טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKrapivka Ariel
SubjectA Hybrid Optimization Model for the Design of Water
Disribution Systems
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Avi Ostfeld
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

A water distribution system is made up of pipes, tanks, pumps, valves and other devices.  Its main purpose is to supply water demand according to the required amounts and pressures.  Over the last four decades, the design of water distribution systems has been extensively analyzed. At the beginning, the problem was studied with respect to the minimization of installation and operation costs.  With the improvement of information technology capabilities and specifically the development of hydraulic simulators, other aspects of the design problem have been studied.  Among the issues studied are water quality and the reliability of supply.

The presented work suggests a solution to the design of a network with a given configuration based on the minimization of installation costs.

The model that was formulated in this work is a combination of two models introduced by Alperovits and Shamir (1977), and Savic and Walters (1997).

The problem is divided into two sub-problems.  The inner problem includes a LP model that was formulated according to the general formulation of Alperovits and Shamir.  The LP model was implemented and solved by the "solver" add-in of Microsoft Excel.  The decision variables of this LP problem are the lengths of pipes sections, where each section has a different diameter, which is chosen from a few candidate diameters.  The objective function is to minimize installation costs, and the problem is subject to the following constraints:

          i.               The sum of the lengths of pipe sections must be equal to the length of the entire pipe.

        ii.               The pipes section lengths must be non-negative.

      iii.               A minimal head is required at each demand junction.

      iv.               Energy continuity must be held in each loop.


The outer problem includes a GA model, which was implemented in a Visual Basic for Applications (VBA) code.  The decision variable of this problem is the flow distribution for each network loop.

The outer problem (GA) and the inner problem (LP) are solved in a loop until a stopping condition or a maximum number of iterations is achieved, leading to minimum installation cost based on an optimal flow distribution and section length for candidate diameters of each pipe.  Due to the combination of the two optimization techniques, the algorithm introduced here is called "LP-GA".


This work showed that the “LP-GA” algorithm can compete with other algorithms for water distribution system design, and it is suggested that this algorithm could serve as a Decision Support System (DSS) for water distribution system designers.