cargoes according to the length and width, and storing an array of arrayArea and arrayC respectively;

1.3, respectively finding three cargoes with the largest side length, area and circumference, and putting the cargoes into a box as the first cargoes.

1.4, selecting three articles to be placed in the box according to skyline scoring rules (see the attached drawing), and selecting a group with the smallest waste space as the placement rules of the first four cargoes of the whole boxing strategy by calculating the waste space after four cargoes are placed.

The detailed procedure for optimizing point 2 is as follows:

2.1 selecting the lowest-height astronomical line, and scoring each cargo according to the scoring rule of the skyline algorithm. It is known from fig. 1 that when the score is less than 8, there is wasted space, i.e., space in the middle of gray goods and white goods.

2.2 the method for calculating the wasted space is as follows:

setting the width between gray goods and white goods as w1, setting the height of the gray goods as h1, and setting the height of the side of the selected astronomical line, which is free, as h2, so that space wastage=w1×min (h 1, h 2) is wasted;

2.3 taking the wasted space as an index for selecting the next cargo, designing and generating functions as follows:

F(X)＝C1*score+C2*wasteS

2.4 selecting the goods with the largest F (X) as the next selected goods by taking F (X) as the final index.

The detailed procedure for the optimization point 3 is as follows:

3.1, when the wasted space appears, selecting a goods which can be put into the wasted space from the rest goods to fill the space;

3.2 repeating the step 3.1 until no wasted space is generated or any goods cannot be put down in the generated wasted space, lifting the space line of the wasted space to be flush with the space line with lower heights on the left side and the right side, and combining the space line of the wasted space with the space line of the wasted space line to facilitate the selection of the next goods.

Example 3

Example 3 is a modification of example 1 and/or example 2

In the case where two-dimensional boxing and three-dimensional boxing problems need to be solved, an optimization system realized according to the application can be utilized to efficiently generate a solution. For example, in the arrangement problem of express boxing, the size of a vehicle is input, the specification of the boxed articles is input, and a boxing strategy can be rapidly given according to the data so as to improve the boxing rate of cargoes.

In the context of cloud computing, it is desirable to provide users with various virtual resources, i.e., to maximize the utilization of data center resources to provide services. The configuration of the existing server can be abstracted into storage, cpu and other dimensional 'articles', and the user demand is abstracted into boxes which need to be filled, so that the resource configuration problem in the cloud computing environment can be solved according to the demand parameters by the method.

In the description of the present application, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present application.

Those skilled in the art will appreciate that the systems, apparatus, and their respective modules provided herein may be implemented entirely by logic programming of method steps such that the systems, apparatus, and their respective modules are implemented as logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc., in addition to the systems, apparatus, and their respective modules being implemented as pure computer readable program code. Therefore, the system, the apparatus, and the respective modules thereof provided by the present application may be regarded as one hardware component, and the modules included therein for implementing various programs may also be regarded as structures within the hardware component; modules for implementing various functions may also be regarded as being either software programs for implementing the methods or structures within hardware components.

The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.

Claims

1. A combinatorial optimization method based on an improved Skyline algorithm, comprising:

step M5: lifting the space-wasting astronomical line to a height which is flush with the astronomical line with lower height on the left side and the right side of the space-wasting astronomical line, combining the space-wasting astronomical line with the space-wasting astronomical line, and repeatedly executing the steps M3 to M5 until the boxing is completed;

the step M1 includes:

step M1.2: finding out three cargoes with the maximum side length, the maximum area or the maximum perimeter respectively, and putting the cargoes into a box as first cargoes respectively;

the skyline scoring rule in the step M2 includes: a general skyline scoring rule and/or a refined skyline scoring rule; step M3 includes:

step M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS(2)

2. The method of claim 1, wherein the step M2 of wasting space comprises:

wasteS＝w1*min(h1,h2)(1)

3. A combinatorial optimization system based on an improved Skyline algorithm, comprising:

module M5: lifting the space-wasting astronomical line to a height which is flush with the astronomical line with lower height on the left side and the right side of the space-wasting astronomical line, combining the space-wasting astronomical line with the space-wasting astronomical line, and repeatedly triggering the modules M3 to M5 to execute until the boxing is completed;

the module M1 includes:

module M1.2: finding out three cargoes with the maximum side length, the maximum area or the maximum perimeter respectively, and putting the cargoes into a box as first cargoes respectively;

the skyline scoring rule in the module M2 includes: a general skyline scoring rule and/or a refined skyline scoring rule;

the module M3 includes:

module M3.2: obtaining a generating function according to the wasted space;

F(X)＝C1*score+C2*wasteS(2)

4. A combination optimization system based on a modified Skyline algorithm according to claim 3, characterized in that the wasted space in the module M2 comprises:

wasteS＝w1*min(h1,h2)(1)