Angus R. Simpson

Genetic Algorithms Compared to Other Techniques for Pipe Optimization

The genetic algorithm technique is a relatively new optimization technique. In this paper we present a methodology for optimizing pipe networks using genetic algorithms. Unknown decision variables are coded as binary strings. We investigate a three-operator genetic algorithm comprising reproduction, crossover, and mutation. Results are compared with the techniques of complete enumeration and nonlinear programming. We apply the optimization techniques to a case study pipe network. The genetic algorithm technique finds the global optimum in relatively few evaluations compared to the size of the search space. INTRODUCTION The construction and maintenance of pipelines for water supply costs many millions of dollars every year. As funds for the development of new infrastructure become increasingly scarce, there is an increasing desire to achieve the highest level of effectiveness for each dollar spent. Traditionally, the design of water distribution networks has been based on experience. However, there is now a significant (and growing) body of literature devoted to optimization of pipe networks. Much of the research to date has applied deterministic optimization techniques (including linear programming, dynamic programming, and nonlinear programming) to the problems of network design. A new and developing field involves the application of stochastic optimization techniques (such as genetic algorithms and simulated annealing) to large combinatorial problems. This paper applies genetic algorithms to the problem of designing pipe networks and compares its performance with the techniques of complete enumeration and nonlinear programming. PIPE NETWORK OPTIMIZATION PROBLEM In its simplest form, the problem of pipe network design for gravity systems is usually formulated in the following way. For a given layout of pipes and specified demands at the nodes, find the combination of pipe sizes that gives the minimum cost, subject to the following constraints: 1. Continuity of flow must be maintained at all junctions or nodes in the network. 2. The head loss in each pipe is a known function of the flow in the pipe, its diameter, length, and hydraulic properties. 3. The total head loss around a loop must equal zero or the head loss along a path between two reservoirs must equal the elevation difference. 4. Minimum and maximum pressure head limitations must be satisfied at certain nodes in the network. 5. Minimum and maximum diameter constraints may apply to certain pipes in the network. In addition, there may be existing pipes in the system with known diameters. One may usually assume steady state flow conditions in the network, although more than one loading condition may need to be considered. Extensions of the problem allow for valves, pumps, and storage tanks to be sized or selected. Goulter (1987) suggested that the minimum cost design for a given layout and single loading case is a branched network (i.e., a network with no loops). In practice, loops are an essential feature of actual distribution systems as they provide an alternative flow path if there is pipe failure or for maintenance. One can achieve a degree of redundancy in pipe network optimization by ensuring that the layout has appropriate loops and by specifying minimum diameters for all pipes. DETERMINISTIC SOLUTION TECHNIQUES A large literature exists on the optimization of pipe networks. Lansey and Mays (1989b) provide a comprehensive review of the published literature up to 1988. The following review will concentrate on the more recent papers. The traditional method for designing pipe networks is by trial and error guided by experience. In design of pipe networks, designers often make use of commercial simulation packages such as KYPIPE (Wood 1980), WATSYS [or WATERMAX in the United States (Olde 1985)] or WATER (Fowler 1990). A common technique is to ensure for each pipe in the system that the slope of the hydraulic grade line lies within reasonable bounds. Monbaliu et al. (1990) have proposed a type of gradient search technique to achieve an efficient design. Initially, they set all pipes at their minimum diameters and a simulation package was used to determine the pressures at all nodes in the network. If the minimum pressure constraints were not satisfied, the pipe with the maximum head loss per unit length was increased to the next available size and a further simulation was carried out. They repeated this process until all pressure constraints were satisfied. They obtained nearoptimal solutions in two test cases. Enumeration Complete enumeration is one approach for the optimization of pipe networks. The technique simulates every possible combination of discrete pipe sizes. One selects the cheapest cost network that satisfies the pressure constraints. The main drawback of this technique is the amount of computer time involved. For example, a relatively small system with eight pipes and eight possible sizes for each has 16,777,216 possible solutions. Gessler (1985) has proposed the use of selective enumeration of a severely pruned search space to optimize the design of a pipe network. One has to base the pruning of the search space on experience. Unfortunately, the global optimum may be eliminated in the process of pruning. Loubser and Gessler (1990) suggested guidelines for pruning the search space to reduce the amount of computational effort involved in enumeration; these included: (1) Grouping sets of pipes and assuming that a single diameter will be used for each group; (2) progressively storing the lowest cost solution which satisfies the constraints and eliminating all other solutions of higher cost; and (3) checking on combinations that violate the constraints. One eliminates all combinations that include the same or smaller pipe sizes. The use of guidelines 2 and 3 removes the need to check for hydraulic feasibility of particular networks since this is computationally demanding. Despite these aids, one requires a considerable amount of computer time for large networks and there is no guarantee that the optimal solution will remain in the pruned search space after applying these heuristics. Linear Programming A number of researchers have used linear programming to optimize a design of a pipe network. Researchers have developed two principal approaches (Alperovits and Shamir 1977; Quindry et al. 1979). These are reviewed in Lansey and Mays (1989b). Nonlinear Programming One can apply a number of nonlinear optimization packages to the network design problem. They include MINOS (Murtagh and Saunders 1987), GINO (Liebman et al. 1986), and GAMS (Brooke et al. 1988). All these packages use a constrained generalized reduced gradient technique to identify a local optimum for the network problem. Constraints can be included explicitly in the model. Examples include the continuity equations, head losses around loops or between reservoirs, minimum and maximum pressure limitations, and minimum and maximum diameters. Costs can be expressed as any nonlinear function of pipe diameter and length. The limitations of the technique are as follows: (1) Because the pipe diameters are continuous variables the optimal values will not necessarily conform to the available pipe sizes; thus, rounding of the final solution is required; (2) only a local optimum is obtained; and (3) there is a limitation on the number of constraints and hence the size of network that can be handled. Researchers have reported a number of applications of nonlinear optimization to pipe network problems (EI-Bahrawy and Smith 1985, 1987; Su et al. 1987; Lansey and Mays 1989a; Lansey et al. 1989; Duan et al. 1990). EI-Bahrawy and Smith (1985) applied MINOS to the design of water collection and distribution systems. Their model included a preprocessor to set up the data files and a postprocessor to round off the pipe sizes to commercial diameters. The model for distribution systems included pumps, check valves, and pressure-reducing valves. They obtained the optimal solution to a 33pipe network in a reasonable amount of computer time. E1-Bahrawy and Smith (1987) applied the aforementioned optimization model to a number of case studies. They demonstrated its ability to: (1) Handle pumps and valves; (2) to find the optimal location of booster pumps and their optimal lifts; and (3) to address the optimal layout problem. Su et al. (1987) used nonlinear programming to optimize looped pipe networks. In addition they included reliability constraints. They based the optimization model on the generalized reduced gradient (GRG) technique. A steady-state simulation model [KYPIPE, Wood (1980)] was used at each iteration to calculate pressure heads throughout the system. A separate model was used to compute the reliability of both system and nodes. They defined reliability as the probability of the design pressure being maintained at appropriate nodes in the system, given the possibility of some pipes being unavailable because of breakage. The model cannot include other elements such as pumps, valves, and storage tanks. The inclusion of constraints on reliability usually produced looped networks. Lansey et al. (1989) considered the optimal design of pipe networks where there is uncertainty in the nodal demands, Hazen-Williams coefficients and the minimum nodal heads. They used a chanceconstrained approach to convert the probabilistic constraints into deterministic ones. The constraints included the probability of the system being able to satisfy the specified nodal demands and heads. The GRG technique identified the optimum pipe sizes. The method tended to produce branched pipe networks. Lansey and Mays (1989a) used nonlinear programming to find the optimum design and layout of pipe networks. Their model was able to simulate pumps, tanks, and multiple loading cases. They embedded a simulation package [KYPIPE, Wood (1980)] in the model to ensure that the continuity and head loss constraints were satisfied. A GRG

An Improved Genetic Algorithm for Pipe Network Optimization

An improved genetic algorithm (GA) formulation for pipe network optimization has been developed. The new GA uses variable power scaling of the fitness function. The exponent introduced into the fitness function is increased in magnitude as the GA computer run proceeds. In addition to the more commonly used bitwise mutation operator, an adjacency or creeping mutation operator is introduced. Finally, Gray codes rather than binary codes are used to represent the set of decision variables which make up i the pipe network design. Results are presented comparing the performance of the traditional or simple GA formulation and the improved GA formulation for the New York City tunnels problem. The case study results indicate the improved GA performs significantly better than the simple GA. In addition, the improved GA performs better than previously used traditional optimization methods such as linear, dynamic, and nonlinear programming methods and an enumerative search method. The improved GA found a solution for the New York tunriels problem which is the lowest-cost feasible discrete size solution yet presented in the literature.

Parametric study for an ant algorithm applied to water distribution system optimization

Much research has been carried out on the optimization of water distribution systems (WDSs). Within the last decade, the focus has shifted from the use of traditional optimization methods, such as linear and nonlinear programming, to the use of heuristics derived from nature (HDNs), namely, genetic algorithms, simulated annealing and more recently, ant colony optimization (ACO), an optimization algorithm based on the foraging behavior of ants. HDNs have been seen to perform better than more traditional optimization methods and amongst the HDNs applied to WDS optimization, a recent study found ACO to outperform other HDNs for two well-known case studies. One of the major problems that exists with the use of HDNs, particularly ACO, is that their searching behavior and, hence, performance, is governed by a set of user-selected parameters. Consequently, a large calibration phase is required for successful application to new problems. The aim of this paper is to provide a deeper understanding of ACO parameters and to develop parametric guidelines for the application of ACO to WDS optimization. For the adopted ACO algorithm, called AS/sub i-best/ (as it uses an iteration-best pheromone updating scheme), seven parameters are used: two decision policy control parameters /spl alpha/ and /spl beta/, initial pheromone value /spl tau//sub 0/, pheromone persistence factor /spl rho/, number of ants m, pheromone addition factor Q, and the penalty factor (PEN). Deterministic and semi-deterministic expressions for Q and PEN are developed. For the remaining parameters, a parametric study is performed, from which guidelines for appropriate parameter settings are developed. Based on the use of these heuristics, the performance of AS/sub i-best/ was assessed for two case studies from the literature (the New York Tunnels Problem, and the Hanoi Problem) and an additional larger case study (the Doubled New York Tunnels Problem). The results show that AS/sub i-best/ achieves the best performance presented in the literature, in terms of efficiency and solution quality, for the New York Tunnels Problem. Although AS/sub i-best/ does not perform as well as other algorithms from the literature for the Hanoi Problem (a notably difficult problem), it successfully finds the known least cost solution for the larger Doubled New York Tunnels Problem.

Accounting for Greenhouse Gas Emissions in Multiobjective Genetic Algorithm Optimization of Water Distribution Systems

Considerable research has been carried out on the optimization of water distribution systems WDSs over the last three decades. In previous research, attention has mainly focused on the minimization of cost, due to the high expenditure associated with the construction and maintenance of such systems. However, the impacts of WDSs on the environment usually have not been considered adequately. The recent increasing awareness of sustainability and climate change, especially global warming, has led to research where greenhouse gas GHG emissions are considered. In the study described in this paper a multiobjective genetic algorithm for WDS optimization has been used as an explorative tool to investigate the trade-offs between the traditional economic objective of minimizing costs and an additional environmental objective of minimizing GHG emissions. The impacts of minimizing GHG emissions on the results of WDS optimization have been explored for a case study in this paper. The results indicate that the inclusion of GHG emission minimization as one of the objectives results in significant trade-offs between the economic and environmental objectives. Furthermore, a sensitivity analysis has been conducted by using different discount rates in a present value analysis for computing both ongoing costs and GHG emissions. The results obtained show that the Pareto-optimal front is very sensitive to the discount rates used. As a result, the selection of discount rates has a significant impact on final decision making.

A SELF-ADAPTIVE BOUNDARY SEARCH GENETIC ALGORITHM AND ITS APPLICATION TO WATER DISTRIBUTION SYSTEMS

The success of the application of genetic algorithms (GA) or evolutionary optimization methods to the design and rehabilitation of water distribution systems has been shown to be an innovative approach for the water industry. The optimal design and rehabilitation of water distribution systems is a constrained non-linear optimization problem. Constraints (for example, the minimum pressure requirements) are generally handled within genetic algorithm optimization by introducing a penalty cost function. The optimal or near optimal solution is found when the pressures at some nodes are close to the minimum required pressure or at the boundary of critical constraints. This paper presents a new approach called the self-adaptive boundary search strategy for selection of penalty factor within genetic algorithm optimization. The approach co-evolves and self-adapts the penalty factor such that the genetic algorithm search is guided towards and preserved around constraint boundaries. Thus it reduces the amount of simulation computations within the GA search and enhances the efficacy at reaching the optimal or near optimal solution. To demonstrate its effectiveness, the self-adaptive boundary search strategy is applied to a case study of the optimization of a water distribution system in this paper. It has been shown that the boundary GA search strategy is effective at adapting the feasibility of GA populations for a wide range of penalty factors. As a consequence, the boundary GA has been able to successfully find the least cost solution in the case study more effectively than a GA without the boundary search strategy. Thus a reliable least cost solution is guaranteed for the GA optimization of a water distribution system.

Experimental verification of the frequency response method for pipeline leak detection

This paper presents an experimental validation of the frequency response method for pipeline leak detection. The presence of a leak within the pipe imposes a periodic pattern on the resonant peaks of the frequency response diagram. This pattern can be used as an indicator of leaks without requiring the “no-leak” benchmark for comparison. In addition to the experimental verification of the technique, important issues, such as the procedure for frequency response extraction and methods for dealing with frequency-dependent friction are considered in this paper. In this study, transient signals are generated by a side-discharge solenoid valve. Non-linearity errors associated with large valve movements can be prevented by a change in the input parameter to the system. The optimum measuring and generating position for two different system boundary configurations—a symmetric and an antisymmetric system—are discussed in the paper and the analytical expression for the leak-induced pattern in these two cases is derived

Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools

This two-part paper investigates key parameters that may affect the pressurewaveform predicted by the classical theory ofwater-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equations is used herein as the basic solution tool. In separate additions: a convolution-based unsteady friction model is explicitly incorporated; discrete vapour and gas cavity models allow cavities to form at computational sections; coupled extended water-hammer and steel-hammer equations describe FSI; viscoelastic behaviour of the pipe-wall material is governed by a generalised Kelvin–Voigt model; and blockages and leakages are modelled as end or internal boundary conditions

Single-objective versus multiobjective optimization of water distribution systems accounting for greenhouse gas emissions by carbon pricing.

Previous research has demonstrated that there are significant trade-offs between the competing objectives of minimizing costs and greenhouse gas (GHG) emissions for water distribution system (WDS) optimization. However, upon introduction of an emission trading scheme, GHG emissions are likely to be priced at a particular level. Thus, a monetary value can be assigned to GHG emissions, enabling a single-objective optimization approach to be used. This raises the question of whether the introduction of carbon pricing under an emission trading scheme will make the use of a multiobjective optimization approach obsolete or whether such an approach can provide additional insights that are useful in a decision-making context. In this paper, the above questions are explored via two case studies. The optimization results obtained for the two case studies using both single-objective and multiobjective approaches are analyzed. The analyses show that the single-objective approach results in a loss of trade-off informa...

Battle of the Water Networks II

The Battle of the Water Networks II (BWN-II) is the latest of a series of competitions related to the design and operation of water distribution systems (WDSs) undertaken within the Water Distribution Systems Analysis (WDSA) Symposium series. The BWN-II problem specification involved a broadly defined design and operation problem for an existing network that has to be upgraded for increased future demands, and the addition of a new development area. The design decisions involved addition of new and parallel pipes, storage, operational controls for pumps and valves, and sizing of backup power supply. Design criteria involved hydraulic, water quality, reliability, and environmental performance measures. Fourteen teams participated in the Battle and presented their results at the 14th Water Distribution Systems Analysis conference in Adelaide, Australia, September 2012. This paper summarizes the approaches used by the participants and the results they obtained. Given the complexity of the BWN-II problem and the innovative methods required to deal with the multiobjective, high dimensional and computationally demanding nature of the problem, this paper represents a snap-shot of state of the art methods for the design and operation of water distribution systems. A general finding of this paper is that there is benefit in using a combination of heuristic engineering experience and sophisticated optimization algorithms when tackling complex real-world water distribution system design problems

ANT COLONY OPTIMIZATION FOR THE DESIGN OF WATER DISTRIBUTION SYSTEMS

During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the optimal design and operation of water distribution systems. More recently, ant colony optimization algorithms (ACOAs), which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to a number of benchmark combinatorial optimization problems. In this paper, a formulation is developed which enables ACOAs to be used for the optimal design of water distribution systems. This formulation is applied to two benchmark water distribution system optimization problems and the results are compared with those obtained using genetic algorithms. The findings of this study indicate that ACOAs are an attractive alternative to GAs for the optimal design of water distribution systems, as they outperformed GAs for the two case studies considered both in terms of computational efficiency and their ability to find near global optimal solutions.