CN107844935A - A kind of vehicle scheduling and paths planning method based on environmental protection and cost savings - Google Patents

A kind of vehicle scheduling and paths planning method based on environmental protection and cost savings Download PDF

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Publication number
CN107844935A
CN107844935A CN201710923857.4A CN201710923857A CN107844935A CN 107844935 A CN107844935 A CN 107844935A CN 201710923857 A CN201710923857 A CN 201710923857A CN 107844935 A CN107844935 A CN 107844935A
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msub
sigma
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CN107844935B (en
Inventor
王长园
艾毅
郭勇
付铁强
颜燕
张梦杰
李勇
孙龙
孙一龙
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China Automotive Technology and Research Center Co Ltd
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China Automotive Technology and Research Center Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/083—Shipping
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/083—Shipping
    • G06Q10/0835—Relationships between shipper or supplier and carriers
    • G06Q10/08355—Routing methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/10—Services
    • G06Q50/26—Government or public services

Abstract

The invention provides a kind of vehicle scheduling based on environmental protection and cost savings and paths planning method, with fuel consumption, urea consumption and the minimum object of planning of pollutant discharge amount, the integer programming model with time window is established.The home-delivery center's vehicle fleet size of the invention inputted by enterprise and model, the loading capacity of vehicle, home-delivery center and Customer Location information, the time requirement of goods delivery, the supply and demand and the priority of goods delivery of each point, using fuel consumption, urea consumption and pollutant discharge amount as target, for enterprise's vehicle scheduling scheme reasonable in design, so that the cost of transportation of enterprise is reduced, reduce the pollution to environment simultaneously, be advantageous to the development of sustainable society.

Description

A kind of vehicle scheduling and paths planning method based on environmental protection and cost savings
Technical field
The invention belongs to logistlcs technology field, more particularly, to a kind of vehicle scheduling based on environmental protection and cost savings and road Footpath planing method.
Background technology
Vehicle scheduling and path planning problem are a key technologies of Enterprise Transportation, pass through the different demands according to client And time requirement, arrangement and route planning are rationally efficiently scheduled to enterprise's vehicle, cost can be reduced, improves Service Quality Amount.And as in recent years, the attention of Environmental protection steps up, the common objective of comprehensive government and enterprise is following enterprise Industry develops basic.Therefore, vehicle scheduling and route planning method based on cost and environment saving are a kind of scheduling in forward position Method, it is following development trend.At home, many scholars carried out studying and inquiring into vehicle dispatching problem, but mostly Number scholars are the cost minimizations that Enterprise Transportation is only realized from the angle of enterprise.
The arrival of Internet era so that the research based on big data achieves quick development.Traditional vehicle scheduling, Simply consider the distance between two clients or running time, and have ignored the influence of road conditions and different automobile types.This scheduling Problems be present in problem：First, the fuel consumption of automobile is not only relevant with vehicle, also has with the road conditions on this section of road Close, including speed, acceleration and deceleration, climb and fall etc..If only considering, distance is most short, is but not necessarily fuel consumption minimum.Secondly, This scheduling method does not consider the influence of pollutant discharge amount.Finally, the cost of urea is also related to the cost of transport, also should It is one of factor that transport needs consider.
The content of the invention
In view of this, the present invention is directed to propose a kind of vehicle scheduling and path planning side based on environmental protection and cost savings Method, pass through vehicle scheduling scheme reasonable in design so that the cost of transportation of enterprise is reduced, while reduces the pollution to environment.
To reach above-mentioned purpose, the technical proposal of the invention is realized in this way：
A kind of vehicle scheduling and paths planning method based on environmental protection and cost savings, are consumed with fuel consumption, urea Amount and the minimum object of planning of pollutant discharge amount establish the integer programming model with time window, wherein
For mesh Scalar functions, Part I are that weight is multiplied by the value after the standardization of fuel consumption, and Part II is multiplied by for expression weight Value after the processing of urea consumption standardization, Part III are that weight is multiplied by the value after pollutant discharge amount standardization, with Three integrates minimum target.
Further, the constraints of the model is
ETjk＜=tjk＜=LTjkJ ∈ { 1,2 ..., N } (7)
Km＞=0 (14)
Wherein, formula (1) represents that the vehicle number that each home-delivery center sends is no more than vehicle fleet；
Formula (2) represents that vehicle from home-delivery center and returns to home-delivery center；
Formula (3) and (4) represent that each client can only be by a car service once；
Formula (5) represents that vehicle can not be by home-delivery center to home-delivery center；
Formula (6) represents that vehicle has into having；
Formula (7) and (8) represent the time windows constraints of goods；
Formula (9) and (10) represent the loading capacity constraint of vehicle；
Formula (11) represents the dispatching of goods or the priority restrictions of consolidating the load；
Formula (12) represents 0-1 variable bounds；
Formula (13), (14) and (15) represents the dead weight right and wrong of the useful load of car, home-delivery center's vehicle number and car Negative；
Wherein, N represents the set of client；
M represents the set of home-delivery center；
KmRepresent home-delivery center m vehicle number；
β1,β2And β3The weight of fuel consumption, urea consumption and pollutant discharge amount is represented respectively；
It is a 0-1 variable, if home-delivery center m vehicle k, from client i to client j, the value is 1, is otherwise 0；
Represent home-delivery center m vehicle k from client i to client j fuel consumption；
FminRepresent fuel consumption minimum in all feasible programs；
FmaxRepresent fuel consumption maximum in all feasible programs；
Represent urea consumptions of the home-delivery center m vehicle k from client i to client j；
UminRepresent urea consumption minimum in all feasible programs；
UmaxRepresent urea consumption maximum in all feasible programs；
Represent home-delivery center m vehicle k from client i to client j pollutant emission；
EminRepresent pollutant discharge amount minimum in all feasible programs；
EmaxRepresent pollutant discharge amount maximum in all feasible programs；
tjkRepresent that vehicle k reaches client j time；
ETjkRepresent the time requirement lower limit of j point goods；
LTjkRepresent the time requirement upper limit of j point goods；
ctiRepresent residence time of the vehicle in i points；
Represent cargo dead-weights of the home-delivery center m vehicle k during client j is driven to from client i；
Represent home-delivery center m vehicle k dead weight；
qjRepresent the demand of client's j points, pjRepresent the supply of client's j points.
Further, in addition to object function it is standardized, Fmin,Fmax,Umin,Umax,Emin,EmaxRepresent Be this programme path all feasible programs in fuel consumption, the minimum value of urea consumption and pollutant discharge amount and Maximum, in the case where constraints is constant, respectively using this following 6 formula as target, calculated, then by calculated value Object function is input to, optimizes solution：
Relative to prior art, a kind of vehicle scheduling and path planning based on environmental protection and cost savings of the present invention Method has the advantage that：The present invention passes through the home-delivery center's vehicle fleet size and model of enterprise's input, the loading capacity of vehicle, dispatching Center and Customer Location information, the time requirement of goods delivery, the supply of each point and demand and goods delivery it is preferential Level, it is enterprise's vehicle scheduling scheme reasonable in design using fuel consumption, urea consumption and pollutant discharge amount as target, So that the cost of transportation of enterprise is reduced, while reduce the pollution to environment, be advantageous to the development of sustainable society.
Brief description of the drawings
The accompanying drawing for forming the part of the present invention is used for providing a further understanding of the present invention, schematic reality of the invention Apply example and its illustrate to be used to explain the present invention, do not form inappropriate limitation of the present invention.In the accompanying drawings：
Fig. 1 is a kind of vehicle scheduling and paths planning method based on environmental protection and cost savings described in the embodiment of the present invention Schematic diagram.
Embodiment
It should be noted that in the case where not conflicting, the feature in embodiment and embodiment in the present invention can phase Mutually combination.
Describe the present invention in detail below with reference to the accompanying drawings and in conjunction with the embodiments.
The present invention is envisaged in the system of government regulation vehicle discharge, considers the common benefit of government and enterprise, with Fuel consumption, urea consumption and the minimum object of planning of pollutant discharge amount, establish the integer programming mould with time window Type.Wherein, the weight relationship of three can determine according to significance level or emphasis.
Above-mentioned formula is object function, and Part I represents that weight is multiplied by the value after the standardization of fuel consumption, Part II represents the value that weight is multiplied by after the processing of urea consumption standardization, and Part III represents that weight is multiplied by pollutant emission The value after standardization is measured, minimum target is integrated with three.
It is the constraints of model below：
ETjk＜=tjk＜=LTjkJ ∈ { 1,2 ..., N } (7)
Km＞=0 (14)
Wherein, formula (1) represents that the vehicle number that each home-delivery center sends is no more than vehicle fleet.Formula (2) represents vehicle From home-delivery center and return to home-delivery center.Formula (3) and (4) represent that each client can only be by a car service once.It is public Formula (5) represents that vehicle can not be by home-delivery center to home-delivery center.Formula (6) represents that vehicle has into having.Formula (7) and (8) table Show the time windows constraints of goods.Formula (9) and (10) represent the loading capacity constraint of vehicle.Formula (11) represent goods dispatching or The priority restrictions of consolidating the load.Formula (12) represents 0-1 variable bounds.Formula (13), (14) and (15) represents the useful load of car, matched somebody with somebody It is non-negative to send the dead weight of central vehicle number and car.
Wherein, N represents the set of client, and M represents the set of home-delivery center, KmRepresent home-delivery center m vehicle number.β1,β2 And β3The weight of fuel consumption, urea consumption and pollutant discharge amount is represented respectively.It is a 0-1 variable, if dispatching For center m vehicle k from client i to client j, then the value is 1, is otherwise 0.Represent home-delivery center m vehicle k from client i to Client j fuel consumption, FminRepresent fuel consumption minimum in all feasible programs, FmaxRepresent in all feasible programs Maximum fuel consumption, the value of the two is by being calculated.Represent home-delivery center m vehicle k from client i to Client j urea consumption, UminRepresent urea consumption minimum in all feasible programs, UmaxRepresent in all feasible programs Maximum urea consumption, the value of the two is also by being calculated.Represent home-delivery center m vehicle k from client i To client j pollutant discharge amount, EminRepresent pollutant discharge amount minimum in all feasible programs, EmaxRepresent all feasible Maximum pollutant discharge amount in scheme, the value of the two is by being calculated.tjkRepresent vehicle k reach client j when Between, ETjkRepresent the time requirement lower limit of j point goods, LTjkRepresent the time requirement upper limit of j point goods, ctiRepresent vehicle in i points Residence time.Cargo dead-weights of the home-delivery center m vehicle k during client j is driven to from client i is represented,Expression is matched somebody with somebody Send center m vehicle k dead weight.qjRepresent the demand of client's j points, pjRepresent the supply of client's j points.
In addition, because fuel consumption, urea consumption are different with the dimension of pollutant discharge amount, and numerical value may differ by It is larger, so object function has cleverly been carried out standardization by the present invention.Fmin,Fmax,Umin,Umax,Emin,EmaxRepresent Be this programme path all feasible programs in fuel consumption, the minimum value of urea consumption and pollutant discharge amount and Maximum.First in the case where constraints is constant, respectively using this following 6 formula as target, calculated.Then will meter Calculation value is input to object function, optimizes solution.
During the vehicle scheduling of reality and path planning：
Because this problem is a np hard problem, with the expansion of scale, the complexity of calculating is presented exponential type and increased.Institute With, the length that the calculating time that exact algorithm solves this problem can be suitable, and heuritic approach quick can be obtained by bionics To can passerby, there is validity to solving extensive problem.So this scheduling and route planning method can use heuritic approach Solved, such as genetic algorithm, ant group algorithm, neural network algorithm.The present invention is asked this by taking Revised genetic algorithum as an example Topic is solved, and is comprised the following steps that：
Step 1：Task is encoded.
G={ w1,w2,...,wN}
Wherein, 3 contents are included in w, home-delivery center's numbering, the car number of the home-delivery center and this path are matched somebody with somebody Sequencing numbers in sending.For example, (121,112,122,111,123,113,211,212) represent that the chromosome length is 8, altogether There are 8 clients for needing to service, and corresponding customer number is corresponded to according to sequencing, first position 121 represents client 1 Dispensed by the 2nd vehicle of the 1st home-delivery center, be ranked first position in service sequences.
Step 2：Initialize population.Multiple initial populations are generated, parallel computation, avoid being absorbed in local optimum.
Step 3：Calculate adaptive value, i.e. object function.
Step 4：Judge whether to meet end condition, if satisfied, terminating algorithm.If not satisfied, carry out step 5.
Step 5：Time windows constraints and loading capacity constraint are calculated, eliminate infeasible task.
Step 6：Selected, intersected and mutation operation.Return to step 3.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention God any modification, equivalent substitution and improvements made etc., should be included in the scope of the protection with principle.

Claims (3)

1. a kind of vehicle scheduling and paths planning method based on environmental protection and cost savings, it is characterised in that：With fuel consumption, Urea consumption and the minimum object of planning of pollutant discharge amount establish the integer programming model with time window, wherein
For object function, Part I is that weight is multiplied by the value after the standardization of fuel consumption, and Part II is expression weight The value being multiplied by after the processing of urea consumption standardization, Part III are after weight is multiplied by pollutant discharge amount standardization Value, minimum target is integrated with three.
2. a kind of vehicle scheduling and paths planning method based on environmental protection and cost savings according to claim 1, it is special Sign is：The constraints of the model is
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ETjk＜=tjk＜=LTjkJ ∈ { 1,2 ..., N } (7)
<mrow> <msub> <mi>t</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ct</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>,</mo> <mi>j</mi> <mo>&amp;Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>L</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>&lt;</mo> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>m</mi> <mi>k</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>L</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>-</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>L</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>-</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>j</mi> <mo>&amp;Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <msub> <mi>t</mi> <mrow> <mi>a</mi> <mi>k</mi> </mrow> </msub> <mo>&lt;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <msub> <mi>t</mi> <mrow> <mi>b</mi> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Or 1 (12)
<mrow> <msubsup> <mi>L</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>&gt;</mo> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
Km＞=0 (14)
<mrow> <msubsup> <mi>Q</mi> <mi>m</mi> <mi>k</mi> </msubsup> <mo>&gt;</mo> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein, formula (1) represents that the vehicle number that each home-delivery center sends is no more than vehicle fleet；
Formula (2) represents that vehicle from home-delivery center and returns to home-delivery center；
Formula (3) and (4) represent that each client can only be by a car service once；
Formula (5) represents that vehicle can not be by home-delivery center to home-delivery center；
Formula (6) represents that vehicle has into having；
Formula (7) and (8) represent the time windows constraints of goods；
Formula (9) and (10) represent the loading capacity constraint of vehicle；
Formula (11) represents the dispatching of goods or the priority restrictions of consolidating the load；
Formula (12) represents 0-1 variable bounds；
Formula (13), (14) and (15) represents that the dead weight of the useful load of car, home-delivery center's vehicle number and car is non-negative；
Wherein, N represents the set of client；
M represents the set of home-delivery center；
KmRepresent home-delivery center m vehicle number；
β1,β2And β3The weight of fuel consumption, urea consumption and pollutant discharge amount is represented respectively；
It is a 0-1 variable, if home-delivery center m vehicle k, from client i to client j, the value is 1, is otherwise 0；
Represent home-delivery center m vehicle k from client i to client j fuel consumption；
FminRepresent fuel consumption minimum in all feasible programs；
FmaxRepresent fuel consumption maximum in all feasible programs；
Represent urea consumptions of the home-delivery center m vehicle k from client i to client j；
UminRepresent urea consumption minimum in all feasible programs；
UmaxRepresent urea consumption maximum in all feasible programs；
Represent home-delivery center m vehicle k from client i to client j pollutant emission；
EminRepresent pollutant discharge amount minimum in all feasible programs；
EmaxRepresent pollutant discharge amount maximum in all feasible programs；
tjkRepresent that vehicle k reaches client j time；
ETjkRepresent the time requirement lower limit of j point goods；
LTjkRepresent the time requirement upper limit of j point goods；
ctiRepresent residence time of the vehicle in i points；
Represent cargo dead-weights of the home-delivery center m vehicle k during client j is driven to from client i；
Represent home-delivery center m vehicle k dead weight；
qjRepresent the demand of client's j points, pjRepresent the supply of client's j points.
3. a kind of vehicle scheduling and paths planning method based on environmental protection and cost savings according to claim 2, it is special Sign is：Also include being standardized object function, Fmin,Fmax,Umin,Umax,Emin,EmaxWhat is represented is this time to plan The minimum value and maximum of fuel consumption, urea consumption and pollutant discharge amount in all feasible programs of route, In the case that constraints is constant, respectively using this following 6 formula as target, is calculated, calculated value is then input to mesh Scalar functions, optimize solution：
<mrow> <msub> <mi>F</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>F</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> </mrow>
<mrow> <msub> <mi>F</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>F</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> </mrow>
<mrow> <msub> <mi>U</mi> <mi>min</mi> </msub> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>U</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> </mrow>
<mrow> <msub> <mi>U</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>U</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> </mrow>
<mrow> <msub> <mi>E</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>E</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> </mrow>
<mrow> <msub> <mi>E</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mi>m</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mi>M</mi> </mrow> </munderover> <msubsup> <mi>E</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> </mrow> </msubsup> <mo>.</mo> </mrow>
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