CN105303818B - Urban road network optimal restoration time sequence method based on greedy algorithm - Google Patents
Urban road network optimal restoration time sequence method based on greedy algorithm Download PDFInfo
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Abstract
The invention discloses an urban road network optimal restoration time sequence method based on a greedy algorithm. The method comprises the following steps: a. a set of road sections to be repaired in a known road network; b. defining a road section importance judgment index from the road network repairing angle; c. calculating importance judgment indexes of all road sections in the road section set to be repaired; d. repairing the most important road section in the road section set to be repaired by using the greedy selection idea; e. after a road section in the road network is repaired, the state of the road network is changed, and the importance judgment index of the road section is also changed, so that the steps c and d are repeated for the remaining road sections to be repaired until the set of the road sections to be repaired in the road network is an empty set; f. and outputting a road section repairing sequence which is the optimal repairing sequence, so that the obtained repairing time sequence is the optimal repairing time sequence of the road network. The method has the advantages that the applicability of the greedy algorithm to the optimal time sequence repairing problem of the road network is theoretically proved, the greedy algorithm avoids a large amount of complex calculation and is high in efficiency, and the result has important guiding significance for repairing the urban road network in actual life.
Description
Technical Field
The invention relates to the field of traffic planning and management, in particular to an urban road network optimal restoration time sequence method based on a greedy algorithm.
Background
The core problems of road network restoration are as follows: under the condition of limited resources, the road section or sections should be repaired preferentially, so that the road network is recovered to the normal condition to the maximum extent at the fastest speed, and the reliability of the road network in the repairing process is improved. At present, the existing road network repairing method is mainly used for preferentially repairing key road sections in the network. But how to define the critical road segments is not uniform. In the early stage of research, the key road sections of the road network are mostly researched by means of a complex network theory, for example, some researches identify the key road sections according to indexes such as the degree and the betweenness of the road sections, and the researches neglect the unique traffic characteristics of the road network, so that inaccuracy of research results is easily caused. Later research has biased the definition of critical road segments by removing road segments, i.e. quantifying the destructiveness of the removal of road segments on the road network, but the results will vary depending on the criteria of the destructiveness of the road network. The existing methods and indexes are static, the change of the road network state is not considered, and from the point of road network failure, the definition and identification of key road sections from the point of road section repair are rarely researched. The road section importance index is provided from the road network repairing angle, and the important road section is defined mainly according to the influence of the road section repairing on the whole performance improvement of the road network, so that the road section importance index is more targeted and has important significance on the repairing of the road network.
In the aspect of a road network restoration method under an emergency, most of the existing researches take earthquake and other serious natural disaster events as research backgrounds. Because of considering problems such as actual rescue and repair, the research mostly takes a vehicle path model as a core, and researches the formulation of road network repair schemes under emergency conditions, but the model has more and harsh constraints and is difficult to solve. This creates a gap between theory and reality, which completely conforms to the actual model and is theoretically difficult to obtain a feasible solution and an optimal solution. Therefore, when modeling, some practical problems which are not very important should be properly ignored, and the theory can guide the practice. The road network restoration method is mainly used for theoretically researching road network restoration, based on the idea of the greedy algorithm, the most important road sections under the current condition are sequentially selected for restoration, namely, the local optimal solution is obtained, the finally obtained restoration sequence is also the global optimal restoration sequence, and the applicability of the greedy algorithm to the road network restoration time sequence problem is theoretically proved. The problem is solved by a greedy algorithm, the trouble of exhausting all repairing sequences is avoided, and the problem solving efficiency is greatly improved. Although the optimal repair time sequence obtained by the greedy algorithm simplifies the road network repair problem in life to a certain extent, the optimal repair time sequence still has important guiding significance for road network repair.
The method mainly takes the research background that the traffic capacity of part of road sections in a road network is reduced or even is zero when the urban road network is subjected to severe weather such as rain, snow and the like or traffic events in a large range. Although the events targeted by the invention are small and far less damaging to the road network than the earthquakes, floods and the like, the frequency of the events in daily life is higher than that of the earthquakes, floods and the like. Therefore, the invention has certain practical significance.
Greedy algorithm (also called greedy algorithm) means that when solving a problem, always the choice that seems best at the present time is made. That is, instead of considering the global optimum, he only makes a locally optimal solution in some sense. The greedy algorithm does not yield an overall optimal solution for all problems, but it can yield an overall optimal solution or an approximate solution to an overall optimal solution for a wide range of problems.
Disclosure of Invention
The purpose of the invention is as follows:
the method aims at the defects brought forward from the point of multi-route network failure for researching the road section importance indexes and the defects that a model in a road network repairing method is complex and difficult to solve. The invention provides the road section importance identification index from the road network repairing perspective, and the index is more targeted to the road network repairing. According to the greedy selection idea, the most important road sections under the current condition are sequentially selected for repairing, namely the local optimal solution, and finally the global optimal solution, namely the optimal repairing sequence of the road network is obtained. The method avoids a large amount of calculation, is easy to realize and has high efficiency. The method has important guiding significance for repairing the urban road network in real life.
The technical scheme is as follows:
an urban road network optimal restoration time sequence method based on a greedy algorithm. It is known that there are m road segments in a road network to be repaired, but the repair resources are limited, and the road segments can only be repaired in a certain order. And (3) repairing the most important road sections under the current situation one by one according to a greedy selection idea, wherein the finally obtained repairing sequence is a global optimal repairing sequence according to the algorithm. The method comprises the following steps:
(1) a set of road sections to be repaired in a known road network;
(2) calculating importance judgment indexes of the road sections to be repaired;
(3) repairing the most important road section in the road section set to be repaired by using the greedy selection idea;
(4) updating the road network state, and repeating the step (2) and the step (3) on the remaining road sections to be repaired until the set of the road sections to be repaired in the road network is an empty set;
(5) and outputting a road section repairing sequence which is the optimal repairing sequence, so that the obtained scheme is the optimal repairing time sequence of the road network.
The proof process of obtaining the global optimal solution from the local optimal solution according to the greedy algorithm is as follows:
variables and meanings used in the proof process:
Enormal: set of normal road segments in road network, hereinafter abbreviated as En
Erepair: set of road segments to be repaired in road network, hereinafter abbreviated as Er
Eni: set of normal road segments in road network before ith restoration
Eri: set of road sections to be repaired in road network before ith repair
c0: running cost of road network in initial state
e: representing road sections
tj、xj: travel time and traffic of road segment obtained by classical UE distribution
E0＝En1+Er1
The most important thing for the problem is to prove the equation
Is established
The demonstration process is as follows:
(1) obviously, the optimal repair timing sequence problem of the urban road network has a feasible solution.
(2) Suppose that the urban road network optimal repair timing problem has an optimal algorithm O, and the optimal solution, i.e. the optimal repair sequence, is T1. The repair sequence obtained by the greedy algorithm is T2, and the T2 solution is a feasible solution because T2! T1, the repair sequence for at least two of the segments in T1 and T2 is exactly reversed. Assuming that T1 is e1- > e2- > e3- > e5- > e4- > T11, T2 is e1- > e2- > e3- > e4- > e5- > T22, wherein T11 and T22 are the repair sequence of the rest of T1 and T2.
Now, a solution T3 is constructed, wherein T3 is the same as T1, but the positions of e5 and e4 are changed, namely T3 is e1- > e2- > e3- > e4- > e5- > T11, the former part of the T3 solution is the same as the T2 solution, the latter part is the same as the T1 solution, and obviously T3 is also a feasible solution for optimally repairing the timing problem of the urban road network.
The T1 solution sums as:
the T3 solution sums as:
for the T1 solution:
En5＝En1+e1+e2+e3+e5
for the T3 solution:
En5＝En1+e1+e2+e3+e4
after 5 times of repairing before the T1 solution and the T3 solution are completed, the normal road section and the road section to be repaired in the road network are completely the same, and the UE is allocated by the used traffic flow allocation methodFlow of, therefore
And because of e in T34Is determined by greedy selection, so
Therefore, it is not only easy to use
Namely, the sum of the terms in T1 is greater than or equal to the sum of the terms in T3.
T1 has n different choices from T2, and can be changed for more than limited times, such as constructing T3 to get it close to T2 gradually, and getting T2; for the T2 solution, the terms sum to
While ensuring that the sum of the terms of the new solution and the terms of the solution less than or equal to T1, i.e. less than or equal to
So equation
This is true.
Namely, the optimal repair time sequence can be obtained by a greedy algorithm for the urban road network repair time sequence problem.
The invention has the characteristics that: the method is a research background on how to arrange road section repair sequences to enable the road network to be improved and improved greatly at the fastest speed and improve the reliability of the road network in the repair process, wherein a plurality of road sections in the urban road network wait for repair and repair resources are very limited. The optimal repair time sequence can be quickly obtained through a greedy algorithm, the complexity of exhausting all repair sequences is avoided, the calculation efficiency is high, and although some practical problems are simplified, the repair time sequence provided by the invention has important guiding significance for the reality.
Detailed Description
The invention will be further elucidated with reference to the following specific examples, wherein the method comprises the following steps:
1. road section set E to be repaired in known urban road networkrepair(hereinafter abbreviated as E)r) Set of normal road sections Enormal(hereinafter abbreviated as E)n)，E0The method comprises the steps of collecting all road sections of a road network, and obtaining an OD matrix, a traffic capacity matrix and a free flow time matrix of the road network. In this case, the user balance flow distribution is carried out on the road network, and the travel cost of the road network at the moment is calculated
2. In the present case, calculate ErThe importance index of each section. The specific steps are sequentially supposed to be ErWhen a certain road section is repaired, namely the road section is recovered to be normal, the UE flow distribution is used for carrying out flow distribution on the road network again, and the travel cost of the road network at the moment is calculated
The link importance index is defined as:
section I of roadeSmaller values indicate greater improvement of the road network by the road segment, more important the road segment, and hence repair IeThe lowest-value road segment, update set ErAnd set En；
3. Repeating the step 2 to
En＝E0. And outputting the road section repairing sequence to obtain the optimal road network repairing time sequence.
Claims (1)
1. An urban road network optimal restoration time sequence method based on a greedy algorithm is characterized by comprising the following steps:
(1) a set of road sections to be repaired in a known road network;
(2) calculating importance judgment indexes of the road sections to be repaired;
(3) based on the thought of greedy selection, repairing the most important road section in the road section set to be repaired;
(4) updating the road network state, and repeating the step (2) and the step (3) on the remaining road sections to be repaired until the set of the road sections to be repaired in the road network is an empty set;
(5) outputting a road section repairing sequence, wherein the sequence is the optimal repairing time sequence of the road network;
obtaining the optimal road network restoration time sequence based on the greedy algorithm, and most importantly, proving that the following equation is established
Variables and meanings used in the proof process:
m: number of road sections to be repaired in road network
Enormal: set of normal road segments in road network, hereinafter abbreviated as En
Erepair: set of road segments to be repaired in road network, hereinafter abbreviated as Er
Eni: set of normal road segments in road network before ith restoration
Eri: set of road sections to be repaired in road network before ith repair
c0: running cost of road network in initial state
e: representing road sections
tj、xj: travel time and traffic of road segment obtained by classical UE distribution
E0＝En1+Er1
The demonstration process is as follows:
(1) obviously, the optimal repair timing sequence problem of the urban road network has a feasible solution;
(2) supposing that the optimal repair time sequence problem of the urban road network has an optimal algorithm O, wherein the optimal solution, namely the optimal repair sequence is T1; the repair sequence obtained by the greedy algorithm is T2, and the T2 solution is a feasible solution because T2! T1, the repair sequence for at least two road segments in T1 and T2 is exactly the opposite; assuming that T1 is e1- > e2- > e3- > e5- > e4- > T11, T2 is e1- > e2- > e3- > e4- > e5- > T22, wherein T11 and T22 are the repair sequence of the rest of T1 and T2;
now, a solution T3 is constructed, wherein T3 is the same as T1, but the positions of e5 and e4 are changed, namely T3 is e1- > e2- > e3- > e4- > e5- > T11, the former part of the T3 solution is the same as the T2 solution, the latter part is the same as the T1 solution, and obviously T3 is also a feasible solution for optimally repairing the timing problem of the urban road network;
the T1 solution sums as:
the T3 solution sums as:
for the T1 solution:
En5＝En1+e1+e2+e3+e5
for the T3 solution:
En5＝En1+e1+e2+e3+e4
after 5 times of restoration before the T1 solution and the T3 solution are completed, the normal road sections in the road network are completely the same as the road sections to be restored, and the used traffic flow distribution method distributes flows for UE (user equipment)
And because of e in T34Is determined by greedy selection, so
Therefore, it is not only easy to use
Namely the sum of the terms in T1 is more than or equal to the sum of the terms in T3;
t1 has n different choices from T2, and can be changed for more than limited times, such as constructing T3 to get it close to T2 gradually, and getting T2; for the T2 solution, the terms sum to
At the same timeEnsuring that the sum of the terms of the new solution and the terms of the T1 solution is less than or equal to the sum of the terms of the new solution in the transformation process, namely less than or equal to
So equation
It is true that the first and second sensors,
namely, the optimal repair time sequence can be obtained by a greedy algorithm for the urban road network repair time sequence problem.
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