Multi-objective Integrated Design Of Transit Routes And Frequencies Setting

Transit route planning is a multi-objective optimization problem.The problem usually relates to two goals which are travel costs and public transportation operating cost.The relationship between these two goals is the trade-off:the optimal solution of one goal will lead to another increase its costs,and vice versa.These two goals cannot achieve optimal solutions simultaneously.Previous studies for bus route planning only optimized for a single goal.This single optimization only takes into account the interests of one party without the interests of the other party.This paper makes public transportation network plan from the perspective of users and public transport enterprises.A compromise solution is found from these two goals.This solution takes account of the interests of all parties.And it can enable operators and users to achieve a win-win situation.This article established a multi-objective integrated design of transit routes and frequencies setting model.It contains two functions in order to minimize travel costs(bus users)and the operating costs of the bus companies(public transport operators).From the point of view of bus users,it makes one objective function and user costs are represented by the average total travel time;from the point of view of public transport operators,it makes the other objective function and operation costs are represented by bus fleet size.User costs objective function meets the minimum total travel costs and operation costs function meets the minimum cost of operation,so this is a multi-objective integrated design issues of bus routes and frequencies,including determination of a set of transit routes and their associated frequency.The main contents of the article include the following:K-shortest paths algorithm to determine the set of transit routes.Using k-shortest paths algorithm,according to certain constraints,it can get the set of transit routes.K-shortest paths algorithm is to find multiple alternate paths from starting point to the destination of the road network.These alternate paths form a shortest paths group,which are the set of transit routes.Set cover algorithm to determine the transit routes.Set cover algorithm can determine a subset of transit routes from the set of transit routes.The subset of transit routes are the public transport transit routes.The public transport transit routes can be solved by the set cover problem.Set cover problem is represented by a matrix,the rows of the matrix represent OD,the columns of the matrix represent transit routes.Set cover problem is solved by greedy select strategy and redundant column processing strategy.Greedy select strategy selects some columns(transit routes)to cover rows(transit OD),until all rows are covered or no columns can cover the left rows.When using greedy select strategy,there are some combination columns covering the same rows.It is just need one combination columns,other combination columns are redundant columns.It can use the redundant processing strategy to remove the redundant columns reducing the scale of the problem.Through both of these two strategies can identify a subset of the transit routes from the transit routes set.This subset of transit routes covered all the transit OD,so as to meet the needs of transit passengers.Transit assignment.This article considers the users travel choice behavior in transit assignment based on the optimum travel strategy.For the direct bus routes,it used the principle of frequency sharing to make transit assignment.For the transfer transit paths,it used the principle of minimum transfer time to make transit assignment.Iteration algorithm of frequencies.For transit assignment,it needs to determine the initial frequency in advance,so it can get the flow of all link sections of the transit routes.A transit route consists of some transit link sections,and the maximum passenger flow of link sections is the maximum cross section passenger flow.The maximum cross section passenger flow divided bus capacity,it can get the new frequencies.With the new frequencies,reassignment transit flow and update frequencies,until meet the convergence criterion.It can get the final frequency through the iteration process.Establishment multi-objective integrated design of transit routes and frequencies setting model.Multi-objective integrated design of transit routes and frequencies setting model includes two important aspects which are the transit routes design and transit assignment.Transit routes design and transit assignment are usually described as convex nonlinear programming problems.This model contains two decision variables,which are the transit routes and transit link flow.The design of transit routes is the discrete decision variables in the model.However,the transit link flow is continuous decision variables.This article refers to the previous solution method,converting this problem into a bi-level programming model.The bi-level programming model calculate discrete decision variables and continuous decision variables separately.The upper level can solve transit route design,and the lower level can solve transit assignment.Example analysis.In the end,it made an example analysis.It used the benchmark transit network(Mandl network)to test the performance of method used in this article.It given three schemes of transit routes,completed three solutions of the three schemes.It used the ideal point method to determine the optimal solution.It made a comparison with previous research did by other authors.The results display,whether operating costs or costs for users,the method used in this article is better than the other methods.