Chapter 4 Research on Multi-Objective Genetic Algorithm
§4.1 Introduction to Multi-Optimization Algorithm
Most of the actual engineering optimization issues are multi-objective optimization issues, and the targets are generally conflicted with each other. Multi-objective optimization has been greatly attached to people, and has developed more methods for solving multi-objective optimization. Let's introduce a definition of multi-objective optimization about non-awareness and non-discipline.
Definition 1: If
(
For multi-objective optimization feasible domains, there is no other feasible point
Make
Established (
For the target number), and at least one of them is established,
It is a non-inferior solution optimized by multi-objective. All non-inferior forms of non-aspirations (Noninferior Set).
A multi-objective optimization If there is a non-corish, there is often an infinity, forming a non-inferior collection. When solving the actual problem, too much non-corrosion is unable to apply. The decision makers can only choose a non-inconnected solve that it is most satisfactory as the final solution. The final solution is three types of methods, and one is the result of seeking a uncommon solution, that is, first find a large number of non-corrosion, constitute a subset of non-abbrevantory, and then find the final solution according to the intention of the decision maker, and A class is interactive, and a lot of non-corrosion is not first obtained, but the final solution is gradually obtained by analytical and decision-making methods. The last category is the relative importance of demand for decision makers to provide the relative importance between the targets. The algorithm is based on this, and the multi-objective problem is converted into a single target problem. This type of method can also be considered a child of the first type. Method, the difficulty of this class is how to get the real weight information of the decision maker, this chapter will propose a multi-objective genetic algorithm based on fuzzy logic, which is better to reflect the power of decision makers.
The generated method mainly has a mixing method of weighting method, constraint method, weighting method, and constraint method, and multi-objective genetic algorithm. The intertency method mainly has a Geoffrion method for solving linear constraint multi-objective optimization, STEMs and Zionts-Wallenius methods, and instead of value exchange.
The author believes that the generation is more attractive to decision makers. First, there is no better multi-objective non-linear optimization interaction. Secondly, under the premise of limited information on decision makers, decision makers often ask decision makers to answer some seems to be Question, policymakers will be very passive during interaction, which means that integrity will pass the contradiction of the problem to decision makers to some extent. If we can seek a better approximate solution to noncompatibility, decision makers have a comprehensive understanding of the problem, so that it can better make decisions and compromise.
In the generating method, the commonly used weighted law has its own inherent disadvantages, and it is impossible for certain areas of unveiled union. As shown in Figure 4.1 is an example of two goals, the arrow refers to the part of the non-corrugated curved curve cannot be obtained by weighting method. The reason for this phenomenon is that the weighting method is actually optimizing the nigramatic combination of each target function. Single goal. That is, the single target of the positive weight coefficient is inevitable is inevitable, and some non-corrosion may not find a set of positive weight coefficients to solve. Adding a constraint method can avoid this, but the calculation cost is too large, and the process is very complicated, and the application prospect is not optimistic. Using multi-objective genetic algorithms to solve non-beta sets in recent years, a new idea of solving, currently in research
Figure 4.1 Weighted Method Unable to find out all non-inconnected examples
The initial stage, but the initial calculation results are very exciting, so another research focus on this chapter is placed in the study of multi-objective non-corrosion set algorithm.
4.2 Multi-objective genetic algorithm based on fuzzy logic
§ 4.2.1 Fuzzy logic
Fuzzy logic is a new type of classification method (classification is one of the basic concepts of aggregation theory). Fuzzy logic imitates human wisdom, introduces the concept of membership, describes the transition process between "true" and "false". In the fuzzy logic, the event does not classify the limit value of the set, but gives each element to a real number between 0 and 1, which describes the intensity belonging to a set. Specific introduction can refer to [116]. § 4.2.2 Thoughts and specific implementation of multi-objective genetic algorithm based on fuzzy logic
Through the previous introduction, we know that fuzzy logic is a good tool for responding to decision makers. Methods of fuzzy logic can be used to react the "trade-off" information of the decision maker for the importance of the various targets. As we all know, the genetic algorithm is based on the individuality of the individual, it can be considered that the decision-making is the comprehensive evaluation of the individual, so that according to the method of fuzzy logic, direct constructing decision maker for the adaptivity of genetic individuals, the decision maker Comprehensive evaluation of individuals. And use this as the basis and power of genetic evolution. The following is a preliminary algorithm step:
(1) The optimal solution of each single target is obtained separately;
(2) Given the membership function of each target satisfaction with the optimal solution and decision maker consultant in (1);
(3) Links the satisfaction of each target and the adaptation of the individual objects by fuzzy logic;
(4) The genetic algorithm is used to solve the genetic algorithm based on the adaptation degree defined by the (3);
The reason why first solving the optimal solution of each single target is that it is hoped to give decision makers a relatively clear concept, that is, if an optimization is optimized, the best optimal solution is. With this information, decision makers can give a subordinate curve for satisfaction with different goals. If you find the defective density optimization, you can give an estimate of the optimal pair target.
The specific calculation method and fuzzy control method are basically the same, and it is also divided into a fuzzification, Fuzzy-Inference and Defuzzification. In the author algorithm, the fuzzy reasoning uses the maximum minimum method, and the deprivenation is an area center of gravity. See References [116] for details.
The following is described in detail the algorithm process as an example of double target optimization in ten rod truss.
Referring to Figure 3.4, the displacement target is the maximum node 1, 2, 3, and 4
Minimize displacement. Here is the largest
The displacement is the maximum absolute value.
In this way, we have two goals, namely the minimization of displacement and weight, can establish a relatively simple fuzzy logic as follows:
(1) If the weight is light and the bit is small, the design is high;
Obviously, both goals have been made in both goals. And if we only care about weight, you can establish the following fuzzy logic:
(2) If the weight is light or the size of the small design should be high;
We can express fuzzy logic more fine and more in line with the actual ideas of decision makers:
(3-1) If the weight is light and the bit is small, the design is high;
(3-2) If the weight is light and the displacement is high;
(3-3) If the weight is light and the displacement is so design;
(3-4) If the weight is medium and the displacement is small, the design is high;
(3-5) If the weight is medium and the displacement is medium;
(3-6) If the weight is medium and the displacement is low;
(3-7) If the weight is large and the bit is small, the design is modeled; (3-8) If the weight is large and the displacement is low;
(3-9) If the weight is large and the displacement is low, the design is low;
We can build the corresponding table representing the above logic:
weight
Displacement
→
Design adaptation
Good
Good
→
Very high
Good
Normal
→
HIGH
Good
Bad
→
Normal
Normal
Good
→
HIGH
Normal
Normal
→
Normal
Normal
Bad
→
Low
Bad
Good
→
Normal
Bad
Normal
→
Low
Bad
Bad
→
Very Low
Table 4.1 Fuzzy logical table
The method of fuzzy logic actually maps the target function to the utility function of the decision maker. In general, the accurate description of the utility function of decision makers is very difficult. An important area of current multi-objective optimization research is how to reasonably construct decision makers. Utility function. However, it is easier to describe the preferences for their own preferences with a fuzzy language. Another advantage of using fuzzy logic is that policymakers can visually observe that if they change the fuzzy logic, the decision changes. That is, the solution to the solution is close to the true idea of decision makers. In the case where the non-inferior decomposition range is large, the fuzzy logic may be the only actual and feasible approach.
§ 4.2.3 Case
In the previous chapter, the lightest weight of ten rods has been 1598.93LB, the corresponding maximum displacement is 7.171639
We can also seek minimum displacement to 0.977492
The corresponding maximum weight is 15349.4496
. Below is a comparison of the minimum and light weight design points.
Displacement minimum design
)
Lightweight design (
)
Rod 1
40.0000
7.9396
Rod 2
40.0000
0.1
Rod 3
40.0000
8.0956
Rod 4
40.0000
3.9613
Rod 5
0.1
0.1
Rod 6
40.0000
0.1
Rod 7
40.0000
5.7554
Rod 8
40.0000
5.5994
Rod 9
40.0000
5.5994
Rod 10
40.0000
0.1
weight(
)
15349.4496
1598.93
Displacement
)
0.977492
7.171639
Table 4.2
From the above table, it can be clearly seen that displacement and weight are two mutually conflicting goals.
In the case of a known single target extreme, we take a simple fuzzy logic to determine the fitness of the individual, if the weight is light and the bit is smaller is so adapted.
For simplicity, assume that the weight of the position is linear, as shown in Figure 4.2.
1
1598.93
15349.4496
weight
Figure 4.2 Weight Light membership functions
The subordinate function of the hypothesis shift is also linear, as shown in Figure 4.4.
The value range of individual adaptation is defined as [0, 1], and the membership function of the adaptation is also assumed to be linear, as shown in Figure 4.3.
The size of the group is 100, the algebra is 500 generation, the replication probability is 0.2, the mutation probability is 0.01, and the random operation is ten times obtained:
Randomly running ten times as follows:
weight(
)
Displacement
)
4567.742671
2.288459
4645.949119
2.349095
4688.605046
2.378970
4714.601695
2.381532
4887.722703
2.460164
4782.497571
2.413273
4604.757758
2.313334
4751.680501
2.3980754792.499324
2.414853
4906.998110
2.467439
Table 4.3
1
Displacement
0.977492
7.171639
Figure 4.3 Displacement membership function
1
Individual fitness
1.0
Figure 4. Substation function with high individual applications
From Table 4.3, it can be seen that the method of fuzzy logic is feasible. We know that the system with fuzzy logic is actually a transformation that maps input to the output. If the traditional fuzzy compromise method is based, the minimum of the subjects of the target is the individual's adaptation, in fact, the idea of the method and the method of solving the method of solving the blur planning proposed by the literature [59] can be considered as literature [59] The algorithm is a simplification of the fuzzy logic algorithm. This method is used to randomly run ten times as follows.
weight(
)
Displacement
)
4595.369459
2.328093
4627.995032
2.341260
4553.618829
2.311908
4957.222200
2.489298
4520.170746
2.304064
4519.372652
2.296146
4753.485746
2.393686
4741.802927
2.393425
4961.276395
2.487161
4528.437249
2.299173
Table 4.4
As can be seen from the previous discussion and examples, using fuzzy logic to indicate that the decision maker is a better way to expect the decision maker to really "preference".
4.3 Research on the genetic algorithm of multi-objective non-corrosion column
4.3.1 Multi-objective non-abundance set genetic algorithm
Multi-Objective Genetic Algorithm is an effective way to solve multi-objective optimization non-aurans in recent years. Currently in the initial stage of development, there are not many ways, and there are fewer methods. There are mainly below: Rank Genetic Algorithm, Two-Branch Tournament Genetic Algorithm and Simple Bad Penalty Algorithm proposed by the Author. Multi-objective non-abuse set algorithms are actually an approximation process. For two-dimensional problems, the process of approximation of non-corrugations. However, if the optimal solution of each single target is not known, it does not know the position of the final non-understanding of the curve end, and does not know the shape of the curve. Therefore, multi-objective genetic planning is much more complicated in theory in theory. However, from the theoretical theory of nonlinear plan, the optimal solution generally occurs on the boundary of the constraint set, and the multi-objective optimized non-aqueous solution is generally a continuous boundary in the feasible domain, even for the feasible domain for the dome, often often It is established. That is to say, there is a correlation between noncompatience, which can be considered a special mode. This makes the efficiency of the genetic operation between the non-affected point are more effective. Coupled with the genetic algorithm itself is based on a group, and the purpose of solving a decoction is consistent. Therefore, the genetic algorithm is used to solve multi-objective optimization problem is suitable.
From the overall performance of the calculation, the classification genetic algorithm belongs to the currently better algorithm. Let's first introduce the concept of multi-objective optimization intermediate level.
Level concept is defined in the target function space. Points in the target function space If it has been classified, in the future, it is not considered in the future, the class is to identify the non-bad point in the current target function space, and the number of levels is specified as the current series.
, Then remove
Level points, add the current level 1, and then repeat the remaining points to the above-level process until all points in the target function space are classified. According to this definition, you can get the following theorem.
Theorem 4.1 for level
Any point in the middle, always
At least one point superior to this point is found.
Note that the concept is better than the concept is defined in the meanings. The proof of theorem can be used directly with the anti-confidence. In a certain level, the design points are inadvertent.
The non-inferior property belongs to a semi-order, does not have delivery property, as examples are taken in Figure 4.5, and A is non-inferior, B is non-inferior, but C is infer to A.
If the design points in Figure 4.5 are graded, the result is: Level 1: A, B; Level 2: C;
B
A
C
Figure 4.5
In fact, we can also treat the level as a half order, that is, the design points between different levels may be unwitten. This is a problem that must be considered by using a grading genetic algorithm.
The grading genetic algorithm is a genetic algorithm that combines the feasibility of the design point, the feasibility of design points and the adaption of design points.
The main disadvantage of the classification algorithm is to easily have a phenomenon of aggregation. The reason for this phenomenon is that due to the extreme value of some target functions "easy to find", it is necessary to result in the final resulting non-aura. The region of the target is far from other comparative "hard-to-see" targets, and ten rod problems under two loads is a typical example. The displacement extreme value of this problem is easier to obtain, while the weight is more difficult to find. It is difficult to obtain an area near the weight of the weight using a grading algorithm.
4.3.2 Steady-state grading multi-objective non-abbreviation collection genetic algorithm
The basic idea of the classified genetic algorithm is briefly introduced, and the phenomenon of the minimum spoofing of the genetic algorithm itself (this is also a biggest reason to use the steady genetic algorithm). And the level mentioned earlier is the objective fact of the semi-order, so the author thinks how to make the algorithm have a certain degree of steady state in the multi-objective non-abbreviated column generating algorithm is the key to the success of the algorithm.
While considering the algorithm is steady state, it is also necessary to consider the uniformity of the calculated non-beta set. The result of too much aggregation is not used. At the same time, it is also desirable that the optimum and problematic true single targets of all single targets in noncomputes concentrated. These requirements make it difficult to construct a multi-objective genetic algorithm.
It is well known that single target genetic algorithm generally uses a way to reserve the optimal individuals per generation to achieve steady state, but it is difficult to define the optimal individual in multi-objective grading genetic plan, a simple method is to reserve the current number of medium levels every time The individual of 1, but as mentioned earlier, the level is only one and a half, and the individual reserves the current generation of the intermediate number 1 is not enough. So the author considers the combination of the previous generation group and the current generation group.
Regarding how to combine levels, feasibility, and individual fitness, the author's process is relatively simple, that is, the non-inflatable, does not participate in the number of evaluation levels, and directly gives a small fitness. After the level is defined, the process of application genetic algorithm can be applied to a new group. Unlike a single target genetic algorithm, all individuals in all old populations are retained.
After getting new and old groups, you need to select a new generation of groups from it. Here are several ways to achieve "steady state" in the author.
(1) Take the following check for all individuals in the new group:
Add individuals in the new population to the old population, re-grade the old group, get the new individual's level and the same number of old individuals as the new individual number, set to newrank and Oldrank, if new rank is greater than Oldrank, we Alternatively replace new individuals with old individuals. Note that the so-called number is the same as that of the old population and new groups are implemented in the form of an array, and the number corresponds to the subscript of the array. The process can be refer to Figure 4.6.
O1
O2
O3
...
Old group
N1
N2
N3
...
New group
O1
O2
O3
...
N1
Re-class
Compare stage
Figure 4.6
(2) Combine the new group and the old group into a large group, grade, get the new individual level and the old individual of the old individual with the new individual, set to newrank and Oldrank, if newrank is greater than Oldrank, we use the old Individual replacement of new individuals. The process can be refer to Figure 4.7.
O1
O2
O3
...
Old group
N1
N2
N3
...
New group
O1
O2
O3
...
N1
N2
N3
...
Re-class
Compare stage
Figure 4.7
The numerical calculation results show that the solution (1) solution effect is better relative to the form (2), and found that in the planning process, most of the new individuals are inferior to the old individual, the same case also occupies considerable proportion. Levels are less than the case. And we only have treated the situation of the new individual's fragment of the old individual, ie, reserved the old individual. It can be concluded that the number of individuals reserved from the previous generation is greater, and the above algorithm is also found to be a relatively rough approximate algorithm, some deception may occur. Below is another form of authors, but also a form of recommendation.
(3) Combine the new group and the old population into a large group of twice the large group, grading the group, and directly selects the first stage of non-auraries, the scale of the temporary group. The size of the newly old population is the same. When you are selected, you should pay attention to the individual's duplicate individual, because multi-objective optimization requires greater than single target optimization, while the individual is too close to keep the individual in the sense of point in the sense function. Uniformity. If the temporary group is full at the end of the above process or before the end, you can select two practices, one is to directly exit the individual in the output temporary group. Another way is to continue to solve, then some non-inferior points will be abandoned, continue to solve the unopened set to the global non-understanding set convergence, of course, we can also increase the minimum distance under individual target space as removed A method of non-inferior point. If the temporary group is not full, we will then add the individuals of Level 2, level 3 to the temporary group, the principle of joining the same, the same amount of individuals, the process repeatedly until the temporary group is full or large groups Individuals are available. Finally, we randomly replace the effective individuals in the temporary group, and if the temporary group is full, it is actually replacing the new group. The process can refer to Figure 4.8.
O1
O2
O3
...
Old group
N1
N2
N3
...
New group
O1
O2
O3
...
N1
N2
N3
...
T1
T2
T3
Temporary group
Add individuals to temporary groups in the order of level 1 and level 2 ...
Re-class
Figure 4.8
It should be pointed out that regarding the definition of the distance of the design point in the target function space, the difference in operation is generally not directly calculated due to the different dimensionality of each target, and the reasonable method is to regularize the target function value, so that it will be converted to the range. [0, 1], but this method also has a disadvantage that two goals are used as an example, the method may change the shape of the non-abbreviated set curve, in some cases, will make the non-abbreviated set curve loss of certain comparison Detail. In the following examples, the author does not use regularization form, and directly according to each target value as a calculated distance, the meaning of the distance is a normal European Distance.
§ 4.3.3 Case
Using the form (3), two targets (Lighter and minimum displacement) ten-pole optimization problems are solved.
Take the size of the mass of 100, the probability of the copy is 0.20, the mutation probability is 0.01, the minimum distance is 10.0, and the temporary group is full of strategies, and the temporary group of the iterative 40 generation is over to solve, and the non-corrosion curve is shown as shown in the figure. 4.9 shows.
0
2000
4000
6000
8000
10,000
12000
14000
16000
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Non-inferior collection
Single target optimal solution
Minimum displacement
weight
weight
Figure
4.9
The units in the above figure and in the middle of each figure are
And the weight unit is
.
The size of the group is 200, the probability of copy is 0.20, the mutation probability is 0.01, the minimum distance is 10.0, the temporary group is full, the temporary group is over, the temporary group is over to solve, the non-corrugation curve is shown as shown in the figure 4.10 shown. Continue to increase the size of the population to 400, the probability of 0.20, the mutation probability is 0.01, the minimum distance is 10.0, the temporary group is full of strategies, the iterative 230 generation, the temporary group is over to solve, and the non-corrugation curve, such as Figure 4.11 shows.
0
2000
4000
6000
8000
10,000
12000
14000
16000
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Non-inferior collection
Single target optimal solution
Minimum displacement
weight
Figure 4.10
Non-inferior collection
Maximum displacement
Single target optimal solution
0
2000
4000
6000
8000
10,000
12000
14000
16000
0
1
2
3
4
5
6
Seduce
8
weight
Figure 4.11
From the solution effect, it is feasible and effective, and it is required to have fewer algebraes, high efficiency. At the same time, due to the requirements, it is necessary to use a larger group scale. The optimal solution of non-abbreviated concentration single targets actually has a certain distance, which is expected, which is because the information we basis is only different. From the previous chapter, you can know that appropriate testing is beneficial for single target genetic planning. To this end, we join the test to the above solution, that is, after processing the individual after the resiliency of the new population, the individual's personal single target is optimistic about the single target, which is optimized. After the individual, it randomly replaces individuals in the population.
Non-inferior collection
Take the size of the group
400
, Copy probability
0.20
The probability of variation is
0.01
The minimum distance is
10.0
The strategy of exiting the temporary group is full, the optimal individual is added to the test, and the probability of circulating test is set to
0.8
Iterate
128
After the subsequent group full of solving. The non-corrugation curve obtained is as shown
4.12
Indicated.
0
2000
4000
6000
8000
10,000
12000
14000
16000
0
1
2
3
4
5
6
Seduce
8
Single target optimal solution
Maximum displacement
weight
Figure 4.12
As can be seen from Fig. 4.12, the effect of solving is greatly improved after the starting movement, and the single target penetration exhibits an effect of "opening" non-corrosion curve, the minimum of the non-abundance concentration is 1691.478
69LB, the value of the maximum displacement is 0.98396
And the optimal solution of single target is quite close, its solve effect is comparable to the single target genetic plan, the explanation of this is that there is a correlation between the non-lessonous solutions mentioned above, and if the solution can be obtained, each single target can be obtained. Better solution, it will be conducive to the calculation of non-inferior collection. We use the perturbation method, as long as there is a small amount of calculation, it can greatly improve the performance of solving.
After getting the non-corrosion set curve of the above figure, the decision maker can say that the situation of the model "means" For example, the ten rod has another optimization model is under the constraint of the displacement, that is, all free node displacement is limited to
Due to this structural topology, the vertical displacement phase of the free node can be easily obtained is active constraints for horizontal displacement. With the above non-discovery, we look directly 2
The corresponding weight can be approximately optimal, and we can get two displacements closest to 2 by the above case.
Design, its target value is as follows:
Weight 5166.93275
Corresponding displacement 1.99932
; Weight 5138.79227
Corresponding displacement 2.01026
;
Linear interpolation is displayed to 2
At the time, the weight is approximately 5140.5
From the previous chapter, I know the optimal solution is about 5065.2
The two are quite close, which means that the non-corrupted curve of Fig. 4.12 is very close to the global non-aqueous solution of the problem. With the non-abbreviated set curve shown in Figure 4.12, we no longer need to solve countless single target optimization to verify the idea of decision makers, policymakers can quickly lead to "preference" according to the actual situation and their preferences, or Get a smaller preference range, result in a more identified weight information between various targets, and convert multi-objective problems to a single target problem. Here, it is necessary to explain that since the result of the genetic algorithm has a certain approximation, it is possible to consider a single target optimization algorithm using a higher precision based on the weight information given by the decision maker according to the weight information given according to the non-deterioration set curve.
As mentioned earlier, there is also a way to handle the temporary group is to continue the iteration until it will be exited until a given algeset is met, and the method is subjected to a solution.
Take the mass size of 400, the replication probability is 0.20, the mutation is 0.01, the minimum distance is 10.0, until the 700 generation end, the single target optimal individual adds the perturbation, and the non-corrupted curve obtained is shown in Figure 4.13.
Figure 4.13
From the above figure, it can be opened. If you do not quit, continue iteration, the discharge will continue to approximate the global non-incompatibility set. Among them, the target function value of the minimum design point of non-abbreviated concentration is:
Weight: 15349.4496
;
Maximum displacement: 0.97749
;
The value of this value and single target displacement (weight 15349.4496
Displacement 0.97749
)the same. Similarly, when the displacement constraint is 2
When you can get:
Weight: 5156.07453
Maximum displacement: 1.97631
;
Weight: 5086.85734
Maximum displacement: 2.01602
;
Interpolation is displayed to 2
The lightest weight of 5114.8
It is known that its optimal solution is about 5065.2
And the result of the estimated estimate of the previous example is 5140.5
It can be seen that the temporary group continued iteration indes makes the non-incompatible set to continue to approximate the global noncomputer.
The method for further processing temporary groups and candidate individuals is to increase the spacing of the inspection, but the actual calculation finds that excessive spacing will have some adverse effects on solving. The reason is that the spacing is defined in the target function space and cannot reflect the distribution of design points in the design point space. The non-deterioration of nonlinear multi-objective optimization is generally in the continuous boundary of the feasible domain end, so if the distance in the target function space is increased, the degradation of the boundary capacity of the segment will result in a multi-objective genetic plan. .
Through the above examples, conclusions can be concluded, using improved multi-objective genetically zoom algorithms, which is successful, and the result of solving is quite satisfactory. At the same time, it also proves the meaning of incorporation of circulating in the genetic algorithm. It can be considered that the multi-objective genetic algorithm is a very good algorithm for solving multi-target optimization.
In addition, it is also necessary to mention the problem of multi-objective genetic planning of discrete variables. Due to the dispersion of variables, minor changes in the target may result in a large change in optimization results, so the solving idea of single target genetic planning will be used. There is a considerable difficulty. With a multi-objective genetic planning algorithm, it is very prominent to solve the multi-objective optimization problem of discrete variables. In fact, as long as the genetic algorithm is used to solve the optimization problem is to solve discrete optimization problems, the previous examples also verify the ability of algorithms to solve multi-target discrete optimization non-corrosion.
In the previous discussion, it can be seen that the classification program is repeatedly called in multi-target genetic planning, and thus the efficiency of the classification algorithm must be improved as much as possible. The following is a highly efficient classification algorithm proposed by the author. The key to the algorithm is to minimize the number of repetition comparisons. Once there is no inferior individual in a certain wheel, the entire classification process ends, the specific process is given: The current number of individuals is NSize, array ParetOrank stores the number of individuals, NCURRENTRANK is the level of the current check, BneedMoreCheck indicates whether to continue grading, nCHECKRESULT is the return value of the non-inferior checker.
The process is as follows:
NcurrentRank = 1;
/ / Assume that all individuals are 1
For (j = 0; j Paretorage [J] = NCURRENTRANK / / Calibrate all individuals of all individuals 1 // Start grading DO { / / Assume that further calibration is no longer needed BneedmoreCheck = false; FOR (k = 0; k <(nsize-1); k ) { / / Calibration of the individual K IF (Paretorage [K] == NCURRENTRANK) { // If the number of individual K is the current level For (j = k 1; j { IF (PNParetorage [J] == NCURRENTRANK) { // Only inadvertent judgment on individual individuals nCheckResult = PindividualsObjectives [K] .paretocheck (PindividualsObjectives "; IF (nCheckResult == 1) { // If the individual j is inferior to the individual K, add the individual J level to 1 PNParetorage [J] = NCURRENTRANK 1; // The level of individual changes, so further calibration needs BneedmoreCheck = true; } Else IF (ncheckresult == -1) { / / If the individual K is inferior to the individual J, add the number of individual K plus 1 PNParetorage [K] = NCURRENTRANK 1; // The level of individual changes, so further calibration needs BneedmoreCheck = true; // Individual K calibration, exit cycle, calibrate the next individual Break; } } } } } // Current level plus 1 NCURRENTRANK ; } while (bneedmorecheck); This process is highly graded, and it is helpful for improving the calculation performance of the overall algorithm. § 4.4 conclusion This chapter has proposed a multi-objective genetic algorithm based on fuzzy logic, respectively. Fuzzy logic is an effective tool for expressing decision makers for a plurality of targets, combining it in this algorithm, and the calculation results indicate that the algorithm is effective and convenient. The grading genetic algorithm is an effective tool for solving multi-objective optimization, the key to the algorithm is to maintain "steady state". This chapter discusses several ways to achieve "steady state", and put forward a most effective The way, gives a quick grading algorithm, discusses the importance of single target optimization in multi-objective non-abbreviated intersection, and also proposes a method of ensuring uniformity of non-aurans, and calculates People are satisfied, and the algorithm has actual engineering applications.
