CN104361178A - Indoor evacuation simulating optimization method based on potential energy driving cellular ant colony algorithm - Google Patents

Abstract

The invention provides an indoor evacuation simulating optimization method based on a potential energy driving cellular ant colony algorithm. The method is a personnel evacuation behavior simulating optimization method based on colony intelligence, a two-dimensional cellular automaton mathematic model in accordance with an actual scene is mainly built, personnel evacuation behaviors are simulated by using the cellular ant colony algorithm, and personnel paths are judged and selected according to a potential energy evaluation criterion of an artificial potential energy field, so that the method is more consistent to a true scene evacuation rule, the evacuation efficiency is improved, and a reasonable evacuation scheme is provided.

Description

A kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy

Technical field

The invention belongs to intelligent system modeling and optimization field, concrete is a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy.

Background technology

Evacuation problem can scene is abstract becomes a complicated extensive dynamic network according to evacuating, the simplest directly method utilizes traditional shortest path first to solve, but this algorithm is applicable to the optimum path search of static road network on a small scale, and for extensive dynamic network, when network size increases, the complexity of algorithm will increase sharply, and the arithmetic capability defect of this traditional shortest path first causes the demand that cannot meet system.Because intelligent algorithm obviously can not increase along with the increase of network size computing time, relatively traditional shortest path first, is applicable to the route searching problem solving this large scale network of buildings evacuating personnel more.

Ant colony optimization algorithm (Ant Colony Optimization:ACO) is a kind of new distribution type intelligent bionic class algorithm that Colorni and Dorigo etc. proposed in early 1990s, and its is simulated and has used for reference the foraging behavior feature of ant population in real world.Ant can discharge a kind of special secretion when moving on the path passed through--and information usually finds path.When they encounter one also do not pass by crossing time, just select a paths randomly and move ahead, discharge the pheromones with path-dependent simultaneously.The path that ant walks is longer, then the quantity of information discharged is less.When ant afterwards meets this crossing again time, select the path probability that quantity of information is larger relatively large, so just define a positive feedback mechanism.Quantity of information on optimal path is increasing, and the quantity of information on other paths can be cut down with the passing of time, and final whole ant group can find out optimal path.The method has can strong, the strong adaptability of concurrency, optimizing ability and be easy to the advantages such as other algorithm combinations, but also there is certain defect, as long in search time, strong and easily occur that search is stagnated etc. to the descriptive power of challenge.

Artificial potential energy field (Artificial Potential Field:APF) is a kind of planing method of analog electrical Distribution of Potential Field, and first its concept is proposed by Khatib, and is successfully applied to obstacle avoidance for robotic manipulator.The utilizing thoughts of artificial potential energy field " object of which movement is generally moved to the position that potential energy is lower by the position that potential energy is higher " this physics law, according to initialization grid potentials such as the distribution of personnel on the familiarity of interior of building and outlet, barrier, the impacts from the extraneous factor such as distance, fire of outlet.Be characterized in that planning speed is fast, the safety in path can be ensured, but because potential function exists the gravitation local minimum point equal with repulsion, algorithm can be made to stagnate and target location cannot be arrived at, the optimum in path can not be ensured owing to not having cost function to weigh flight path quality again.

The physical characteristics of artificial potential energy field is very close with the characteristics of motion of in emergency circumstances personnel, and the self-organization that ant group algorithm shows, group are also applicable to the modeling of emergency evacuation problem very much, ant is undertaken exchanging and message intercommunication by release pheromone in the process of looking for food, to help companion to find food quickly, this and people mutual cooperation the in evacuation process has very large similarity.Individuality in evacuating with ant representative, ant can find path towards fire exit by the negative gradient direction of potential energy value, can accelerate evacuation process, and optimum results overcomes the local minimum problem of artificial potential energy field simultaneously.

Summary of the invention

In order to overcome the deficiencies in the prior art, the present invention proposes a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy, the self-organization of the physical characteristics of potential energy field and ant group algorithm, positive feedback mechanism is utilized to simulate the characteristics of motion of personnel from microcosmic on the one hand, the optimization in evacuating personnel path is completed on the other hand while emulation, solve the local minimum problem of artificial potential energy field, improve evacuation efficiency.

Technical scheme of the present invention is, a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy, comprises the steps:

Step 1. sets up the buildings evacuation model of two dimensional cellular automaton;

Two dimensional cellular automaton C is defined as following four-tuple:

C＝(D ₂,S,N,f)

Wherein, D ₂for two-dimentional cellular space, S is finite state machine set, can be expressed as being positioned at the state of the cellular on case r in t:

S＝{S ₁(r,t),S ₂(r,t),…,S _z(r,t)}

S in formula _z(r, t) represents z the state of the cellular on case r in the t time; N is the neighborhood of cellular centered by r, N={N ₁, N ₂..., N _nd ₂limited sequence subset, n is neighbours' cellular number of the cellular on case r, cellular r and backfence movement rule centered by f;

Step 2. arranges model parameter; Comprise ant group algorithm correlation parameter and potential energy field gain coefficient, the pheromones of evacuation personnel number m, ant group algorithm and heuristic information significance level α and β, pheromones volatility coefficient q, potential energy field gain coefficient ξ ₁and ξ ₂, pheromones intensity initial value Q, the maximum iteration time T of algorithm;

Scene is evacuated in step 3. initialization; According to layout in buildings, evacuation scenario simulation is carried out to two-dimentional cellular space, to place obstacles at random the position of thing and size, according to buildings real scene mark outlet cellular position, evacuation personnel residing cellular position when evacuating beginning is set at random, according to each cellular by barrier, personnel occupy or the free time arranges its original state, pheromones intensity between initialization cellular on path is the Q that step 2 is arranged, and " is not evacuated " by all personnel's state mark for people;

Step 4. calculates the artificial potential energy field of scene;

According to the distribution of step 3 personnel in cellular, calculate total potential energy of each cellular as follows:

$U_{\mathrm{att}}\left(i\right)=\frac{1}{2}{\mathrm{\ξ}}_1{\mathrm{\ρ}}_g^2\left(i\right)---\left(1\right)$

$U_{\mathrm{rep}}\left(i\right)=\left\{\begin{array}{cc}\frac{1}{2}{\mathrm{\ξ}}_2{(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})}^2,& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(2\right)$

U in formula _att(i) and U _repi () is gravitational potential energy and the repulsion potential energy at cellular i place respectively, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ξ ₁, ξ ₂be corresponding potential energy field gain coefficient, ρ (i) is the minimum distance between personnel k and barrier, ρ ₀for the ultimate range that barrier has an impact to people;

The gravitation that personnel are subject at cellular i place and repulsion the negative gradient of corresponding potential energy respectively:

$\stackrel{\‾}{F_{\mathrm{att}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{att}}\left(i\right)\right]={\mathrm{\ξ}}_1{\mathrm{\ρ}}_g\left(i\right)---\left(3\right)$

$\stackrel{\‾}{F_{\mathrm{rep}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{rep}}\left(i\right)\right]=\left\{\begin{array}{cc}\frac{{\mathrm{\ξ}}_2}{{\mathrm{\ρ}}^2\left(i\right)}(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})\▿\mathrm{\ρ}\left(i\right),& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(4\right)$

Wherein ,-grad [U _att(i)] and-grad [U _rep(i)] represent the negative gradient of cellular i point place attractive force potential energy and the negative gradient of repulsive force potential energy respectively, ξ ₁, ξ ₂corresponding potential energy field gain coefficient, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ▽ ρ (i) represents that barrier points to the vector of unit length of cellular i;

Therefore, composite factor can be expressed as total potential energy that personnel produce at cellular i place:

U _i＝ΣU _att(i)+ΣU _rep(i) (5)

Personnel, under the combined action of gravitation and repulsion, move along potential field force direction.The introducing of artificial potential energy field effectively can simulate the driving force in evacuating personnel, makes personnel avoid known barrier, and arrives exit position.

The personnel that step 5. obtains according to step 4, in total potential energy value of current removable cellular, calculate the heuristic information in mobile path;

In t, personnel are moved on cellular j by cellular i, utilize artificial potential energy field to outlet and the perception of barrier, to the heuristic information η of ant group algorithm _ijt () improves, namely heuristic information is determined apart from the distance exported jointly by potential energy and personnel, and guide personnel's avoiding obstacles also fast near exporting, its formula is:

${\mathrm{\η}}_{\mathrm{ij}}\left(t\right)=\frac{1}{\min \left\{d_{j,\mathrm{exits}}\right|j\∈J_i\}\×U_i}---\left(6\right)$

Wherein, η _ijt () is the heuristic information on path between cellular i and cellular j, d _{j, exits}the distance of cellular j to outlet, min{d _{j, exits}| j ∈ J _irepresent the shortest Euclidean distance that cellular j distance exports, J _ithe neighborhood near cellular i, U _ifor total potential energy value of the cellular i that step 4 obtains;

Step 6. arranges iteration count NC=1;

Step 7. Stochastic choice personnel from all evacuation personnel evacuate, if k=1 as first;

Step 8. judges whether the current state of a kth personnel is " evacuating " state, if then perform step 15, otherwise performs next step;

Step 9., according to the cellular at a kth personnel place, obtains the set of its neighbours' cellular;

Neighbours' cellular set that step 10. obtains according to step 9, judges the state of its current time, and neighbours' cellular is idle removable point or by the irremovable point of occupy-place, judges the moveable cellular neighbours collection of a kth personnel according to neighbours' cellular state and taboo rule;

The removable cellular neighbours collection that step 11. obtains according to step 10, judges whether a kth personnel have moveable cellular, if having, perform next step; If not, rest on current cellular position in this moment, perform step 15;

The heuristic information that pheromones intensity on step 12. cellular and neighbours' cellular path residing for the kth of a current time personnel and step 5 obtain, calculates the probability of a kth removable cellular of personnel selection neighbours;

In t, the state transition probability formula that a kth personnel transfer to cellular j by cellular i is as follows:

In formula, that personnel k transfers to the transition probability of cellular j by cellular i, τ _ijt () is the pheromones intensity between cellular i and cellular j on path, η _ijt () is the heuristic information between cellular i and cellular j on path, α and β is constant parameter, is used for representing the significance level of pheromones and heuristic information, J _irepresent the neighborhood near cellular i; represent the cumulative sum that cellular i seizes the opportunity to heuristic information and the pheromones of all neighbours' cellulars;

Step 13. draws according to the transition probability that step 12 obtains and a kth personnel is moved to neighbours' cellular that the transition probability of a kth personnel is maximum this cellular place, upgrades the state of this cellular, this cellular is added the evacuation path of these personnel;

The up-to-date cellular moved to of the kth personnel that step 14. obtains according to step 13, judges whether personnel k reaches outlet, if arrive, then marks these personnel for " evacuating " state, otherwise marks these personnel for " evacuation " state;

Step 15. is evacuated personnel's counting and is added 1, i.e. k=k+1, carries out removable cellular search to next personnel;

If step 16. k≤m, then illustrate and also do not travel through all evacuation personnel, turn back to step 8, otherwise show that all personnel completes the search of a time step, perform next step;

Step 17. judges whether the current state of all personnel is all " evacuating " state, if then show that all personnel completes the route searching from initial cellular to outlet, namely epicycle evacuation simulative iteration completes, and performs next step, otherwise returns step 7;

Each personnel that step 18. obtains according to step 13 to the evacuation path of outlet, upgrade pheromones intensity each evacuating personnel path on cellular between according to formula (8)-(10) from its initial cellular:

τ _ij(t+Δt)＝(1-q)×τ _ij(t)+Δτ _ij(t+Δt) (8)

$\mathrm{\Δ}{\mathrm{\τ}}_{\mathrm{ij}}(t+\mathrm{\Δt})=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})---\left(9\right)$

${\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})=\left\{\begin{array}{c}\frac{Q}{L_k},\mathrm{edge}(i,j)\∈{\mathrm{path}}_k\\ 0,\mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein, τ _ijt () represents the pheromones strength function between t cellular i and cellular j on path, Q is constant, is the pheromones intensity initial value that step 2 is arranged, L _kfor the path that k personnel the walk in this circulation, edge (i, j) represents the path between cellular i and cellular j, path _kit is the path of personnel k process; Q is the pheromones intensity volatility coefficient that step 2 is arranged; Pheromones intensity between cellular on path is larger, and the probability of this paths of personnel selection will be larger.Due to this positive feedback mechanism, evacuation personnel finally can attracted in the shortest evacuation route;

Step 19. iteration count NC adds 1, i.e. NC=NC+1;

Step 20. is as NC≤T, and each personnel returns personnel's initial cellular separately that step 3 is arranged, and repeat step 7-19, until NC > T, iteration terminates, and performs next step;

Step 21. exports optimum evacuation path and evacuation time, demonstrates optimum dispersal plan.

Preferably, in described step 1, centered by f, cellular r and backfence movement rule adopt Moore type neighbours to define, be its neighbours with the cellular on the upper and lower, left and right of center cellular, upper left, lower-left, upper right, these eight directions, bottom right, now neighbours' radius is similarly r=l, and pedestrian can move to reach contiguous idle cellular at one time to these eight directions.

Preferably, the location sets obtaining its neighbours' cellular in described step 9 is the upper of a kth personnel position, under, left, right, upper left, lower-left, upper right, the cellular in 8 directions, bottom right.

Preferably, the optimum configurations of this method is: ant group algorithm parameter alpha=1, β=2, ρ=0.5, Q=1, maximum cycle T=100; Potential energy field gain coefficient ξ ₁=2, ξ ₂=1.

Preferably, the taboo rule in described step 10 is:

(1) cellular can only hold personnel;

(2) can move to idle cellular and outlet the personnel of buildings, can not move to the cellular in buildings from the cellular of outlet;

(3) if multiple personnel compete same idle cellular simultaneously, Stochastic choice one people enters, other people rerouting, until all personnel finds oneself subsequent time unique objects on grid;

(4) when personnel can not select current optimum erect-position, then do not considering that Way out situation writes selection suboptimum cellular as erect-position;

(5) personnel selection cellular can not be the cellular at oneself previous step place, unless around other cellular all can not be accessed.

The present invention has the following advantages compared with prior art:

1, the present invention adopts cellular to divide evacuation scene, can intend evacuating personnel process better from microcosmic patrix.

2, the present invention adopts the thought of artificial potential energy field, utilize potential energy negative gradient direction to complete path planning, personnel are under the combined action of repulsive force exporting attractive force and the barrier generation produced, and the direction declined along potential energy is moved, and more meets evacuation real processes.

3, the present invention introduces ant group algorithm on the basis of potential energy field, utilizes potential energy to know the searching route of ant, can complete evacuation optimum path search sooner, improves evacuation efficiency.

4, the present invention is relative to other optimized algorithms, has better speed of convergence and convergence effect.

Accompanying drawing explanation

Fig. 1 is experiment flow figure of the present invention;

Fig. 2 is that 500 people of the present invention evacuate process design sketch;

Fig. 3 is the algorithm iteration graph of a relation in 500 people paths of the present invention;

Fig. 4 is the evacuation path figure of different number of the present invention.

Embodiment

1, the buildings evacuation model of two dimensional cellular automaton is set up:

Cellular automaton can be defined as a four-tuple:

C＝(D ₂,S,N,f)

Wherein D ₂be 2 dimension cellular spaces; S is finite state machine set, can be expressed as being positioned at the state of the cellular on case r in t:

S＝{S ₁(r,t),S ₂(r,t),…,S _k(r,t)}

S in formula _k(r, t) represents kth the state of the cellular on case r in the t time; N is the neighborhood of cellular centered by r, N={N ₁, N ₂..., N _nd ₂limited sequence subset.

Cellular r and backfence movement rule centered by f, here Moore type neighbours definition is adopted, namely the cellular on the upper and lower, left and right of center cellular, upper left, lower-left, upper right, these eight directions, bottom right is its neighbours, now neighbours' radius is similarly r=l, and this neighbor model is also referred to as eight neighborhood usually.Pedestrian can move to these eight directions at one time.According to evolution rule, namely the state of a cellular subsequent time depends on the state of this moment state own and its neighbours' cellular, the all cellular state of initial time are different, and each cellular is determined by t oneself state and neighbor state combination jointly at the state value in t+1 moment.

Crowd evacuation process in simulating chamber is carried out with cellular automaton, go to simulate the crowd movement under concrete some scenes by computer technology exactly, under this model, the plane space of teaching building can be divided into equal-sized grid, each like this grid is with regard to the sub-fraction in corresponding reality scene, and each cellular has different states and attribute.In teaching building is evacuated, every one deck can be considered as a two dimensional surface, and be applicable to the cellular Automation Model setting up two dimension, namely environment space is divided into the square node of many rules, each grid represents a cellular.Buildings is carried out stress and strain model, is divided into the equal-sized grid that can hold a people, generate two-dimentional cellular space.The space of the corresponding 0.5m × 0.5m of each cellular is typical personnel's allocation of space in the stream of people.At any one time, the state of cellular is for being occupied by barrier, being occupied by pedestrian or the free time, and each cellular can only hold one and evacuate individual, and each individuality can within the unit interval upwards, under, a left side, right, upper left, lower-left, upper right, a direction in direction, 8, bottom right is moved, and can arrive contiguous idle cellular within a time.

2, the parameter arranging model parameter and initialization evacuation model of place comprises ant group algorithm correlation parameter and potential energy field gain coefficient, the setting of evacuating scene comprises position and the size setting of barrier, personnel's initial distribution is arranged, and initialization comprises the initialization of pheromones in cellular and personnel state initialization and ant group algorithm.

3, introduce artificial potential energy field to be described evacuation scene:

The personnel evacuated in scene, barrier are placed within a grid, mark outlet cellular.Outlet in scene produces gravitational field, and the barrier such as wall, tables and chairs produces repulsion field.Personnel, under the combined action of gravitation and repulsion, move along potential field force direction.Artificial potential energy field effectively can simulate the driving force in evacuating personnel, makes personnel avoid known barrier, and arrives exit position.

4, the heuristic information of potential energy driving: intelligent and enlightening for making evacuating personnel process have, mobile route between cellular has heuristic information, its size is by the potential energy of cellular node and jointly determine relative to the distance of outlet, thus guides pedestrian to avoid obstacle to go and fast near outlet.

5, the ant group algorithm inspired with potential energy information is utilized to carry out Evacuation optimization:

Ant group algorithm is the inspiration proposition that M.Dorigo is subject to the true ant collective behavior of occurring in nature.Utilize pheromones interchange and positive feedback mechanism can find food and ant nest shortest path very soon between ant group.So-called positive feedback refers to that the ant quantity of process on a paths is more, and the pheromones stayed will be more, and ant selects the probability of certain paths to select increasing of this paths along with ant before and to increase.

When utilizing ant group algorithm to carry out evacuation optimization, personnel in evacuation process represent the ant in ant group algorithm, personnel can the cellular position of movement according to the condition adjudgement of current neighbours cellular, according to the position of probability selection cellular as the next moment from these optional cellulars, discharge a certain amount of pheromones on the path simultaneously, other staff are subject to when selecting paths the guiding that potential energy drives heuristic information on the one hand, the pheromone concentration that other staff discharge on the path can be experienced on the other hand, thus judge individual and environment sensing makes decision making package.When all personnel arrives outlet, complete and once evacuate process, after evolution several times, compare the evacuation result obtained, thus draw optimum dispersal plan.

Fig. 1 and Fig. 2 is the key step of system architecture diagram of the present invention and experiment flow figure, and as can be seen from the figure its specific implementation process is as follows:

Step 1. sets up the buildings evacuation model of two dimensional cellular automaton;

Two dimensional cellular automaton C can be defined as following four-tuple:

C＝(D ₂,S,N,f)

Wherein, D ₂be 2 dimension cellular spaces; S is finite state machine set, can be expressed as being positioned at the state of the cellular on case r in t:

S＝{S ₁(r,t),S ₂(r,t),…,S _z(r,t)}

S in formula _z(r, t) represents z the state of the cellular on case r in the t time; N is the neighborhood of cellular centered by r, N={N ₁, N ₂..., N _nd ₂limited sequence subset, n is neighbours' cellular number of the cellular on case r.

Cellular r and backfence movement rule centered by f, here Moore type neighbours definition is adopted, namely the cellular on the upper and lower, left and right of center cellular, upper left, lower-left, upper right, these eight directions, bottom right is its neighbours, now neighbours' radius is similarly r=l, and this neighbor model is also referred to as eight neighborhood usually.Pedestrian can move to reach contiguous idle cellular at one time to these eight directions.

Crowd evacuation process in simulating chamber is carried out with cellular automaton, go to simulate the crowd movement under concrete some scenes by computer technology exactly, under this model, the plane space of buildings can be divided into the equal-sized grid of 0.5m × 0.5m, each grid only can hold one and evacuate individual, each like this grid is with regard to the sub-fraction in corresponding reality scene, and each cellular has different states and attribute.In buildings is evacuated, every one deck can be considered as a two dimensional surface, and be applicable to the cellular Automation Model setting up two dimension, namely environment space is divided into the square node of many rules, each grid represents a cellular.At any one time, cellular has three kinds of possible states: occupied by barrier, is occupied and the free time by pedestrian.

Step 2. arranges model parameter;

Model parameter is set, comprises ant group algorithm correlation parameter and potential energy field gain coefficient, the pheromones of evacuation personnel number m, ant group algorithm and heuristic information significance level α and β, pheromones volatility coefficient q, potential energy field gain coefficient ξ ₁and ξ ₂, pheromones intensity initial value Q, the maximum iteration time T of algorithm.

Scene is evacuated in step 3. initialization;

According to layout in buildings, evacuation scenario simulation is carried out to two-dimentional cellular space, to place obstacles at random the position of thing and size (i.e. the number of cellular shared by it), according to buildings real scene mark outlet cellular position, evacuation personnel residing cellular position when evacuating beginning is random setting, according to each cellular by barrier, personnel occupy or the free time arranges its original state, pheromones intensity between initialization cellular on path is the Q that step 2 is arranged, and " is not evacuated " by all personnel's state mark for people.

Step 4. calculates the artificial potential energy field of scene;

Artificial potential energy field is the feature structure for describing pedestrian's space proposed by Khatib, utilizes potential field negative gradient direction to complete path planning.Outlet in region produces gravitational field, and the barrier such as wall, tables and chairs produces repulsion field.Personnel, under the combined action of gravitation and repulsion, move along potential field force direction.Artificial potential energy field effectively can simulate the driving force in evacuating personnel, makes personnel avoid known barrier, and arrives exit position.

According to the distribution of step 3 personnel in cellular, calculate total potential energy of each cellular as follows:

$U_{\mathrm{att}}\left(i\right)=\frac{1}{2}{\mathrm{\ξ}}_1{\mathrm{\ρ}}_g^2\left(i\right)---\left(1\right)$

$U_{\mathrm{rep}}\left(i\right)=\left\{\begin{array}{cc}\frac{1}{2}{\mathrm{\ξ}}_2{(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})}^2,& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(2\right)$

U in formula _att(i) and U _repi () is gravitational potential energy and the repulsion potential energy at cellular i place respectively, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ξ ₁, ξ ₂be corresponding potential energy field gain coefficient, ρ (i) is the minimum distance between personnel k and barrier, ρ ₀for the ultimate range that barrier has an impact to people.

The gravitation that personnel are subject at cellular i place and repulsion the negative gradient of corresponding potential energy respectively:

$\stackrel{\‾}{F_{\mathrm{att}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{att}}\left(i\right)\right]={\mathrm{\ξ}}_1{\mathrm{\ρ}}_g\left(i\right)---\left(3\right)$

$\stackrel{\‾}{F_{\mathrm{rep}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{rep}}\left(i\right)\right]=\left\{\begin{array}{cc}\frac{{\mathrm{\ξ}}_2}{{\mathrm{\ρ}}^2\left(i\right)}(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})\▿\mathrm{\ρ}\left(i\right),& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(4\right)$

Wherein ,-grad [U _att(i)] and-grad [U _rep(i)] represent the negative gradient of cellular i point place attractive force potential energy and the negative gradient of repulsive force potential energy respectively, ξ ₁, ξ ₂corresponding potential energy field gain coefficient, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ▽ ρ (i) represents that barrier points to the vector of unit length of cellular i.

Therefore, composite factor can be expressed as total potential energy that personnel produce at cellular i place:

U _i＝ΣU _att(i)+ΣU _rep(i) (5)

The personnel that step 5. obtains according to step 4, in total potential energy value of current removable cellular, calculate the heuristic information in mobile path;

In t, personnel are moved on cellular j by cellular i, utilize artificial potential energy field to outlet and the perception of barrier, to the heuristic information η of ant group algorithm _ijt () improves, guide personnel searching path, its formula is formula (6):

${\mathrm{\η}}_{\mathrm{ij}}\left(t\right)=\frac{1}{\min \left\{d_{j,\mathrm{exits}}\right|j\∈J_i\}\×U_i}---\left(6\right)$

Wherein, η _ijt () is the heuristic information on path between cellular i and cellular j, d _{j, exits}the distance of cellular j to outlet, min{d _{j, exits}| j ∈ J _irepresent the shortest Euclidean distance that cellular j distance exports, J _ithe neighborhood near cellular i, U _ifor total potential energy value of the cellular i that step 4 obtains.

Step 6. arranges iteration count NC=1;

Step 7. Stochastic choice personnel from all evacuation personnel evacuate, if k=1 as first;

Step 8. judges whether the current state of a kth personnel is " evacuating " state, if then perform step 15, otherwise performs next step;

Step 9., according to the cellular at a kth personnel place, obtains the set of its neighbours' cellular, and namely a kth personnel position is upper, under, left, right, upper left, lower-left, upper right, the cellular in 8 directions, bottom right.

Neighbours' cellular that step 10. obtains according to step 9, judge the state of its current time, namely neighbours' cellular is idle removable point or by the irremovable point of occupy-place, judges the moveable cellular neighbours collection of a kth personnel according to neighbours' cellular state and following taboo rule;

On cellular movement rule basis, the taboo rule of model is:

(1) cellular can only hold personnel.

(2) can move to idle cellular and outlet the personnel of buildings, can not move to the cellular in buildings from the cellular of outlet.

(3) if multiple personnel compete same idle cellular simultaneously, Stochastic choice one people enters, other people rerouting, until all personnel finds oneself subsequent time unique objects on grid.

(4) when personnel can not select current optimum erect-position, then do not considering that Way out situation writes selection suboptimum cellular as erect-position

(5) personnel selection cellular can not be the cellular at oneself previous step place, unless around other cellular all can not be accessed.

The removable cellular neighbours collection that step 11. obtains according to step 10, judges whether a kth personnel have moveable cellular, if having, perform next step; If not, rest on current cellular position in this moment, perform step 15;

Pheromones intensity on step 12. cellular and neighbours' cellular path residing for the kth of a current time personnel is (during NC=1, pheromones intensity level is the initial information element intensity Q that step 3 is arranged, when NC is not 1, pheromones intensity for step 18 calculates) and the heuristic information that obtains of step 5, calculate the probability of a kth removable cellular of personnel selection neighbours;

In t, the state transition probability formula that a kth personnel transfer to cellular j by cellular i is as follows:

In formula, that personnel k transfers to the transition probability of cellular j by cellular i, τ _ijt () is the pheromones intensity between cellular i and cellular j on path, η _ijt () is the heuristic information between cellular i and cellular j on path, α and β is constant parameter, is used for representing the significance level of pheromones and heuristic information, J _irepresent the neighborhood near cellular i, with the J in formula (6) _iidentical. represent the cumulative sum that cellular i seizes the opportunity to heuristic information and the pheromones of all neighbours' cellulars.

Step 13. draws according to the transition probability that step 12 obtains and a kth personnel is moved to neighbours' cellular that the transition probability of a kth personnel is maximum this cellular place, upgrades the state of this cellular, this cellular is added the evacuation path of these personnel;

The up-to-date cellular moved to of the kth personnel that step 14. obtains according to step 13, judges whether personnel k reaches outlet, if reach, then marks these personnel for " evacuating " state, otherwise marks these personnel for " evacuation " state;

Step 15. is evacuated personnel's counting and is added 1, i.e. k=k+1, carries out removable cellular search to next personnel;

If step 16. k≤m, then illustrate and also do not travel through all evacuation personnel, turn back to step 8, otherwise show that all personnel completes the search of a time step, perform next step;

Step 17. judges whether the current state of all personnel is all " evacuating " state, if then show that all personnel completes the route searching from initial cellular to outlet, namely epicycle evacuation simulation (iteration) completes, and performs next step, otherwise returns step 7;

Each personnel that step 18. obtains according to step 13 from its initial cellular to the evacuation path of outlet, the pheromones intensity on the evacuation path upgrading each personnel between cellular; Once after the search of outlet, lastest imformation element is carried out by formula (8)-(10) from initial position when all personnel completes.

τ _ij(t+Δt)＝(1-q)×τ _ij(t)+Δτ _ij(t+Δt) (8)

$\mathrm{\Δ}{\mathrm{\τ}}_{\mathrm{ij}}(t+\mathrm{\Δt})=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})---\left(9\right)$

${\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})=\left\{\begin{array}{c}\frac{Q}{L_k},\mathrm{edge}(i,j)\∈{\mathrm{path}}_k\\ 0,\mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein, τ _ijt () represents the pheromones strength function between t cellular i and cellular j on path, Q is constant (i.e. the pheromones intensity initial value of step 2 setting), L _kfor the path that k personnel the walk in this circulation, edge (i, j) represents the path between cellular i and cellular j, path _kit is the path of personnel k process.Q is the pheromones intensity volatility coefficient that step 2 is arranged, As time goes on pheromones on path can vapor away, so pheromones ((1-q) × τ that pheromones between current time cellular i and cellular j on path is namely for this reason remaining after volatilizing on path _ij(t)) add time increment during all this cellulars of process personnel Xin Sa under pheromones (Δ τ _ij(t+ Δ t)) sum.

Therefore, the pheromones intensity on path is larger, and the distance between path is shorter, and so personnel k selects the probability of this paths will be larger.Due to this positive feedback mechanism, all personnel can attracted on the shortest route.

Step 19. iteration count NC adds 1, i.e. NC=NC+1;

Step 20. is as NC≤T, and each personnel returns personnel's initial cellular separately that step 3 is arranged, and repeat step 7-19, until NC > T, iteration terminates, and performs next step;

Step 21. exports optimum evacuation path and evacuation time, demonstrates optimum dispersal plan.

In order to verify validity of the present invention, the present invention has carried out emulating comparing with Basic Ant Group of Algorithm by we, in emulation experiment process, chooses true teaching building scene and carries out l-G simulation test.Optimum configurations of the present invention is: ant group algorithm parameter alpha=1, β=2, ρ=0.5, Q=1, maximum iteration time T=100.Potential energy field gain coefficient ξ ₁=2, ξ ₂=1.

Fig. 3 is the graph of a relation of optimum results of the present invention (evacuating path total length) and iterations, as can be seen from the figure, along with the increase of iterations, evacuate path total length obviously to decline, illustrate that the present invention can effectively optimize evacuation path, after iterations reached for 50 generations, evacuate path total length and change not obvious, show that optimization method of the present invention is convergence, and about 50 generations, reach optimum.Fig. 4 is the iteration convergence figure of the present invention and control methods, can draw from figure, and speed of convergence of the present invention is obviously faster.

Table 1 lists the present invention and control methods to the experimental result of different number of evacuation.Can find out for different number of evacuation, the average path drawn by potential energy field ant group algorithm and optimal path can find better solution, and outgoing route is comparatively stable.

Table 1 the present invention and the experimental result of Basic Ant Group of Algorithm to different number of evacuation

Claims (5)

1. drive an indoor evacuation emulation optimization method for cellular ant group algorithm based on potential energy, it is characterized in that, comprise the steps;

Step 1. sets up the buildings evacuation model of two dimensional cellular automaton;

Two dimensional cellular automaton C is defined as following four-tuple:

C＝(D ₂,S,N,f)

Wherein, D ₂be 2 dimension cellular spaces, S is finite state machine set, can be expressed as being positioned at the state of the cellular on case r in t:

S＝{S ₁(r,t),S ₂(r,t),…,S _z(r,t)}

S in formula _z(r, t) represents z the state of the cellular on case r in the t time; N is the neighborhood of cellular centered by r, N={N ₁, N ₂..., N _nd ₂limited sequence subset, n is neighbours' cellular number of the cellular on case r, cellular r and backfence movement rule centered by f;

Step 2. arranges model parameter; Comprise ant group algorithm correlation parameter and potential energy field gain coefficient, the pheromones of evacuation personnel number m, ant group algorithm and heuristic information significance level α and β, pheromones volatility coefficient q, potential energy field gain coefficient ξ ₁and ξ ₂, pheromones intensity initial value Q, the maximum iteration time T of algorithm;

Scene is evacuated in step 3. initialization; According to layout in buildings, evacuation scenario simulation is carried out to two-dimentional cellular space, to place obstacles at random the position of thing and size, according to buildings real scene mark outlet cellular position, evacuation personnel residing cellular position when evacuating beginning is set at random, according to each cellular by barrier, personnel occupy or the free time arranges its original state, pheromones intensity between initialization cellular on path is the Q that step 2 is arranged, and " is not evacuated " by all personnel's state mark for people;

Step 4. calculates the artificial potential energy field of scene;

According to the distribution of step 3 personnel in cellular, calculate total potential energy of each cellular as follows:

$U_{\mathrm{att}}\left(i\right)=\frac{1}{2}{\mathrm{\ξ}}_1{\mathrm{\ρ}}_g^2\left(i\right)---\left(1\right)$

$U_{\mathrm{rep}}\left(i\right)=\left\{\begin{array}{cc}\frac{1}{2}{\mathrm{\ξ}}_2{(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})}^2,& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(2\right)$

U in formula _att(i) and U _repi () is gravitational potential energy and the repulsion potential energy at cellular i place respectively, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ξ ₁, ξ ₂be corresponding potential energy field gain coefficient, ρ (i) is the minimum distance between personnel k and barrier, ρ ₀for the ultimate range that barrier has an impact to people;

The gravitation that personnel are subject at cellular i place and repulsion the negative gradient of corresponding potential energy respectively:

$\stackrel{\‾}{F_{\mathrm{att}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{att}}\left(i\right)\right]={\mathrm{\ξ}}_1{\mathrm{\ρ}}_g\left(i\right)---\left(3\right)$

$\stackrel{\‾}{F_{\mathrm{rep}}}\left(i\right)=-\mathrm{grad}\left[U_{\mathrm{rep}}\left(i\right)\right]=\left\{\begin{array}{cc}\frac{{\mathrm{\ξ}}_2}{{\mathrm{\ρ}}^2\left(i\right)}(\frac{1}{\mathrm{\ρ}\left(i\right)}-\frac{1}{{\mathrm{\ρ}}_0})\▿\mathrm{\ρ}\left(i\right),& \mathrm{\ρ}\left(i\right)\≤{\mathrm{\ρ}}_0\\ 0,& \mathrm{\ρ}\left(i\right)>{\mathrm{\ρ}}_0\end{array}\right.---\left(4\right)$

Wherein ,-grad [U _att(i)] and-grad [U _rep(i)] represent the negative gradient of cellular i point place attractive force potential energy and the negative gradient of repulsive force potential energy respectively, ξ ₁, ξ ₂corresponding potential energy field gain coefficient, ρ _gi () is for cellular i is to target cellular i _geuclidean distance, ▽ ρ (i) represents that barrier points to the vector of unit length of cellular i;

Therefore, composite factor can be expressed as total potential energy that personnel produce at cellular i place:

U _i＝ΣU _att(i)+ΣU _rep(i) (5)

The personnel that step 5. obtains according to step 4, in total potential energy value of current removable cellular, calculate the heuristic information in mobile path;

In t, personnel are moved on cellular j by cellular i, utilize artificial potential energy field to outlet and the perception of barrier, to the heuristic information η of ant group algorithm _ijt () improves, guide personnel searching path, its formula is:

${\mathrm{\η}}_{\mathrm{ij}}\left(t\right)=\frac{1}{\min \left\{d_{j,\mathrm{exits}}\right|j\∈J_i\}\×U_i}---\left(6\right)$

Wherein, η _ijt () is the heuristic information on path between cellular i and cellular j, d _{j, exits}the distance of cellular j to outlet, min{d _{j, exits}| j ∈ J _irepresent the shortest Euclidean distance that cellular j distance exports, J _ithe neighborhood near cellular i, U _ifor total potential energy value of the cellular i that step 4 obtains;

Step 6. arranges iteration count NC=1;

Step 7. Stochastic choice personnel from all evacuation personnel evacuate, if k=1 as first;

Step 8. judges whether the current state of a kth personnel is " evacuating " state, if then perform step 15, otherwise performs next step;

Step 9., according to the cellular at a kth personnel place, obtains the set of its neighbours' cellular;

Neighbours' cellular set that step 10. obtains according to step 9, judges the state of its current time, and neighbours' cellular is idle removable point or by the irremovable point of occupy-place, judges the moveable cellular neighbours collection of a kth personnel according to neighbours' cellular state and taboo rule;

The removable cellular neighbours collection that step 11. obtains according to step 10, judges whether a kth personnel have moveable cellular, if having, perform next step; If not, rest on current cellular position in this moment, perform step 15;

The heuristic information that pheromones intensity on step 12. cellular and neighbours' cellular path residing for the kth of a current time personnel and step 5 obtain, calculates the probability of a kth removable cellular of personnel selection neighbours;

In t, the state transition probability formula that a kth personnel transfer to cellular j by cellular i is as follows:

In formula, that personnel k transfers to the transition probability of cellular j by cellular i, τ _ijt () is the pheromones intensity between cellular i and cellular j on path, η _ijt () is the heuristic information between cellular i and cellular j on path, α and β is constant parameter, is used for representing the significance level of pheromones and heuristic information, J _irepresent the neighborhood near cellular i; represent the cumulative sum that cellular i seizes the opportunity to heuristic information and the pheromones of all neighbours' cellulars;

Step 13. draws according to the transition probability that step 12 obtains and a kth personnel is moved to neighbours' cellular that the transition probability of a kth personnel is maximum this cellular place, upgrades the state of this cellular, this cellular is added the evacuation path of these personnel;

The up-to-date cellular moved to of the kth personnel that step 14. obtains according to step 13, judges whether personnel k reaches outlet, if arrive, then marks these personnel for " evacuating " state, otherwise marks these personnel for " evacuation " state;

Step 15. is evacuated personnel's counting and is added 1, i.e. k=k+1, carries out removable cellular search to next personnel;

If step 16. k≤m, then illustrate and also do not travel through all evacuation personnel, turn back to step 8, otherwise show that all personnel completes the search of a time step, perform next step;

Step 17. judges whether the current state of all personnel is all " evacuating " state, if then show that all personnel completes the route searching from initial cellular to outlet, namely epicycle evacuation simulation completes, and performs next step, otherwise returns step 7;

Each personnel that step 18. obtains according to step 13 to the evacuation path of outlet, upgrade pheromones intensity each evacuating personnel path on cellular between according to formula (8)-(10) from its initial cellular:

τ _ij(t+Δt)＝(1-q)×τ _ij(t)+Δτ _ij(t+Δt) (8)

$\mathrm{\Δ}{\mathrm{\τ}}_{\mathrm{ij}}=(t+\mathrm{\Δt})=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})---\left(9\right)$

${\mathrm{\τ}}_{\mathrm{ij}}^k(t+\mathrm{\Δt})=\left\{\begin{array}{c}\frac{Q}{L_k},\mathrm{edge}(i,j)\∈{\mathrm{path}}_k\\ 0,\mathrm{otherwise}\end{array}\right.---\left(10\right)$

Wherein, τ _ijt () represents the pheromones strength function between t cellular i and cellular j on path, Q is constant, is the pheromones intensity initial value that step 2 is arranged, L _kfor the path that k personnel the walk in this circulation, edge (i, j) represents the path between cellular i and cellular j, path _kit is the path of personnel k process; Q is the pheromones intensity volatility coefficient that step 2 is arranged;

Step 19. iteration count NC adds 1, i.e. NC=NC+1;

Step 20. is as NC≤T, and each personnel returns personnel's initial cellular separately that step 3 is arranged, and repeat step 7-19, until NC > T, iteration terminates, and performs next step;

Step 21. exports optimum evacuation path and evacuation time, demonstrates optimum dispersal plan.

2. a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy according to claim 1, it is characterized in that: in described step 1, centered by f, cellular r and backfence movement rule adopt Moore type neighbours to define, be its neighbours with the cellular on the upper and lower, left and right of center cellular, upper left, lower-left, upper right, these eight directions, bottom right, now neighbours' radius is similarly r=l, and pedestrian can move to reach contiguous idle cellular at one time to these eight directions.

3. a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy according to claim 2, it is characterized in that: the location sets obtaining its neighbours' cellular in described step 9 is the upper of a kth personnel position, under, left, the right side, upper left, lower-left, upper right, the cellular in 8 directions, bottom right.

4. a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy according to claim 1, it is characterized in that, the optimum configurations of this method is: ant group algorithm parameter alpha=1, β=2, ρ=0.5, Q=1, maximum cycle T=100; Potential energy field gain coefficient ξ ₁=2, ξ ₂=1.

5. a kind of indoor evacuation emulation optimization method driving cellular ant group algorithm based on potential energy according to claim 1 or 2 or 3 or 4, it is characterized in that, the taboo rule in described step 10 is:

(1) cellular can only hold personnel;

(2) can move to idle cellular and outlet the personnel of buildings, can not move to the cellular in buildings from the cellular of outlet;

(3) if multiple personnel compete same idle cellular simultaneously, Stochastic choice one people enters, other people rerouting, until all personnel finds oneself subsequent time unique objects on grid;

(4) when personnel can not select current optimum erect-position, then do not considering that Way out situation writes selection suboptimum cellular as erect-position;

(5) personnel selection cellular can not be the cellular at oneself previous step place, unless around other cellular all can not be accessed.