CN113821972A - Multi-robot collaborative assembly line balancing method considering energy efficiency - Google Patents

Multi-robot collaborative assembly line balancing method considering energy efficiency Download PDF

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CN113821972A
CN113821972A CN202110943604.XA CN202110943604A CN113821972A CN 113821972 A CN113821972 A CN 113821972A CN 202110943604 A CN202110943604 A CN 202110943604A CN 113821972 A CN113821972 A CN 113821972A
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靳文瑞
朱雨彤
周炳海
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Abstract

A multi-robot collaborative assembly line balancing method considering energy efficiency is characterized in that a first partial process comprises the following steps: constructing a multi-robot collaborative assembly line balance problem considering energy efficiency, wherein the optimization target comprises the beat of an assembly line, the total energy consumption and the total robot investment cost in the assembly process; and a second part of the process: a multi-objective hybrid empire competition algorithm (MOHICA) is constructed, which includes empire initialization, empire assimilation, LAHC algorithm for local search, empire update, and colonial competition. The invention provides an RALBP multi-objective optimization research of multi-robot cooperative assembly based on energy efficiency, and aims to reduce the total energy consumption of an assembly line and the total input cost of a robot as far as possible while ensuring the beat of the assembly line.

Description

Multi-robot collaborative assembly line balancing method considering energy efficiency
Technical Field
The invention relates to the technical field of assembly line balance.
Background
The assembly line is an important mode for organizing large-scale standardized production, and the improvement of the assembly line efficiency can effectively promote the production and improve the economic benefit. Therefore, the assembly line balance problem has been the focus of attention and research since the past century and the fifties. In recent years, robots are being widely used in assembly lines with the continuous development of robotics and their industries. The application of the robot improves the efficiency and flexibility of the assembly line, improves the quality of products and reduces the cost consumption. However, the same issues arise with robot assembly line balancing; moreover, the robot also consumes a lot of energy during the assembly of the product. Siemens corporation, through statistical data analysis, predicts that there is about 10% energy consumption reduction space for industrial robots widely used in automobile manufacturing, and automobile manufacturing enterprises have 30% energy consumption reduction potential overall in the product manufacturing process. In addition, the cost of the current robot is relatively high. Therefore, how to improve the efficiency of the robot assembly line and how to balance the efficiency of the assembly line, the total energy consumption of the robot and the total input cost of the robot is a problem which needs to be solved urgently.
The Assembly Line Balancing Problem (ALBP) is to distribute each operation element of an assembled product into a workstation as uniformly as possible under the condition of satisfying a certain constraint, and pursue optimization of one or more targets. This problem is essentially a combinatorial optimization problem. However, unlike general combinatorial optimization problems such as the binning problem, the assignment of each task in the assembly line balancing problem must satisfy the Precedence relationship between tasks, i.e., the Precedence order of the assembly lines between tasks.
Along with the increasingly wide application of robot in the assembly field, the assembly efficiency of product has obtained great promotion. However, the robot consumes a lot of energy during the product assembly process, and the cost of the robot is relatively high at present. Therefore, how to seek a balance point between improving the production efficiency, reducing the total energy consumption and reducing the total cost of the robot input becomes a new concern in the field of automatic assembly. In recent years, more and more industries have focused on the balance Problem (RALBP) of robot Assembly Line with energy-saving awareness.
Therefore, the invention provides an RALBP multi-objective optimization research of multi-robot cooperative assembly based on energy efficiency, and aims to reduce the total energy consumption of an assembly line and the total input cost of a robot as much as possible while ensuring the rhythm of the assembly line body.
Disclosure of Invention
The invention aims to overcome the problem that in actual production, a plurality of robots may be required for cooperative assembly in a single station due to the limitation of factory space resources, and a proper balance point is found in the aspects of production efficiency, assembly line total energy consumption and assembly line body total robot input cost.
Technical scheme
A multi-robot collaborative assembly line balancing method considering energy efficiency is characterized by comprising the following steps:
the first part
Constructing a multi-robot collaborative assembly line balance problem considering energy efficiency, wherein the assembly line balance problem is a multi-objective optimization problem, and optimization objectives are the beat of an assembly line, the total energy consumption and the total robot investment cost in the assembly process respectively;
and solving the assembly line balance problem, and acquiring an optimal robot task allocation strategy for assembly operation. As a preferred embodiment, the expression of the objective function is:
MinF＝(f1,f2,f3)
the constraints of the problem include the beat constraint f of the assembly line1Assembly line Total energy consumption constraint f2Total input cost constraint f of assembly line robot3The constraint expressions are respectively:
Figure BDA0003215785410000021
Figure BDA0003215785410000022
Figure BDA0003215785410000023
in the formula, I is a task serial number I (I is 1, 2.. gtoreq.i), j is a task immediately following the task I in the task priority map, S is a station serial number S (S is 1, 2.. gtoreq.s), R is a robot species serial number R (R is 1, 2.. gtoreq.r), n is a robot species serial number R (R is 1, 2.. gtoreq.r), andsthe number of robots at the station s,
Figure BDA0003215785410000024
is the kth of station ssTable robot (from front to back), ks＝1,...N，ti bIs the start time, t, of task ii fThe completion time of the task i, N is the maximum number of distributable robots in the station,
Figure BDA0003215785410000025
is the r-th of station ssThe energy consumption per unit time while the robot is waiting,
Figure BDA0003215785410000026
is the r-th of station ssThe energy consumption per unit time of the robot when performing task i,
Figure BDA0003215785410000027
is the kth of station ssThe time at which the station robot performed task i,
Figure BDA0003215785410000028
for the set of all tasks i assigned to a workstation s,
Figure BDA0003215785410000029
for the set of predecessor tasks of all tasks i assigned to a workstation s,
Figure BDA00032157854100000210
all tasks assigned to the kth robot position of workstation s, pre (i) the set of tasks that are immediately preceding task i,
Figure BDA00032157854100000211
is a sufficiently large integer that the number of the molecules,
Figure BDA00032157854100000212
if at workstation s
Figure BDA00032157854100000213
The location is assigned to task i, then
Figure BDA00032157854100000214
Otherwise
Figure BDA00032157854100000215
If at workstation s
Figure BDA00032157854100000216
The position is assigned to the robot r, then
Figure BDA00032157854100000217
If not, then,
Figure BDA00032157854100000218
zij: in work s, if task i completes earlier than task j, then z ij1, otherwise, zij＝0。
The constraints of the problem further include: ensuring that the number of robots in each station does not exceed the maximum number of robots that can be accommodated by the station; ensuring the priority relationship among various tasks; each task must be assigned to a workstation; each station is assigned to at least one robot; the priority relationship between stations and between tasks in the stations; the range that the number of tasks allocated by each robot should meet; the priority relationship of each task in the workstation.
The number of robots in each station is guaranteed not to exceed the maximum robot number constraint which can be contained in the station:
Figure BDA0003215785410000031
ensuring the priority relation constraint among various tasks:
Figure BDA0003215785410000032
each task must be assigned to a workstation:
Figure BDA0003215785410000033
each workstation is assigned to at least one robot constraint:
Figure BDA0003215785410000034
and (3) priority relation constraint between stations and between tasks in the stations:
Figure BDA0003215785410000035
Figure BDA0003215785410000036
the number of tasks assigned to each robot should satisfy a range constraint:
Figure BDA0003215785410000037
Figure BDA0003215785410000038
and (3) the priority relation constraint of each task in the station:
Figure BDA0003215785410000039
Figure BDA00032157854100000310
Figure BDA00032157854100000311
the variables 0 to 1:
Figure BDA00032157854100000312
Figure BDA00032157854100000313
zip∈{0，1}，i＝1，2，...I，p＝1，2...，P
the second part
The empire competition algorithm is used as a main body, a non-dominated level and crowding distance evaluation strategy is integrated, a delay Hill Climbing algorithm (LAHC) is integrated into a frame of the empire competition algorithm, and a multi-target mixed empire competition algorithm (MOHICA) is constructed. The specific steps of the multi-target hybrid empire competition algorithm comprise empire initialization, empire internal assimilation, LAHC algorithm for local search, empire internal updating, colonial competition and the like.
The multi-target mixed empire competition algorithm specifically comprises the following steps:
for the multi-target problem, the quality of each solution during initialization directly influences the convergence speed of the algorithm and the overall quality of the solution in the Pareto solution set solved finally, so a better coding mode must be selected to strive for higher quality of the solution generated during initialization; the processing process of the multi-target hybrid empire competition algorithm comprises the following steps:
s21: the invention adopts three bar codes for coding, wherein one is a station code based on a station serial number, the second is a task code based on an assembly task, and the third is a robot code based on a robot serial number. The concrete solving steps are as follows:
s211: the station code sequence code randomly generates a repeatable integer sequence with the length of I in ascending order in the interval [1, S ]; the task code sequence is used for generating an assembly task sequence on the basis of the task priority relationship; the robot code sequence is based on the position with length I, 0 and robot serial number are randomly distributed to the positions, at least one position in the position with the same number of station codes is not 0 (namely, at least one robot is distributed to each station) and the number of the robots not 0 is less than N (namely, the number of the robots distributed to each station is not more than the upper limit value which can be contained by the station), the serial number represents the robot distributed to the station, and the number of the robot serial number not 0 represents the number of the robots distributed to the station. Determining assignment of tasks and robots through the three barcodes;
s212: the assembly tasks distributed to the stations correspond to the robots, namely the positions of the station codes and the robot codes corresponding to the task codes indicate the stations distributed to the tasks and which robots in the stations execute the tasks, and if the robot codes are 0, the tasks are executed along with other robots distributed to the stations;
s22: as robots of the same model can be distributed in the stations, the invention adopts a 'station distribution matrix' mode to define the tasks distributed to the stations S and the corresponding situation of the robots. Wherein: the first column of the matrix represents the robot serial number to which the station is assigned, while for a particular robot, the other columns that follow represent the tasks that the robot performs at that station. Where 0 indicates that the robot has a priority relationship between the task in the column and the immediately following task. On the basis that the tasks and the robots are distributed to the stations by the codes, according to the station distribution matrix, the beat value of each colonial area and the total input cost of the robots are calculated, and then the total energy consumption of the assembly line is calculated according to the beat and the station distribution matrix.
S23: the cost calculation formula of the country is as follows:
Figure BDA0003215785410000041
in the formula, the name of Pareto optimal solution set is set to 1, cnIs the fitness of the individual n, fk(N) is the kth target value for individual N, NrankRefers to the number of individuals in the Pareto solution set at the same level. rank (n) is a random number between 0 and 1. The formula can distinguish the individual fitness of different Pareto levels. The energy after normalization for each country can then be calculated according to the following formula:
Cn＝max(cn)-cn
in the formula, CnStandardized cost values for the nth colonial country. Cost after normalization CnRepresents the energy of the colonial countries, i.e. the smaller the cost, the greater the energy for minimizing the questions. The number of niter people surrounding the nth niter people can then be calculated:
Figure BDA0003215785410000051
in the formula, NcolIs the number of colonists, NimpIs the number of colonial countries. The higher the national cost of the colonizers is, the more the colonizers are;
the assimilation process of the algorithm adopts cross and variation operations, each colonial country carries out the assimilation by carrying out the cross operation with colonial places of the empire, a new solution obtained after the assimilation probably dominates an original solution, the original solution is replaced by the new solution, the new solution probably is in the same Pareto grade with the solution in an existing Pareto solution set, and the new solution is reserved in the Pareto solution set.
The solution process of assimilation in emperor comprises the following steps:
s31: and selecting the task codes in the three bar codes of the breeding country and the breeding place of the breeding country to carry out cross operation.
S32: and performing variation operation of different strategies aiming at the station and the robot codes respectively to generate more feasible solutions and ensure that the input quantity of the robot in the feasible solutions is as small as possible. For the variation of the robot code, in the robot code of the position corresponding to the station code, on the premise of ensuring that each station has at least one robot, a position is randomly generated so that the value becomes 0.
In order to improve the optimization speed of the global algorithm and obtain a better solution, the invention integrates a delay-Acceptance Hill-Climbing (LAHC) algorithm into a colonial competition algorithm to form a mixed colonial competition algorithm, and the solving process of the delay-Acceptance Hill-Climbing algorithm comprises the following steps;
s41: generating a vector of size L p ═ p0，...pL-1To record previous solutions;
s42: starting the vector records the energy of the initial country, and in each iteration i, a candidate solution S is generated*；
S43: for multi-objective problems, if the solution is a candidate S*Three target values that can govern the position δ (δ i mod L) are received as the solution candidate S*Using S as the three target values of the position*The target value of (2) is replaced.
The solving process of imperial update and colonial competition comprises the following steps:
after assimilation and LAHC in the empire, the objective function of some colonists can dominate their corresponding colonists. This allows the location of the colonial country and the colonial site to be exchanged. The process is an imperial update. Each colonizer "country" always competes with one another to occupy more of its colonizers, in addition to occupying its current colonizer. The colonial competition is to redistribute the worst colonial places in the empire China with the lowest energy value according to the energy of each empire country in a competitive mode. The result of the competition is a decrease in the weak empire energy value and an increase in the strong empire energy value. The energy value of each empire is determined by the "Country" of the colonists and the cost values of all colonists, i.e.
Power(i)＝Cost(imp)+β*mean(Cost(col))
NPower(i)＝max(Power(i))-Power(i)+1
In the formula, β is an energy ratio of each colonizer in its corresponding country, and is set to 0.2. The following formula is the normalization of the energy value for each empire, from which the probability calculation is derived that the empire has a released colonial place:
Figure BDA0003215785410000061
Figure BDA0003215785410000062
Figure BDA0003215785410000063
Figure BDA0003215785410000064
the invention also provides a multi-robot collaborative assembly line balancing system with energy efficiency considered, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the method.
Drawings
FIG. 1 NS statistics Box map of 32 examples
FIG. 2 MS statistics Box map of 32 examples
FIG. 3 is a diagram of SP statistics box of 32 examples
FIG. 4 is a block diagram of the CPU statistics box of the 32 embodiments
Fig. 5 is a comparison graph of results of different algorithms of Rosenberg (I25, S6)
FIG. 6 schematic diagram of multi-target hybrid empire competition algorithm
Detailed Description
The technical scheme of the invention is further explained by combining the drawings and the embodiment.
Experiment of
Based on the prior priority relation graph of 5 classical problems (Jackson, Rosenberg, Gunther, Hahn, Tong) of http:// www.assembly-line-balancing.de /) proposed by assembly line balance problem research, the time and energy consumption of each task assembled by the robot are randomly generated, each problem is divided into 4 different work stations, and 20 groups of data are used for carrying out experiments.
Meanwhile, the Multi-target mixed empire competition Algorithm (MOHICA) provided by the invention is compared with a Multi-Objective Imperial competition Algorithm (MOICA) and a classical Algorithm non-dominated selection genetic Algorithm (NSGA-II) with superior performance in solving the Multi-target problem at present, and the performance of the Algorithm is tested. Since the result of a single operation of the algorithm has certain randomness, 10 independent experiments are respectively carried out on each example by the 3 algorithms,the results are shown in Table 1. As can be observed from Table 1, MOICA is superior to NSGA-II algorithm in the aspects of the number of solutions, the maximum propagation speed and the solution space; after the delay hill climbing algorithm is introduced into the MOICA algorithm, the searching speed of the algorithm can be increased, and a better solution can be obtained; however, at run-time, NSGAII is slightly more dominant than MOHICA and MOICA algorithms.
In order to observe the experimental result more intuitively, the statistical box diagram is used as a statistical analysis tool to obtain the index characteristics of NS, MS, SP and CPU obtained by the algorithms through multiple operations aiming at different arithmetic examples. The distribution of the operation results of each algorithm on the number of solutions, the maximum propagation speed and the space of the solutions can be more intuitively seen from fig. 1, fig. 2, fig. 3 and fig. 4.As can be seen from FIG. 1In terms of the number of solutions, MOHICA has greater advantages than MOICA and NSGA-II, and provides more alternatives for decision makers.From FIG. 2, it can be seen thatMOHICA is significantly greater than MOICA and NSGA-II in solution propagation velocity; and alsoFrom FIG. 3, it can be seen thatMOHICA is also smaller in solution space than MOICA and NSGA-II. Although MOHICA is longer in solution time than MOICA and NSGA-II, its running time is within an acceptable range in view of the excellent performance of MOHICA in other performances, so that it is still an efficient algorithm in solving this multi-objective problem.
TABLE 1 results of experiments on different scale problems
Figure BDA0003215785410000071
Figure BDA0003215785410000081
In order to better illustrate the competitiveness of MOHICA in terms of solving the problem, the invention takes the Rosenberg (I25, S6) problem as an example, and respectively uses 3 algorithms to solve the problem, and takes an average scheme of the number of previous solutions of the non-dominant scheme in 10 running results thereofAs shown in fig. 5. As can be seen from the figure, the number of solutions obtained by MOHICA is 15, while the number of solutions of MOICA and NSGA-II are 11 and 9 respectively, and MOHICA is obviously superior to the latter two; and in the aspect of optimizing the target value of the target, the target value in the scheme obtained by MOHICA also has great advantages compared with MOICA and NSGA-II.

Claims (1)

1. A multi-robot collaborative assembly line balancing method considering energy efficiency is characterized by comprising the following steps:
the first part of the process:
constructing a multi-robot collaborative assembly line balance problem considering energy efficiency, wherein the optimization target comprises the beat of an assembly line, the total energy consumption and the total robot investment cost in the assembly process;
solving the balance problem of the assembly line, obtaining an optimal robot task allocation strategy for carrying out assembly operation, wherein the expression of the objective function is as follows:
MinF＝(f1,f2,f3)
the constraints of the problem include the beat constraint f of the assembly line1Assembly line Total energy consumption constraint f2Total input cost constraint f of assembly line robot3The constraint expressions are respectively:
Figure FDA0003215785400000011
Figure FDA0003215785400000012
Figure FDA0003215785400000013
in the formula, I is a task serial number I (I is 1, 2.. gtoreq.i), j is a task immediately following the task I in the task priority map, S is a station serial number S (S is 1, 2.. gtoreq.s), R is a robot species serial number R (R is 1, 2.. gtoreq.r), n is a robot species serial number R (R is 1, 2.. gtoreq.r), andsthe number of robots at the station s,
Figure FDA0003215785400000014
is the kth of station ssTable robot (from front to back), ks＝1,...N，
Figure FDA0003215785400000015
Is the start time of the task i,
Figure FDA0003215785400000016
the completion time of the task i, N is the maximum number of distributable robots in the station,
Figure FDA0003215785400000017
is the r-th of station ssThe energy consumption per unit time while the robot is waiting,
Figure FDA0003215785400000018
is the r-th of station ssThe energy consumption per unit time of the robot when performing task i,
Figure FDA0003215785400000019
is the kth of station ssThe time at which the station robot performed task i,
Figure FDA00032157854000000110
for the set of all tasks i assigned to a workstation s,
Figure FDA00032157854000000111
for the set of predecessor tasks of all tasks i assigned to a workstation s,
Figure FDA00032157854000000112
all tasks assigned to the kth robot position of workstation s, pre (i) the set of tasks that are immediately preceding task i,
Figure FDA00032157854000000113
is a sufficiently large integer that the number of the molecules,
Figure FDA00032157854000000114
if at workstation s
Figure FDA00032157854000000115
The location is assigned to task i, then
Figure FDA00032157854000000116
Otherwise
Figure FDA00032157854000000117
Figure FDA00032157854000000118
If at workstation s
Figure FDA00032157854000000121
The position is assigned to the robot r, then
Figure FDA00032157854000000119
If not, then,
Figure FDA00032157854000000120
zij: in work s, if task i completes earlier than task j, then zij1, otherwise, zij＝0；
The constraints of the problem further include: ensuring that the number of robots in each station does not exceed the maximum number of robots that can be accommodated by the station; ensuring the priority relationship among various tasks; each task must be assigned to a workstation; each station is assigned to at least one robot; the priority relationship between stations and between tasks in the stations; the range that the number of tasks allocated by each robot should meet; the priority relation of each task in the station; wherein:
the number of robots in each station is guaranteed not to exceed the maximum robot number constraint which can be contained in the station:
Figure FDA0003215785400000021
ensuring the priority relation constraint among various tasks:
Figure FDA0003215785400000022
each task must be assigned to a workstation:
Figure FDA0003215785400000023
each workstation is assigned to at least one robot constraint:
Figure FDA0003215785400000024
and (3) priority relation constraint between stations and between tasks in the stations:
Figure FDA0003215785400000025
Figure FDA0003215785400000026
the number of tasks assigned to each robot should satisfy a range constraint:
Figure FDA0003215785400000027
Figure FDA0003215785400000028
and (3) the priority relation constraint of each task in the station:
Figure FDA0003215785400000029
Figure FDA00032157854000000210
Figure FDA00032157854000000211
the variables 0 to 1:
Figure FDA00032157854000000212
Figure FDA00032157854000000213
zip∈{0,1},i＝1,2,...I,p＝1,2...,P
and a second part of the process:
constructing a multi-target hybrid empire competition algorithm (MOHICA) which comprises empire initialization, empire internal assimilation, LAHC algorithm for local search, empire internal update and colonial competition;
the processing process of the empire state initialization algorithm comprises the following steps:
s21: three bar codes are adopted for encoding, wherein one bar code is a station code based on a station serial number, the second bar code is a task code based on an assembly task, and the third bar code is a robot code based on a robot serial number; the concrete solving steps are as follows:
s211: the station code sequence code randomly generates a repeatable integer sequence with the length of I in ascending order in the interval [1, S ]; the task code sequence is used for generating an assembly task sequence on the basis of the task priority relationship; the robot code sequence is that on the basis of generating the position with the length of I, 0 and robot serial numbers are randomly distributed to the positions, and at least one position of the position code with the same number is not 0 and the number of robots not 0 is less than N, the serial number represents the robot distributed to the position, and the number of the robot serial numbers not 0 represents the number of the robots distributed to the position; determining assignment of tasks and robots through the three barcodes;
s212: the assembly tasks distributed to the stations correspond to the robots, namely the positions of the station codes and the robot codes corresponding to the task codes indicate the stations distributed to the tasks and which robots in the stations execute the tasks, and if the robot codes are 0, the tasks are executed along with other robots distributed to the stations;
s22: as robots with the same model can be distributed in the stations, the corresponding conditions of tasks distributed to the stations s and the robots are defined in a 'station distribution matrix' mode; wherein: the first column of the matrix represents the robot serial number assigned to the station, and for a particular robot, the other columns in the following represent the tasks performed by the robot at the station; wherein 0 indicates that the robot has a priority relationship between the task in the row and the directly succeeding task; on the basis that the tasks and the robots are distributed to the stations by the codes, calculating a beat value of each colonial area and the total input cost of the robots according to a station distribution matrix, and then calculating the total energy consumption of the assembly line body according to the beat and the station distribution matrix;
s23: the cost calculation formula of the country is as follows:
Figure FDA0003215785400000031
in the formula, the name of Pareto optimal solution set is set to 1, cnIs the fitness of the individual n, fk(N) is the kth target value for individual N, NrankThe number of individuals in the Pareto solution set at the same level is referred to; rank (n) is a random number between 0 and 1; the formula distinguishes the individual fitness of different Pareto levels, and then calculates the energy after each country is standardized according to the following formula:
Cn＝max(cn)-cn
in the formula, CnA normalized cost value for the nth colonial country; cost after normalization CnRepresents the energy of the colonial countries, i.e. the smaller the cost, the greater the energy for minimization problems; then, calculating the number of colonists in the nth colonized country:
Figure FDA0003215785400000032
in the formula, NcolIs the number of colonists, NimpIs the number of colonists; the higher the national cost of the colonizers is, the more the colonizers are;
the assimilation algorithm adopts cross and variation operations, each colonial country needs to carry out cross operation with colonial places of the empire to carry out assimilation, new solutions obtained after assimilation probably dominate original solutions, the original solutions are replaced by the new solutions, and if the new solutions and the solutions in an existing Pareto solution set are in the same Pareto grade, the new solutions are reserved in the Pareto solution set;
the solution process of assimilation in emperor comprises the following steps:
s31: selecting a breeding country and a task code in the three bar codes of the breeding land of the breeding country to carry out cross operation;
s32, performing variation operation of different strategies on the station and the robot codes respectively, and randomly generating a position to enable the value to become 0 on the premise of ensuring that each station has at least one robot;
the LAHC algorithm for local search is characterized in that a delay Hill Climbing (LAHC) algorithm is integrated into a colonial competition algorithm to form a mixed colonial competition algorithm, and the solving process of the delay Hill Climbing receiving algorithm comprises the following steps;
s41: generating a vector of size L p ═ p0,...pL-1To record previous solutions;
s42: starting the vector records the energy of the initial country, and in each iteration i, a candidate solution S is generated*；
S43: for multi-objective problems, if the solution is a candidate S*Three target values that can govern the position δ (δ i mod L) are received as the solution candidate S*Using S as the three target values of the position*Target value replacement of (2);
the solving process of imperial update and colonial competition comprises the following steps: after assimilation and LAHC in the empire, the positions of the colonial countries and the colonial sites are exchanged, and the process is updated in the empire; each colonizer "country" always competes with one another to occupy more of its colonizers, in addition to occupying its current colonizer; the colonial competition is that the worst colonial land in the monarch with the lowest energy value is redistributed according to the energy of each monarch in a competition mode; the result of the competition is that the weak empire energy value is reduced and the strong empire energy value is increased; the energy value of each empire is determined by the "Country" of the colonists and the cost values of all colonists, i.e.
Power(i)＝Cost(imp)+β*mean(Cost(col))
NPower(i)＝max(Power(i))-Power(i)+1
Wherein, beta is the energy ratio of each colonial place in the corresponding place, and is set to be 0.2; the following formula is the normalization of the energy value for each empire, from which the probability calculation is derived that the empire has a released colonial place:
Figure FDA0003215785400000041
Figure FDA0003215785400000042
Figure FDA0003215785400000043
Figure FDA0003215785400000044
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