Automating Layouts of Sewers in Subdivisions Neil Burch and Rob Holte and Martin M¨ uller and David O’Connell and Jonathan Schaeffer 1 Abstract. An important part of the creation of a housing subdivi- sion is the design and layout of sewers underdeath the road. This is a challenging cost optimization problem in a continuous three- dimensional space. In this paper, heuristic-search-based techniques are proposed for tackling this problem. The result is new algorithms that can quickly find near optimal solutions that offer important re- ductions in the cost of design and construction. 1 INTRODUCTION The design of a housing subdivision is a complex civil engineering task. In the concept phase, the designer decides on how a tract of land will be subdivided into housing lots connected by roads. In the design phase, the core infrastructure is planned, including the analysis of the terrain, grading of the land (elevation), sewers (water, sanitary), and conduits (power, telephone). Finally, in the layout phase, all the de- sign considerations are mapped to an implementation. The design is typically done as part of the tendering process by a civil engineering firm. If they are the successful bidder, then they do the layout. Most of the design and layout of a subdivision is manually done, with a professional civil engineer required to verify its adequacy and compliance with regulations. One of the labor-intensive aspects is the design and layout of the sewers. This is a difficult problem for engi- neers. It is a three-dimensional optimization problem in a continuous search space. Typically, engineers adopt a least-effort solution, such as laying the sewers down underneath the middle of the road. These solutions are demonstrably suboptimal, adding to the subdivision de- veloper’s construction costs. This paper poses the problem of automating the design and layout of sewers in subdivisions as an interesting AI application. Although the sewer problem is a small part of the overall process of creating a subdivision, automating this process has cost advantages. First, it will reduce the manual effort required for the design and layout phases. Second, a (near) optimal solution will reduce the construction costs. Automation of the sewer problem has been tackled by several re- searchers in the engineering community. Their solutions are typically genetic algorithm or simulated annealing based. In contrast, we take a heuristic search approach. The contributions of this paper are as follows: 1. An understanding of an important real-world engineering applica- tion. Given the difficult cost function and numerous special cases, an elegant all-encompassing solution is not possible. 2. A new algorithm for determining and placing the minimum num- ber of manholes (ground connections to the sewer) on a single road. Dynamic programming is used to obtain an optimal global layout cost, subject to a restriction on the location of manholes in intersections. 1 Department of Computing Science, University of Alberta, Canada, email: {holte,jonathan}@ualberta.ca 3. The road layout, expressed as a graph, has cycles. The sewer sys- tem cannot have cycles. We present a new approach for “cutting” the graph into a tree and exploring the search space of possible spanning trees to find a high-quality solution. 4. A complete working system that can produce an anytime solution. It scales to larger networks than have been solved previously. Although this research deals with sewer system planning, these ideas are applicable to other types of pipe networks (e.g., water dis- tribution networks [1]). 2 SEWER SYSTEMS A sewer system is a subterranean system used to convey waste to one or more collection points (outfalls). There are two types of sewer sys- tems: sanitary, to convey industrial and household waste, and storm, to prevent flooding by draining surface water. In this paper, without loss of generality we limit the discussion to storm sewers. Each segment of pipe in a sewer system is connected by a man- hole. A sewer design is a list of manholes and pipes. Each manhole has a location and depth. Every pipe has an upstream and down- stream manhole, a diameter, and an upstream and downstream depth. The difficulties in designing a sewer arise from a large set of con- straints. For example, the sewer must have the capacity to handle the load it is expected to experience. All roads in a subdivision must have a pipe, and all pipes must go under the road. The slope of all pipes must be over some minimum value so that they drain (we only con- sider systems which use gravity to properly drain) and under some maximum so that the pipes do not wear too quickly. There are only certain fixed diameters of pipes available. Pipes must be buried to a minimum depth. Segments of pipe must not exceed some fixed maxi- mum length. We consider all of these in our work, but there are a few other parameters not included that would be needed for a production system (e.g., curved pipe segments, and constraints on the angle at which two pipes can meet). An important issue that needs to be considered when burying pipes is the slope. Pipe slope affects both the flow velocity and the pressure within the pipes. The goal of design is to keep the flow velocity above the minimum self cleansing velocity. If the velocity of the flow is too low, deposits may build up within the pipe, obstructing the flow. However, if the velocity is high enough these deposits are prevented, and thus the system is self cleansing. Sewer systems where the slope of the pipes alone convey the sewage are known as gravity sewer systems; more complex systems may need pumps. In this paper, we only consider gravity-based systems. The rules for the design and layout of a sewer system are governed by the regulations of the local municipality in which the housing subdivision is located. There are numerous constraints imposed by municipalities, with no standardization across jurisdictions. A pro- duction quality sewer design tool needs to handle the plethora of pa- rameter settings.