論文

Various modes of transportation are available when people travel within cities, and trips can be classified into two types depending on whether some type of vehicle is used. Compared to vehicular travel, trips conducted only by walking have the advantages of lower environmental impact and less space required for road networks. By assuming that the proportion of walking-only trips decreases exponentially with the distance traveled, we explore the problem of finding a city shape with a fixed land area that maximizes the number of walking-only trips based on Manhattan distance. For many-to-one travel with the city center as the destination, we show that the optimal city shape is a diamond. For many-to-many travel, a method is presented that expresses the number of walking-only trips as a double integral, originally formulated as a four-dimensional integral. Using this, an optimization problem is formulated whose variables are the vertex coordinates of a polygon, and approximate solutions for the optimal city shape under several different settings are obtained numerically. For many-to-many travel, it is shown that a large number of walking-only trips occur when the city shape is close to being circular, although the exact shape varies with the distance deterrence coefficient.

We develop a variant of the flow interception problem (FIP) in which it is more desirable for travelers to be intercepted as early as possible in their trips. In addition, we consider flows being intercepted probabilistically instead of the deterministic view of coverage assumed in the FIP literature. We call the proposed model the probabilistic minisum FIP (PMFIP); it involves minimizing the sum of the expected distance that each flow travels until intercepted at a facility among placed facilities. This extension allows us to evaluate the effect of facility location under any given value of the interception probability and to apply the model to a variety of situations. We apply the proposed model to an example network by assuming a hypothetical situation in which people gather at a stadium from various nodes on the network, and receive some goods or services on the way to the stadium. We analyze optimal solutions obtained by varying the number of facilities and interception probability. It is shown that the expected travel distance until intercept is greatly reduced by means of a few optimally located facilities under a moderate interception probability.

We consider the problem of dividing a given convex polygon into p convex polygons called zones, each of which receives a designated land area. The position and shape of each zone is determined so that intra- and inter-zonal trips for the resulting zones are conducted efficiently. To evaluate the compactness of the resulting zones, we derive the average squared distance between two points uniformly distributed in each zone, as well as the average squared distance between two points uniformly distributed in two zones. The weighted sum of these measures is used as the objective function, and a Voronoi-based heuristic algorithm is proposed that iteratively updates the positions of p generator points placed inside a convex polygon. The method is used to divide several regular polygons, and the results show that zones become (i) rounded when intra-zonal trips are prioritized and (ii) elongated with longer boundary lines when inter-zonal trips are prioritized.

This paper proposes a mathematical optimization model for designing safe walking routes for children from school to homes. We focus on the existing bi-objective model, the safe walking route design problem, which minimizes both the total walking risk and the total route distances for all children from school to home. The original problem assumes that the combined routes for all children forms a directed out-tree rooted at the school. However, making this assumption excludes solutions such as those involving cycles. This paper explores how to relax the assumption that the graph is an out-tree by using a layered network constructed from the original network. Using the layered network formulation, we obtain some solutions that have better objective values than those obtained by the original formulation when we strongly emphasize reducing the risk objective. The results also show that the new formulation produces the same out-tree solution when minimization of the risk objective and the distance objective are suitably balanced.

The flow interception location model (FILM) focuses on vehicular traffic in a road network and locates a fixed number of facilities so as to maximize the total flow that can be serviced at facilities along preplanned routes, such as a daily commute to work. This paper develops a version of FILM, the railway flow interception location model (R-FILM), that explicitly focuses on railway passenger flows. For railway users, accessing a facility placed at an origin, destination, or transfer station (ODT station) is easier than visiting a facility at other stations included in the travel path. Accessing a facility at a non-ODT station involves the additional cost of disembarking the train to obtain a service and then boarding another train after consuming the service. R-FILM introduces this railway-specific structure to FILM by introducing two different coverages according to the types of station intercepted for each flow. Concretely, a given flow is called strongly covered when at least one facility is located at an ODT station. Similarly, a given flow is called weakly covered when no facility is located at an ODT station, but at least one facility is located among stations included in the travel path. We present an integer programming formulation of the proposed R-FILM. Using it, we conduct a large-scale case study of the Tokyo metropolitan railway network, which includes about 1500 railway stations. Input flow is constructed using census data for commuter traffic, with about 100,000 distinct flow paths. Optimal solutions of both models for single- and multi-facility problems are analyzed. In R-FILM solutions, large terminal stations tend to be selected more often than with FILM.