CN104360660B - Based on the Extrusion Process of Aluminum Alloy Profile workshop energy optimization dispatching method of ant group algorithm - Google Patents

Abstract

The invention discloses a kind of aluminium section bar car based on ant group algorithm extruding workshop energy optimization dispatching method, the present invention by abstract for Extrusion Process of Aluminum Alloy Profile Workshop Production scheduling process be a kind of aniso-Parallel Machine Scheduling Problems considering time difference electricity price extremely energy consumption, on basis by the analysis to this type of scheduling problem, a kind of ant colony optimization algorithm based on iterative calculating is proposed, ant realizes the scheduling of machine and workpiece through " machine-workpiece-machine " iterative mode, decrease traditional ant group algorithm machine and workpiece are dispatched separately bring solve error.

Description

Based on the Extrusion Process of Aluminum Alloy Profile workshop energy optimization dispatching method of ant group algorithm

Technical field

The present invention relates to workshop energy optimization dispatching technique, particularly relate to a kind of aluminium section bar car based on ant group algorithm extruding workshop energy optimization dispatching method.

Background technology

In reality is manufactured, the machine (aniso-parallel machine) of different efficiency often runs simultaneously, and this formulates to the production schedule and brings great difficulty.Therefore, under guarantee enterprise normal existence condition, reducing the energy resource consumption of aniso-parallel machine production run and reduce production cost, is one of key problem of manufacturing industry concern.Particularly with in Extrusion Process of Aluminum Alloy Profile workshop, the rock gas that the consumption of Extrusion Process of Aluminum Alloy Profile need of production is a large amount of and electricity, belong to high energy consumption manufacture process. there is peak period and low peak period in electric power supply, namely so-called " peak, paddy, flat ", it is the power price (time difference electricity price) of different time sections shown in Fig. 1, utilize the mistiming plan of arranging production, the scheduling of production of low ebb phase of increasing electric power can reduce energy loss effectively. during this external extruding is produced, just can close after the complete all aluminium bars of machine pusher, midway can not be shut down, therefore when extruder terminates the extruding of a collection of product, and fail new aluminium bar when entering, very high unloaded cost can be caused.In actual production, usually new second-hand machine uses together, and the production efficiency of machine differs, and the power surges phase high new engine of efficiency of arranging production is produced, and electric power low ebb phase inefficient second-hand machine of then can arranging production is produced to reach energy-conservation object.

But need in actual production consider processing deadline and workpiece drag time phase, minimize deadline or the time phase of dragging often with the loss of machine energy consumption for cost, for the scheduling scheme of 3 workpiece, 1 machine, process time of workpiece, the time of reaching and time of delivery are as shown in table 1, and machine operation energy consumption and unit interval standby energy consumption are respectively 0.5kwh/h and 1kwh/h.The machine energy consumption of different scheduling schemes and deadline are as shown in Figure 2.

Process time of table 1. workpiece, the time of reaching and time of delivery

The people such as Tang Wan He (Tang Wan and, Yang Haidong, Li Zhantao, Deng. consider energy consumption cost and the non-equally parallel machine scheduling dragging current cost. software, 2014,35 (3): 52-57.) with sulfurizing rubber tyre workshop for research background, propose a class and consider power consumption constraint, adjust problem with energy consumption cost and the non-equally parallel machine dragging the weighted sum of current cost minimum for regulation goal, and adopt the heuritic approach based on Optimized Operation rule, the heuritic approach based on energy optimization and combination heuritic approach to carry out problem solving respectively.

The scheduling problem of workpiece time of arrival is np hard problem, according to complexity theory, and R _m| R _i, (M ₁, M ₂..., M _m) | E _minr _m| (M ₁, M ₂... M _m), ST _sd| E _minproblem is also that NP is difficult. for np hard problem, ant colony optimization algorithm is current one of most efficient scheduling algorithm. in order to reduce the complicacy solved, separate structure be generally divided into two benches: the first stage ant select certain machine as processing machine, subordinate phase ant selects certain workpiece to process on this machine, a two benches of ant is sought footpath and is represented machine choice work pieces process, and ant repeatedly two benches seeks footpath until all workpiece are scheduled.The supposed premise of the constructing plan of this two stage solution is: workpiece drags the energy consumption cost of current cost and machine to be independently.But as shown in Figure 2, drag current cost sub-goal and machine energy consumption cost sub-goal and dependent, but connect each other, minimize and drag current cost often to sacrifice machine energy consumption for target (see Fig. 2 scheme 1, scheme 2), simply two sub-goals are carried out separately pheromones search and algorithm performance can be caused to decline.

Summary of the invention

In view of this, fundamental purpose of the present invention is to provide a kind of aluminium section bar car based on ant group algorithm to extrude workshop energy optimization dispatching method, by using the method can draw the optimum solution of Extrusion Process of Aluminum Alloy Profile workshop least energy consumption, thus can the power consumption in arranged rational Extrusion Process of Aluminum Alloy Profile workshop.

To achieve these goals, technical scheme of the present invention is achieved in that

Based on the aluminium section bar car extruding workshop energy optimization dispatching method of ant group algorithm, described Optimization Scheduling comprises the following steps:

Step 1: build Extrusion Process of Aluminum Alloy Profile workshop energy consumption scheduling mathematic model, determine Extrusion Process of Aluminum Alloy Profile workshop least energy consumption objective function E _min, described objective function E _mincomprise two sub-goals: workpiece drags the energy consumption cost of current cost, machine; Objective function E _minas shown in formula (1.1):

$E_{Min}=w_1\underset{i=1}{\overset{n}{\Σ}}\max \left(0,d_i-c_i\right)\·p_{i1}+w_2(\underset{t=1}{\overset{c_{\max }}{\Σ}}f\left(t\right)\·(\underset{j=1}{\overset{m}{\Σ}}\underset{i=1}{\overset{n}{\Σ}}{X}_{ij}\·(c_i-s_i)\·p_{j2}+\underset{j=1}{\overset{m}{\Σ}}\underset{i=1}{\overset{H_j}{\Σ}}\left(s_i-c_{i-1}\right)\·p_{j3}\left)\right)---\left(1.1\right)$

This objective function should meet following condition:

$\underset{j=0}{\overset{m}{\Σ}}\underset{i=0}{\overset{n}{\Σ}}{U}_{ij}=1---\left(1.2\right)$

c _i＝s _i+t _ij·X _ij(1.3)

                     

c ₀＝0

s _i＝max{r _i,c _i-1} (1.4)

Formula (1.2) represents that workpiece can only be processed on a machine;

Formula (1.3) represents when the deadline of workpiece is by start time and machining Time dependent;

Formula (1.4) represents that the start time of workpiece depends on the deadline of a workpiece and the time of arrival of this workpiece;

Below the parametric variable of objective function:

N: the quantity of workpiece;

M: the quantity of machine;

H _j: the piece count being arranged in processing on machine j;

W ₁: workpiece drags current cost coefficient;

W ₂: machine energy consumption cost coefficient;

R _i: each workpiece i independently time of arrival;

D _i: each workpiece i time of delivery;

T _ij: machine is to the process time of workpiece;

P _i1: the unit interval of i-th workpiece drags current cost;

P _j2: the unit interval operation energy consumption cost of jth platform machine;

P _j3: the unit interval standby energy consumption cost of jth platform machine;

F (t): the power price of different time sections;

Decision-making scalar:

X _ijfor judging whether certain workpiece is processed in specified machine, if X _ij=1 represents that workpiece i processes on machine j, otherwise does not process on machine j;

Step 2: pheromones and initialization thereof

Seek footpath process according to the two benches of ant, pheromones is divided into τ j and τ ij two parts, and τ j represents the pheromones on machine Mj, and initial value is τ _j=1/M; τ ij represents the pheromones between machine Mj and workpiece i, initial value τ ij=0;

Step 3: the structure that ant group algorithm three stage separates

First the machine j that can obtain the earliest is selected ^*, then select the workpiece i that workpiece on machine drags current cost minimum ^*, finally according to the machine j that workpiece i selects machine energy consumption cost minimum ^*; The process selected again by machine will drag current cost sub-goal and machine energy consumption cost sub-goal to connect, boosting algorithm performance; Specific as follows:

1. select machine

First the machine of Choice and process, the heuristic rule of employing is the machine that can obtain the earliest, and this can make the deadline of workpiece minimum; In order to increase search randomness, given parameters g _m0∈ [0,1] and random number g _mif, g _m< g _m0, ant selects the machine that can obtain the earliest, otherwise the probability distribution J pressing formula (1.6) selects machine j ^*:

$j^{*}=\left\{\begin{array}{ccc}\underset{1\&le;j\&le;m}{\min }{q}_j,& if& g_m<g_{m0}\\ J,& otherwise& \end{array}\right.---\left(1.5\right)$

$J=\frac{1/p_j}{\underset{j=1}{\overset{m}{\&Sigma;}}1/p_j},j=1,2,...,m---\left(1.6\right)$

2. select workpiece

According to Number of Jobs, use taboo list tabu _k(k=1,2 ..., n) record the workpiece selected by current ant, taboo list makes dynamic conditioning along with ant seeks footpath. and given parameters g _i0∈ [0,1] and random number g _iif, g _i< g _i0, ant selects the minimum workpiece dragging current cost, otherwise the probability distribution I pressing formula (1.8) selects workpiece i ^*:

$i^{*}=\left\{\begin{array}{ccc}\underset{i}{\max }\left({\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}\right),& if& g_i<g_{i0}\\ I,& otherwise& \end{array}\right.---\left(1.7\right)$

$I=\left\{\begin{array}{ccc}\frac{{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}}{\underset{l\&Element;\mathrm{\&Psi;}}{\&Sigma;}{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{lj}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{lj}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}},& if& i\&Element;\mathrm{\&Psi;}\\ 0,& otherwise& \end{array}\right.---\left(1.8\right)$

${\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)=\frac{1}{p_{i1}\&times;\max \{q_{j^{*}}+t_{{\mathrm{ij}}^{*}}-d_i,0\}+1}---\left(1.9\right)$

heuristic function, reflection machine j ^*upper processing work i drags current cost, and the minimum workpiece of prioritizing selection integrated cost is produced on this machine; α is information heuristic factor, reflects the impact that ant group motion process accumulating information is selected current ant; β expects heuristic factor, represents the attention degree of heuristic information in ant is selected;

3. select machine

For workpiece i ^*, the machine j that can obtain the earliest ^*might not be process the minimum machine of this workpiece energy consumption, therefore adopt the method for iteration, again according to machining energy consumption minimum selection machine j ^*, shown in (2.0):

$j^{**}=\arg min\{\underset{t=s_{i^{*}}}{\overset{c_{i^{*}}}{\&Sigma;}}f\left(t\right)\&CenterDot;p_{j2}\&CenterDot;(c_{i^{*}}-s_{i^{*}})\}---\left(2.0\right)$

< workpiece i ^*, machine j ^*> is the result that ant once seeks footpath, namely selects workpiece i ^*at machine j ^*on process; Ant carries out seeking footpath repeatedly, until all work pieces process complete, namely the job sequence of workpiece is the sequence of separating;

Step 4: Pheromone update

After ant has traveled through all workpiece, need to carry out adjustment k to current quantity of information of seeking in the result in footpath, adjusted according to formal style (2.1) below:

τ _ij(t)＝(1-ρ)·τ _ij(t)+Δτ _ij(t)

Wherein, 1-ρ is that pheromones remains the factor, and what represent current iteration seeks footpath result seeks footpath influence degree to whole ant group, Δ τ _ijt () represents that pheromones increment .Q represents pheromones intensity in current iteration, affects convergence of algorithm speed to a certain extent, what E (t) represented ant current iteration seeks footpath result.

Aluminium section bar car based on ant group algorithm extruding workshop provided by the invention energy optimization dispatching method, has following technical advantage:

The present invention by abstract for Extrusion Process of Aluminum Alloy Profile Workshop Production scheduling process for a kind of consider time difference electricity price extremely energy consumption aniso-Parallel Machine Scheduling Problems, on basis by the analysis to this type of scheduling problem, a kind of ant colony optimization algorithm based on iterative calculating is proposed, ant realizes the scheduling of machine and workpiece through " machine-workpiece-machine " iterative mode, decrease traditional ant group algorithm machine and workpiece are dispatched separately bring solve error.

Accompanying drawing explanation

Fig. 1 is the power price distribution plan of different time sections;

Fig. 2 be different scheduling scheme machine total energy consumption, drag time phase and deadline comparison diagram;

Fig. 3 is of the present invention based on the aluminium section bar car extruding workshop energy optimization dispatching method process flow diagram based on ant group algorithm;

Fig. 4 is the process flow diagram of the structure that ant group algorithm three stage separates

Embodiment

Below in conjunction with drawings and the specific embodiments, detailed, complete description is carried out to technical scheme of the present invention and application principle; described by obvious embodiment is only the part of technical solution of the present invention and application principle; any amendment that those skilled in the art is non-to make through creative work, equivalently to replace and improvement etc., all should be included within protection scope of the present invention.

See Fig. 3, for the present invention is based on the aluminium section bar car extruding workshop energy optimization dispatching method process flow diagram based on ant group algorithm, specifically comprise the following steps,

Step 1: build Extrusion Process of Aluminum Alloy Profile workshop energy consumption scheduling mathematic model, determine Extrusion Process of Aluminum Alloy Profile workshop least energy consumption objective function E _min, described objective function E _mincomprise two sub-goals: workpiece drags the energy consumption cost of current cost, machine; Objective function E _minas shown in formula (1.1):

$E_{Min}=w_1\underset{i=1}{\overset{n}{\&Sigma;}}\max \left(0,d_i-c_i\right)\&CenterDot;p_{i1}+w_2(\underset{t=1}{\overset{c_{\max }}{\&Sigma;}}f\left(t\right)\&CenterDot;(\underset{j=1}{\overset{m}{\&Sigma;}}\underset{i=1}{\overset{n}{\&Sigma;}}{X}_{ij}\&CenterDot;(c_i-s_i)\&CenterDot;p_{j2}+\underset{j=1}{\overset{m}{\&Sigma;}}\underset{i=1}{\overset{H_j}{\&Sigma;}}\left(s_i-c_{i-1}\right)\&CenterDot;p_{j3}\left)\right)---\left(1.1\right)$

This objective function should meet following condition:

$\underset{j=0}{\overset{m}{\&Sigma;}}\underset{i=0}{\overset{n}{\&Sigma;}}{U}_{ij}=1---\left(1.2\right)$

c _i＝s _i+t _ij·X _ij(1.3)

                         

c ₀＝0

s _i＝max{r _i,c _i-1} (1.4)

Formula (1.2) represents that workpiece can only be processed on a machine;

Formula (1.3) represents when the deadline of workpiece is by start time and machining Time dependent;

Formula (1.4) represents that the start time of workpiece depends on the deadline of a workpiece and the time of arrival of this workpiece;

Below the parametric variable of objective function:

N: the quantity of workpiece;

M: the quantity of machine;

H _j: the piece count being arranged in processing on machine j;

W ₁: workpiece drags current cost coefficient;

W ₂: machine energy consumption cost coefficient;

R _i: each workpiece i independently time of arrival;

D _i: each workpiece i time of delivery;

Ti _j: machine is to the process time of workpiece;

P _i1: the unit interval of i-th workpiece drags current cost;

P _j2: the unit interval operation energy consumption cost of jth platform machine;

P _j3: the unit interval standby energy consumption cost of jth platform machine;

F (t): the power price of different time sections;

Decision-making scalar:

X _ijfor judging whether certain workpiece is processed in specified machine, if X _ij=1 represents that workpiece i processes on machine j, otherwise does not process on machine j;

Step 2: pheromones and initialization thereof

Seek footpath process according to the two benches of ant, pheromones is divided into τ j and τ ij two parts, and τ j represents the pheromones on machine Mj, and initial value is τ _j=1/M; τ ij represents the pheromones between machine Mj and workpiece i, initial value τ ij=0;

Step 3: the structure that ant group algorithm three stage separates

First the machine j that can obtain the earliest is selected ^*, then select the workpiece i that workpiece on machine drags current cost minimum ^*, finally according to the machine j that workpiece i selects machine energy consumption cost minimum ^*; The process selected again by machine will drag current cost sub-goal and machine energy consumption cost sub-goal to connect, boosting algorithm performance; Specific as follows:

1. select machine

First the machine of Choice and process, the heuristic rule of employing is the machine that can obtain the earliest, and this can make the deadline of workpiece minimum; In order to increase search randomness, given parameters g _m0∈ [0,1] and random number g _mif, g _m< g _m0, ant selects the machine that can obtain the earliest, otherwise the probability distribution J pressing formula (1.6) selects machine j ^*:

$j^{*}=\left\{\begin{array}{ccc}\underset{1\&le;j\&le;m}{\min }{q}_j,& if& g_m<g_{m0}\\ J,& otherwise& \end{array}\right.---\left(1.5\right)$

$J=\frac{1/p_j}{\underset{j=1}{\overset{m}{\&Sigma;}}1/p_j},j=1,2,...,m---\left(1.6\right)$

2. select workpiece

According to Number of Jobs, use taboo list tabu _k(k=1,2 ..., n) record the workpiece selected by current ant, taboo list makes dynamic conditioning along with ant seeks footpath. and given parameters g _i0∈ [0,1] and random number g _iif, g _i< g _i0, ant selects the minimum workpiece dragging current cost, otherwise the probability distribution I pressing formula (1.8) selects workpiece i ^*:

$i^{*}=\left\{\begin{array}{ccc}\underset{i}{\max }\left({\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}\right),& if& g_i<g_{i0}\\ I,& otherwise& \end{array}\right.---\left(1.7\right)$

$I=\left\{\begin{array}{ccc}\frac{{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}}{\underset{l\&Element;\mathrm{\&Psi;}}{\&Sigma;}{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{lj}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{lj}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}},& if& i\&Element;\mathrm{\&Psi;}\\ 0,& otherwise& \end{array}\right.---\left(1.8\right)$

${\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)=\frac{1}{p_{i1}\&times;\max \{q_{j^{*}}+t_{{\mathrm{ij}}^{*}}-d_i,0\}+1}---\left(1.9\right)$

heuristic function, reflection machine j ^*upper processing work i drags current cost, and the minimum workpiece of prioritizing selection integrated cost is produced on this machine; α is information heuristic factor, reflects the impact that ant group motion process accumulating information is selected current ant; β expects heuristic factor, represents the attention degree of heuristic information in ant is selected;

3. select machine

For workpiece i ^*, the machine j that can obtain the earliest ^*might not be process the minimum machine of this workpiece energy consumption, therefore adopt the method for iteration, again according to machining energy consumption minimum selection machine j ^*, shown in (2.0):

$j^{**}=\arg min\{\underset{t=s_{i^{*}}}{\overset{c_{i^{*}}}{\&Sigma;}}f\left(t\right)\&CenterDot;p_{j2}\&CenterDot;(c_{i^{*}}-s_{i^{*}}\left)\right\}---\left(2.0\right)$

< workpiece i ^*, machine j ^*> is the result that ant once seeks footpath, namely selects workpiece i ^*at machine j ^*on process; Ant carries out seeking footpath repeatedly, until all work pieces process complete, namely the job sequence of workpiece is the sequence of separating;

Step 4: Pheromone update

After ant has traveled through all workpiece, need to carry out adjustment k to current quantity of information of seeking in the result in footpath, adjusted according to formal style (2.1) below:

τ _ij(t)＝(1-ρ)·τ _ij(t)+Δτ _ij(t)

Wherein, 1-ρ is that pheromones remains the factor, and what represent current iteration seeks footpath result seeks footpath influence degree to whole ant group, Δ τ _ijt () represents that pheromones increment .Q represents pheromones intensity in current iteration, affects convergence of algorithm speed to a certain extent, what E (t) represented ant current iteration seeks footpath result.

In order to verify validity of the present invention, the present invention adopts and carries out emulation experiment by split-run test method (split-plot), and the factor of influence affecting algorithm performance has: t process time of machine quantity m, piece count n, workpiece _ij, workpiece r time of arrival _i, workpiece time of delivery d _iwith the ratio (ratio of unit interval machine switching on and shutting down energy consumption cost and unit interval machine standby energy consumption) of unit consumption of energy, arranging of each factor is as shown in table 2.

T process time of workpiece _ijobedience is uniformly distributed, and is designated as t _ij=U [2,30] and t _ij=U [2,50] two kinds, r time of arrival of workpiece _i, time of delivery d _ican calculate according to process time: wherein c represents the well-to-do coefficient of delivery. adopt the ratio p of unit interval production of machinery energy consumption cost and unit interval machine standby energy consumption herein _j2/ p _j3reflect machine energy consumption ratio. the unit interval drags current cost p _i1with unit interval energy consumption cost p _j2get from the random integers randi (10,1) between 1 to 10, workpiece drags current cost coefficient w ₁with machine energy consumption cost coefficient w ₂get from the random number between 0 to 1 and w ₁+ w ₂=1. form 24 kinds of simulation example altogether according to the factor of influence of table 2. and time difference electricity price f (t) represents with following formula:

$f\left(t\right)=\left\{\begin{array}{cc}5& 24n-3\&le;t<24n+7\\ 8& 24n+7\&le;t<24n+11\\ 10& 24n+11\&le;t<24n+17\\ 8& 24n+17\&le;t<24n+21\end{array}\right.---\left(2.2\right)$

Factor of influence in table 2. simulation example

The present invention by abstract for Extrusion Process of Aluminum Alloy Profile Workshop Production scheduling process for a kind of consider time difference electricity price extremely energy consumption aniso-Parallel Machine Scheduling Problems, on basis by the analysis to this type of scheduling problem, a kind of ant colony optimization algorithm based on iterative calculating is proposed, ant realizes the scheduling of machine and workpiece through " machine-workpiece-machine " iterative mode, decrease traditional ant group algorithm machine and workpiece are dispatched separately bring solve error.

Claims (1)

1., based on the Extrusion Process of Aluminum Alloy Profile workshop energy optimization dispatching method of ant group algorithm, it is characterized in that, described Optimization Scheduling comprises the following steps:

Step 1: build Extrusion Process of Aluminum Alloy Profile workshop energy consumption scheduling model, determine Extrusion Process of Aluminum Alloy Profile workshop least energy consumption objective function E _min, described objective function E _mincomprise two sub-goals: workpiece drags the energy consumption cost of current cost, machine; Objective function E _minas shown in formula (1.1):

$E_{Min}=w_i\underset{i=1}{\overset{n}{\&Sigma;}}\max (0,d_i-c_i)\&CenterDot;p_{i1}+w_2(\underset{t=1}{\overset{c_{\max }}{\&Sigma;}}f\left(t\right)\&CenterDot;(\underset{j=1}{\overset{m}{\&Sigma;}}\underset{i=1}{\overset{n}{\&Sigma;}}{X}_{ij}\&CenterDot;(c_i-s_1)\&CenterDot;p_{j2}+\underset{j=1}{\overset{m}{\&Sigma;}}\underset{i=1}{\overset{H_j}{\&Sigma;}}(s_i-c_{i-1})\&CenterDot;p_{j3}\left)\right)---\left(1.1\right)$

This objective function should meet following condition:

$\underset{j=0}{\overset{m}{\&Sigma;}}\underset{i=0}{\overset{n}{\&Sigma;}}{U}_{ij}=1---\left(1.2\right)$

c _i＝s _i+t _ij·X _ij

(1.3)

c ₀＝0

s _i＝max{r _i,c _i-1} (1.4)

Formula (1.2) represents that workpiece can only be processed on a machine;

Formula (1.3) represents when the deadline of workpiece is by start time and machining Time dependent;

Formula (1.4) represents that the start time of workpiece depends on the deadline of a workpiece and the time of arrival of this workpiece;

Below the parametric variable of objective function:

N: the quantity of workpiece;

M: the quantity of machine;

H _j: the piece count being arranged in processing on machine j;

W ₁: workpiece drags current cost coefficient;

W ₂: machine energy consumption cost coefficient;

R _i: each workpiece i independently time of arrival;

D _i: each workpiece i time of delivery;

T _ij: machine is to the process time of workpiece;

P _i1: the unit interval of i-th workpiece drags current cost;

P _j2: the unit interval operation energy consumption cost of jth platform machine;

P _j3: the unit interval standby energy consumption cost of jth platform machine;

F (t): the power price of different time sections;

Decision-making scalar:

X _ijfor judging whether certain workpiece is processed in specified machine, if X _ij=1 represents that workpiece i processes on machine j, otherwise does not process on machine j;

Step 2: pheromones and initialization thereof

Seek footpath process according to the two benches of ant, pheromones is divided into τ j and τ ij two parts, and τ j represents the pheromones on machine Mj, and initial value is τ _j=1/M; τ ij represents the pheromones between machine Mj and workpiece i, initial value τ ij=0;

Step 3: the structure that ant group algorithm three stage separates

First the machine j that can obtain the earliest is selected ^*, then select the workpiece i that workpiece on machine drags current cost minimum ^*, finally according to the machine j that workpiece i selects machine energy consumption cost minimum ^*; The process selected again by machine will drag current cost sub-goal and machine energy consumption cost sub-goal to connect, boosting algorithm performance; Specific as follows:

Select machine

First the machine of Choice and process, the heuristic rule of employing is the machine that can obtain the earliest, and this can make the deadline of workpiece minimum;

In order to increase search randomness, given parameters g _m0∈ [0,1] and random number g _mif, g _m< g _m0, ant selects the machine that can obtain the earliest, otherwise the probability distribution J pressing formula (1.6) selects machine j ^*:

$j^{*}=\{\begin{array}{c}\begin{array}{ccc}\underset{1\&le;j\&le;m}{\min }{q}_j,& if& g_m<g_{m0}\end{array}\\ \begin{array}{cc}J,& otherwise\end{array}\end{array}---\left(1.5\right)$

$\begin{array}{cc}J=\frac{1/p_j}{\underset{j=1}{\overset{m}{\&Sigma;}}1/p_j}& j=1,2,...,m\end{array}---\left(1.6\right)$

Select workpiece

According to Number of Jobs, use taboo list tabu _k(k=1,2 ..., n) record the workpiece selected by current ant, taboo list makes dynamic conditioning along with ant seeks footpath. and given parameters g _i0∈ [0,1] and random number g _iif, g _i< g _i0, ant selects the minimum workpiece dragging current cost, otherwise the probability distribution I pressing formula (1.8) selects workpiece i ^*:

$i^{*}=\left\{\begin{array}{c}\begin{array}{ccc}\underset{i}{\max }({\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&alpha;}}\&CenterDot;{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}),& if& g_i<g_{i0}\end{array}\\ \begin{array}{cc}I,& otherwise\end{array}\end{array}\right.---\left(1.7\right)$

$I=\left\{\begin{array}{c}\begin{array}{ccc}\frac{{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^a.{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\&CenterDot;\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}}{\underset{l\&Element;\mathrm{\&Psi;}}{\&Sigma;}{\&lsqb;{\mathrm{\&tau;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^a.{\&lsqb;{\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)\&rsqb;}^{\mathrm{\&beta;}}},& if& i\&Element;\mathrm{\&Psi;}\end{array}\\ \begin{array}{cc}0,& otherwise\end{array}\end{array}\right.---\left(1.8\right)$

${\mathrm{\&eta;}}_{{\mathrm{ij}}^{*}}\left(t\right)=\frac{1}{p_{i1}\&times;\max \{q_{j^{*}}+t_{{\mathrm{ij}}^{*}}-d_i,0\}+1}---\left(1.9\right)$

heuristic function, reflection machine j ^*upper processing work i drags current cost, and the minimum workpiece of prioritizing selection integrated cost is produced on this machine; α is information heuristic factor, reflects the impact that ant group motion process accumulating information is selected current ant; β expects heuristic factor, represents the attention degree of heuristic information in ant is selected;

Select machine

For workpiece i ^*, the machine j that can obtain the earliest ^*might not be process the minimum machine of this workpiece energy consumption, therefore adopt the method for iteration, again according to machining energy consumption minimum selection machine j ^*, shown in (2.0):

$j^{**}=\mathrm{argmin}\{\underset{t=s_{i^{*}}}{\overset{c_{i^{*}}}{\&Sigma;}}f\left(t\right)\&CenterDot;p_{j2}.(c_{i^{*}}-s_{i^{*}})\}---\left(2.0\right)$

< workpiece i ^*, machine j ^*> is the result that ant once seeks footpath, namely selects workpiece i ^*at machine j ^*on process;

Ant carries out seeking footpath repeatedly, until all work pieces process complete, namely the job sequence of workpiece is the sequence of separating;

Step 4: Pheromone update

After ant has traveled through all workpiece, need to carry out adjustment k to current quantity of information of seeking in the result in footpath, adjusted according to formal style (2.1) below:

τ _ij(t)＝(1-ρ)·τ _ij(t)+Δτ _ij(t)

Wherein, 1-ρ is that pheromones remains the factor, and what represent current iteration seeks footpath result seeks footpath influence degree to whole ant group, Δ τ _ijt () represents that pheromones increment .Q represents pheromones intensity in current iteration, affects convergence of algorithm speed to a certain extent, what E (t) represented ant current iteration seeks footpath result.