CN106611280A - Imperialism competition algorithm based on real variable function side distance - Google Patents
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Abstract
The invention provides an imperialism competition algorithm based on a real variable function side distance for solving a job shop scheduling problem. The invention provides the imperialism competition algorithm based on the real variable function side distance for solving the problems of easy premature convergence of the traditional imperialism competition algorithm, low solution precision and inflexible application in the job shop scheduling problem. The improvement of the algorithm is as follows: 1, a machine is directly defined as an empire and a work is defined as a colony; 2, the colony belonging property is determined by the imperial group forces and the side distance, so that the final result of the algorithm is more applicable to the actual problems; 3, the geographic position advantage problem of the empire to invade the colony is evaluated by the real variable function side distance, so that the complex problems become simple; 4, in combination with the social evolution process and specific conditions of actual application examples, the generation conditions of a new colony and a new empire in the algorithm are designed, thereby being practical, simple, visual and high in calculation precision; and 5, the algorithm describes the machine utilization rate by the survival rate of the empire, thereby being simple and understandable.
Description
Field of the invention
The invention relates to the field of job shop scheduling, in particular to a method for solving a job shop scheduling problem by using an algorithm.
Background
The Job-Shop Scheduling Problem (JSP) is one of the core and the focus of manufacturing execution system research, and the research not only has important practical significance, but also has far-reaching theoretical significance. The JSP reasonably distributes resources according to the manufacturing requirements of the products, and further achieves the purposes of reasonably utilizing the manufacturing resources of the products and improving the economic benefits of enterprises. JSP is a problem coexisting in the product manufacturing industry, is closely related to factory management and product manufacturing hierarchy of Computer Integrated Manufacturing Systems (CIMS), and is an important subject of research in the field of CIMS. JSP is a typical NP-hard problem, and the research of JSP has a meaningful influence on the research of NP problem.
In recent years, many algorithms for solving the problem of job shop scheduling have been proposed, including target heuristic algorithms such as genetic and tabu search algorithms, algorithm simulated annealing algorithms, particle swarm algorithms, hybrid vehicle algorithms, as well as enumeration, mathematical programming, branch and bound, precedence rules, iterative local search algorithms, evolutionary algorithms, and the like.
An imperial sense algorithm (ICA) is also called as a colonial competition algorithm, is an evolutionary algorithm based on an imperial sense colonial competition mechanism and is proposed by Atashaz _ Gargari and Lucas in 2007, and belongs to a random optimization search method inspired by society. The ICA algorithm controls more countries according to the empire's social policy, using their resources when colonial countries are subject to some discipline support, which other countries will possess if one empire loses its strength. The basic idea of the empire sense competition algorithm is as follows: like other evolutionary algorithms, empire sense competition algorithms start with a set of individuals defined as countries, all of which are divided into two categories: empire nations and colonial countries. The country with a strong initial momentum is taken as the empire nationality and the other countries are taken as the colonial countries. Colonial areas are assigned to different empire countries according to the momentum of each country. The empire state and the colonists it contains are referred to as an empire. The purpose of obtaining more colonial areas is achieved through competition among empires, the empire with greater momentum has a greater possibility of fighting the weakest colonial area, the empire with weak intelligence will gradually lose its colonial area, and the algorithm ends when all colonial areas are occupied by one empire.
The empire-oriented competition algorithm has the advantages of simplicity, high convergence speed, global optimal search and the like, but like other intelligent optimization algorithms, the empire-oriented competition algorithm also has the defects of premature convergence, insufficient accuracy and the like in the scheduling problem of a job shop.
Disclosure of Invention
Aiming at the defects in the existing empire meaning competition algorithm, the invention aims to solve the technical problem of providing the empire meaning competition algorithm based on the side distance of the real variable function to solve the scheduling problem of the job shop.
The invention aims to overcome the defects existing in the prior art that: the empire kingdom competition algorithm is easy to converge; the solving accuracy of the empire kingdom competitive algorithm is not high enough; the empire-oriented algorithm is not flexible enough to be applied to the shop scheduling problem.
The technical scheme adopted by the invention for realizing the purpose is as follows: an empire-oriented competition algorithm based on real variable function side distance solves a job shop scheduling problem, and the algorithm comprises the following steps:
step 1: initializing empire sense competition algorithm parameters: number of initialized countries, empire country, colonial country.
Step 2: calculating the relative strength of the empire: processing capacity C by machinenTo depict.
And step 3: calculating the potential of the empire nationality: used as a business runtime.
And 4, step 4: initializing empire nationality groups: different numbers of colonial countries are allocated to the empire nations according to the empire's powers, the greater the empire's powers, the more colonial countries the empire has.
And 5: calculating the total force of the empire group: the total force of an empire nationality group includes two parts, one part is the force of the empire nationality and the other part is the force of its own colonial country
Step 6: calculating the advantages of empire geographic positions: and measuring the occupation advantage of the geographical positions of two empires occupying the same colonial area by adopting the lateral distance based on the real variable function.
And 7: and (4) determining the attribution of the colonial area, wherein the attribution property of the colonial area is determined by two factors of the empire group strength and the lateral distance.
And 8: the colonial place moves towards the empire: when the empire nations are formed, the colonial countries approach the empire along a direction that points toward the empire to which they belong.
And step 9: competition of empire group: the competition process of empire nations occurs between empire nations, as each empire nations attempts to occupy and control the colonists of the other empire nations.
Step 10: death in the colonial countries: in the infringement process of the empire, there is a death in the colonial countries.
Step 11: creation of new colonial countries: in the social evolution process, new colonial sites will be produced.
Step 12: death of the vulnerable empire: in empire competition, an empire group who loses its strength will die and its own colonial area will be disbursed by other empire groups.
Step 13: creation of the new empire: in empire competition, new empires are created.
Step 14: and (3) calculating the survival rate of the empire: using machine availability to characterize
Step 15: and finally, reserving the final rest empire states and taking the fitness value as an optimal solution.
The invention has the beneficial effects that:
1. the relative momentum of the empire state is directly characterized by the processing operation capacity of the machine, and the calculation complexity of the algorithm is reduced.
2. The machine is directly defined as the empire state, the operation is colonized, the uncertainty caused by randomly generating an initial solution is avoided, and the operation time of the algorithm is reduced.
3. The attribution property of the colonial area is determined by two factors, namely the empire country group momentum and the lateral distance, so that on one hand, the algorithm result is more accurate, on the other hand, the algorithm is more appropriate to the actual situation, and the final result of the algorithm is more suitable for the actual problem.
4. The complex location problem can be systematically simplified by measuring the geographical location dominance of a certain empire country encroaching on a certain colonial area by using the lateral distance in the real variable function.
5. The operation running time is used for calculating the strength of the empire nationality, and the method is simple, practical and spectrum-dependent.
6. The machine operation capacity is used as a rule for allocation of the imperial country colonial area, and the method is simple and visual and has high solution accuracy.
7. The calculation mode of the total force of the empire is changed, and the algorithm is more flexible.
Drawings
FIG. 1 is a basic flow chart of the algorithm of the present invention
FIG. 2 is a diagram showing a positional relationship between an empire country and a colonial country
Detailed Description
The traditional empire state meaning competition algorithm has the advantages of simplicity, accuracy, time saving and the like, is an efficient and easy-to-use optimization algorithm, saves memory, has short optimization time, and can quickly converge to an optimal solution in a search space. However, the optimization of the job shop scheduling problem is easy to converge, the empire-oriented algorithm cannot obtain a sufficiently accurate solution, and the empire-oriented algorithm finally obtains a solution instead of a group of solutions, which is not suitable for solving the management and arrangement problem of the job shop.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description is made with reference to the flowchart.
One, empire kingdom competition algorithm
In the empire sense competition algorithm, each country is represented by a real number array or vector.
For one NvarDimension optimization problem, the array is defined as follows:
the magnitude of the potential force of a country is obtained by calculating a certain objective function, and the variable is
Is that
Second, the concrete implementation step
Step 1: initializing empire sense competition algorithm parameters: number of initialized countries NpopEmpire country NimpCountry of colonial land Ncol. Wherein the empire country is represented by a machine, colonized by the machineCountry is represented by homework.
Npop＝Nimp+Ncol
Step 2: calculating the relative strength of the empire: processing capacity C by machinenTo depict.
Where Ncn indicates the number of jobs that it is possible to wait for a particular machine Mn to process, and Mcn indicates the number of machines that can process these Ncn jobs.
And step 3: calculating the potential of the empire nationality: the strength of the force in the nth empire country is defined as:
in the formula, tiThe running time, i.e., cost value, at the nth machine for the ith job.
And 4, step 4: initializing empire nationality groups: different numbers of colonial countries are allocated to the empire nations according to the empire's powers, the greater the empire's powers, the more colonial countries the empire has. The empire and its owned colonial area form an empire group. In the shop scheduling problem, the number of jobs actually handled by the machine is equal to the number of colonists owned by the empire. Thus, the method of colonial distribution is as follows:
in the formula, N.CnRepresenting the colonial place owned by the nth empire.
And 5: calculating the total force of the empire group: the overall force of an empire nationality group consists of two parts, one being the force of the empire nationality and the other being the force of its own colonial country, of which the force of the empire nationality has a greater influence on the force. Thus, the overall force of an empire is calculated as follows:
in the formula, T.CnIs the total cost function value, t, of the nth empire groupnAs a function of the cost of the nth empiric country, tiThe cost function value of the imperial group's colonial area, i.e. the running time of a certain machine in the workshop scheduling problem, is 0 < mu < 1, is a real number, and is generally mu ∈ [0.1, 0.5 [ ]]。
Step 6: calculating the advantages of empire geographic positions: the side distance based on the real variable function is adopted to measure the dominance of two empires occupying the same colonial area, and the empire with the bigger dominance has the opportunity to invade the colonial area. The specific implementation mode is as follows:
the positional relationship between the empire country and the colonial country is shown in FIG. 2
For the attribution of any one colonial area, the attribution needs to be determined by calculating the size of the dominance of two empires nearest to the colonial area. The monarch with great dominance has the right to own the colonial area, and the colonial area with relatively small dominance will lose the colonial area. The magnitude of the dominance is measured by the side distance in the real function. Overview of the clinical laterals:
definition 1: given the interval X ═ a, b >, ifBalance
Is x with respect to point x0Left side distance of the sum interval X, denoted as pl(x，x0，X)。
Definition 2: given the interval X ═ a, b >, ifBalance
Is x with respect to point x0The distance to the right of the interval X is denoted by pr(x，x0，X)。
In the scheduling problem of the job shop, the qualitative variation interval is X ═ a, b >, any point X is the position of the colonial place, two empires relatively close to the colonial place X are in the qualitative variation interval X, and the point X is used0And (4) showing.
And 7: and (4) determining the attribution of the colonial area, wherein the attribution property of the colonial area is determined by two factors of the empire group strength and the lateral distance. The specific judgment process is as follows:
(1) is calculated as x with respect to point x0Left side distance p of sum interval Xl(x，x0X) and the right side distance pr(x，x0，X)。
(2) Calculating an attribution coefficient:
kl＝|pl(x，x0，X)|+·T.Cl
kr＝|pl(x，x0，X)|+·T.Cr
wherein, the general ∈ (0, 1) is the dominant influence parameter of the potential force.
(3) Judging attribution properties: that attribution is large in nature, and the colonial place x belongs to that empire. I.e. if kr＜klIf the place x belongs to the left empire country; if k isr≥klThen colonial x belongs to the left empire.
And 8: the colonial place moves towards the empire: when the empire nations are formed, the colonial countries approach the empire along a direction that points toward the empire to which they belong. In the process, a revolution is generated in some countries, that is, the location of the colonial randomly changes. The colonial place approaches its empire as follows:
in order to move the colonists from all directions to the empire of which they belong, and to enhance the convergence of the empire to the global optimum, two random parameters x, θ are established which are subject to a normal distribution:
x～N(d，ρ)
θ～N(0，γ)
where d is the distance between the colonial area and the empire, β is a number greater than 1, β > 1 causes the colonial area to move from all directions to its empire, γ is typically π/4.
And step 9: competition of empire group: the competition process of empire nations occurs between empire nations, as each empire nations attempts to occupy and control the colonists of the other empire nations. Through competition, a powerful empire group is stronger, and a weak empire group is weaker. In the ICA algorithm, the weakest one of the weakest empire nations will be occupied by other empire nations by competition. Each empire state group is likely to occupy the weakest country. The magnitude of this probability is defined by:
wherein N.T. CnOf the nth empire groupThe relative cost function value is defined as follows:
vector P:
vector R is the same specification vector as vector P:
vector D has the following arrival:
D＝P-R
the empire nations group corresponding to the largest element in vector D will occupy the weakest colonial country.
Step 10: death in the colonial countries: in the infringement process of the empire, there is a death in the colonial countries.
In the workshop scheduling problem, the death of the colonial area indicates that the order processing is finished. At this time, the number of colonists will decrease.
k is the number of deceased colonists, and e is the e-th time of social evolution.
Step 11: creation of new colonial countries: in the social evolution process, new colonial sites will be produced.
In the workshop scheduling problem, the generation of new colonial sites is an increasing number of orders. At this time, the number of colonists increases.
h is the number of colonists increased and e is the e-th time of social evolution.
Step 12: death of the vulnerable empire: in empire competition, an empire group who loses its strength will die and its own colonial area will be disbursed by other empire groups. In the workshop scheduling problem, machine faults and machine completion can be expressed by empire death, and the number of empires is reduced when the empire death is finished.
l is the number of deceased empires and e is the social evolution e-th time.
Step 13: creation of the new empire: in empire competition, new empires are created. In the workshop scheduling problem, adding a new machine is the generation of a new empire.
g is the number of newly added empires, and e is the e-th time of social evolution.
Step 14: and (3) calculating the survival rate of the empire: plotted by machine utilization ρ, defined as follows:
e is the social evolution e.
Step 15: and finally, reserving the final rest empire states and taking the fitness value as an optimal solution.
Claims (3)
1. The invention discloses an empire and national meaning competition algorithm based on a real variable function side distance, which relates to the field of job shop scheduling,
in particular to a method for solving the scheduling problem of a job shop by using an algorithm, which is characterized in that: the steps of the algorithm are as follows:
step 1: initializing empire sense competition algorithm parameters: initializing the number of countriesEmpire nationalityCountry of colonial landWherein empire country is represented by machine and colonial country is represented by homework
Step 2: calculating the relative strength of the empire: handling capacity by machineCome to depict
Wherein Ncn represents the number of jobs that can be processed by a machine Mn, Mcn represents the number of machines that can process Ncn jobs
And step 3: calculating the potential of the empire nationality: the strength of the force in the nth empire country is defined as:
in the formula,run time at nth machine for ith job, i.e. cost value
And 4, step 4: initializing empire nationality groups: allocating a different number of colonial countries to the empire nations according to the empire's powers, the greater the empire's powers, the more colonial countries the empire has, the empire and its owned colonial sites forming an empire group, in the workshop scheduling problem the number of colonial sites the empire has equal to the number of jobs actually handled by the machine, so that the colonial site allocation method is as follows:
in the formula,representing the colonial place owned by the nth empire,
and 5: calculating the total force of the empire group: the total force of an empire nationality group comprises two parts, one part is the force of the empire nationality and the other part is the force of its own colonial countries, in which the force of the empire nationality has a greater influence on the force, and therefore the total force of an empire nationality is calculated as follows:
in the formula,is the total cost function value of the nth empire group,the value of the cost function for the nth empiric country,the cost function value of the dominating place of the empire group, namely the running time of a certain machine operated in the workshop scheduling problem,is a real number, taken in general
Step 6: calculating the advantages of empire geographic positions: the method adopts the side distance based on the real variable function to measure the size of the occupation advantage of the geographical positions of two empires occupying the same colonial area
And 7: determining the attribution of the colonial area, wherein the attribution property of the colonial area is determined by two factors of the forces and the lateral distances of the empire nationality group
And 8: the colonial place moves towards the empire: when the empire nations are formed, the colonial countries approach the empire nations in a direction towards their belonged empire, in the process, part of the countries revolutionize, i.e. the colonial countries randomly change their position, in the following way:
in order to move the colonial area from all directions to the empire of its owner and to enhance the convergence of the empire to a global optimum, two random parameters are set which are subject to a normal distribution：
Wherein d is the distance between the colonial area and the empire,is a number greater than 1 and is,the colonial country can move from all directions to eight directions,generally get
And step 9: competition of empire group: the process of empire-oriented competition occurs between empire nations, because each empire nations tries to occupy and control the colonial sites of the other empire nations, by competition making the strong empire nations stronger and the weaker empire nations weaker, in the ICA algorithm the weakest one of the empire nations will be occupied by the other empire nations by competition, each empire nations likely to occupy the weakest country, the magnitude of this probability being defined by the following equation:
in the formula,the value of the relative cost function for the nth empire group is defined as follows:
vector P:
vector R is the same specification vector as vector P:
vector D has the following arrival:
the empire nationality corresponding to the largest element in vector D will occupy the weakest colonial country
Step 10: death in the colonial countries: in the infringement process of the empire, there is a death in the colonial countries
In the workshop scheduling problem, the death of the colonists indicates that the order processing is finished, and at the moment, the number of colonists is reduced
k is the number of deceased colonists and e is the e-th time of social evolution
Step 11: creation of new colonial countries: in the social evolution process, new colonial areas are generated
In the workshop scheduling problem, the generation of new colonial sites is greatly increased, and at the same time, the number of colonial sites is increased
h is the number of colonists increased, e is the e-th time of social evolution
Step 12: death of the vulnerable empire: in the competition of empire, the empire group losing the potency will die, and its owned colonial place will be divided by other empire groups, in the workshop scheduling problem, the machine failure and machine completion can be represented by empire die of empire, and empire die, so that the number of empires is reduced
l is the number of empires reduced and e is the e-th time of social evolution
Step 13: creation of the new empire: in the empire competition, a new empire is generated, and in the workshop scheduling problem, adding a new machine is the generation of the new empire
g is the number of newly added empires, e is the e-th time of social evolution
Step 14: and (3) calculating the survival rate of the empire: utilization rate of machineTo depict, the following definitions are:
e is the social evolution e.
Step 15: and finally, reserving the final rest empire states and taking the fitness value as an optimal solution.
2. The empire and imperial competition algorithm based on side distances of real variable functions as claimed in claim 1, wherein said algorithm is applied to a real variable function
The method comprises the following steps: the step 6 of calculating the empire geographical position dominance problem specifically comprises the following steps:
step 6: calculating the advantages of empire geographic positions: the method adopts the side distance based on the real variable function to measure the advantages of two empires occupying the same colonial area, the empire with larger advantages has the opportunity to occupy the colonial area, and the specific implementation mode is as follows:
the positional relationship between the empire country and the colonial country is shown in FIG. 2
For the attribution of any one colonial area, the dominance of the colonial area is determined by calculating the size of the dominance of the two empires nearest to the colonial area, the dominance empire is entitled to own the colonial area, the colonial area with relatively small dominance will lose the colonial area, the size of the dominance is measured by the lateral distance in a real variable function, and the summary of the dominance is developed:
definition 1: given intervalIf, ifBalance of
Is x with respect to a pointLeft side distance of interval X, noted
Definition 2: given intervalIf, ifBalance of
Is x with respect to a pointRight side distance of the sum interval X, is recorded as
In the job-shop scheduling problem, the constant quality change interval isMeaning that a point X is the position of a colonial area, and two empires relatively close to the colonial area X are within a quality change interval X, using the pointAnd (4) showing.
3. The empire state-based competition algorithm for laterals based on real variable functions as claimed in claim 1, wherein:
in the step 7, the attribution of the colonial area is determined by the following specific judgment process:
calculated as x with respect to a pointLeft side distance of the sum interval XAnd right side distance
Calculating an attribution coefficient:
wherein,for influence of force dominance on the parameters, in general
(3) Judging attribution properties: that attribution is of a large nature, and the colonial place x is attributed to that empire, i.e., ifIf the place x belongs to the left empire country; if it isThen colonial x belongs to the left empire.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108091384A (en) * | 2017-11-09 | 2018-05-29 | 南京耐久软件科技有限公司 | A kind of medical image processing system based on micro services frame |
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