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In this paper, a weighted cellular automata (CA) is proposed to solve bi-objective reservoir operation optimisation problem considering two objectives of water supply and hydropower production. A mathematically derived updating rule is used contributing to the efficiency of the proposed CA method. The updating rule of the problem is derived by converting the bi-objective problem to a single-objective problem using the well-known weighting method. The proposed method is used to operate the Dez reservoir in Iran over various operation periods of 60, 120, 240 and 480 months to test the performance of the method for operational problems of different scales. Performance of the method is also compared with that of a non-dominated sorting genetic algorithm (NSGAII) as one of the most popular multi-objective evolutionary algorithms. The results indicate that the proposed method is highly efficient compared to the NSGAII while producing comparable results. This is in line with the early findings of superior efficiency and comparable effectiveness of the CA method with the existing evolutionary algorithms for single objective optimisation problems. [ABSTRACT FROM AUTHOR]

A novel hybrid genetic algorithm and cellular automata method is presented here for solving reliability-based reservoir operation problems. The method uses a decomposition approach in which the reliability part of the problem is handled with a GA, while the operational side of the problem is solved by a CA method. In the proposed method, a binary genetic algorithm is employed to determine success/failure periods of the operation. A period is considered as a success period if the corresponding gene value is one, and failure period if otherwise. The success/failure pattern suggested by the genetic algorithm is used to explicitly rewrite the reliability constraints of the operation problem in terms of the reservoir releases. A CA method is then used to solve the resulting problem in which the two types of the constraints, namely operational constraints and reliability constraints, are dealt with differently. Operational constraints are applied to all periods, while reliability constraints are only applied to the success periods determined by genetic algorithm. The proposed method is used for monthly water supply and hydropower operation of Dez reservoir in Iran, and the results are presented and compared with those of a GA model. The efficiency and effectiveness of the method are tested for the short-, medium- and long-term operation periods assuming different target reliabilities. Comparison of the results with those of a GA model shows that the proposed method is both more effective and efficient compared to GA. [ABSTRACT FROM AUTHOR]

An adaptive hybrid genetic algorithm (GA) and cellular automata (CA) method is proposed for solving implicit stochastic optimization of reservoir operation problems. The method is based on a decomposition approach in which the reliability constraints are handled with GA, whereas the resulting deterministic problem is solved with a CA model. Two versions, binary and integer GA, were employed for handling the reliability constraints of the problem. In the first one, GAwas used to determine the success/failure pattern of the operation, whereas in the latter, only failure periods were determined with GA. The proposed method was used for monthly water supply and hydropower operation of an existing reservoir and the results are presented and compared with those of a GA model. To demonstrate the efficiency and scale independency of the model, short-term, medium-term, and long-term operations are considered assuming different target reliabilities. Comparison of the results with those of a GA model shows the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid mixed-integer linear programming-linear programming-linear programming (MILP-LP-LP) methodology for simultaneous optimal design and operation of unconfined groundwater utilization systems. The proposed model is an extension to the earlier LP-LP model introduced by the authors for the optimal design and operation of confined groundwater utilization systems. The proposed model can be used to minimize the total cost, including the well drilling, pump installation cost and energy cost, of utilizing a two-dimensional unconfined aquifer under both steady-state and transient flow conditions. The solution of the problem is defined by the well numbers and location, well drilling depth and the corresponding pumping rates, satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown in the wells. A discretized version of the differential equation governing the aquifer is first embedded into the model formulation as additional constraints. The resulting mixed-integer non-linear programming problem is then decomposed into three sub-problems with different sets of decision variables, namely, hydraulic head, well numbers and locations and their pumping rates, and well depths. Startingwith a set of randomvalues for all decision variables, the three sub-problems are solved assuming fixed values for the other variables. This process is iterated until convergence is achieved. [ABSTRACT FROM AUTHOR]

In this article, cellular automata based hybrid methods are proposed for the optimal design of sewer networks and their performance is compared with some of the common heuristic search methods. The problem of optimal design of sewer networks is first decomposed into two sub-optimization problems which are solved iteratively in a two stage manner. In the first stage, the pipe diameters of the network are assumed fixed and the nodal cover depths of the network are determined by solving a nonlinear sub-optimization problem. A cellular automata (CA) method is used for the solution of the optimization problem with the network nodes considered as the cells and their cover depths as the cell states. In the second stage, the nodal cover depths calculated from the first stage are fixed and the pipe diameters are calculated by solving a second nonlinear sub-optimization problem. Once again a CA method is used to solve the optimization problem of the second stage with the pipes considered as the CA cells and their corresponding diameters as the cell states. Two different updating rules are derived and used for the CA of the second stage depending on the treatment of the pipe diameters. In the continuous approach, the pipe diameters are considered as continuous variables and the corresponding updating rule is derived mathematically from the original objective function of the problem. In the discrete approach, however, an adhoc updating rule is derived and used taking into account the discrete nature of the pipe diameters. The proposed methods are used to optimally solve two sewer network problems and the results are presented and compared with those obtained by other methods. The results show that the proposed CA based hybrid methods are more efficient and effective than the most powerful search methods considered in this work. [ABSTRACT FROM PUBLISHER]

The particle swarm optimisation algorithm is a global optimisation method proposed and mainly used for continuous optimisation problems. The method shows interesting features, in particular fast convergence characteristics. It does, however, lack sufficient exploration, especially when the grouping of the swarm starts leading to sub-optimal solutions when solving difficult problems. This paper introduces two mutation mechanisms to balance the exploitative characteristics of the algorithm. The timing of the proposed mutations is designed such that the inherent exploration of the method is not disturbed. The proposed mutated algorithms cannot, therefore, produce inferior results to that of the original method. Furthermore, mutation is only carried out on those particles that are already converged to the global best position and, in effect, are not of any particular use to the collective intelligence of the swarm. The performance of the proposed mutated algorithms is tested against two reservoir operation problems and the results are presented and compared with those of the standard algorithm. The mutated algorithms show improved performance for the examples considered. [ABSTRACT FROM AUTHOR]

In this paper, an efficient and accurate method for the extended period simulation of pipe networks under dynamic loading is proposed. The method uses the modified Euler method to discretise the ordinary differential equation governing the variation of water level in the reservoirs to yield a non-linear algebraic equation in terms of the reservoir head and inflow. These equations are then embedded into the non-linear system of equations describing the steady-state flow in the pipe network to obtain the final system of equations. A Newton-Raphson method of linearisation is used for the equation governing the tank water level variation along with a gradient formulation of the pipe networks. The solution of the resulting system of equations automatically yields the distribution of nodal heads along with the reservoir head at the end of each period. The method uses only one steady-state simulation per period to predict accurately and efficiently the reservoir water elevation. Application of the proposed method does not require special coding and can be easily embedded into the existing pipe network simulation codes. The method is applied to four test problems and the results are presented and compared with those of a conventional extended period simulation method and some other existing methods. The results show that the proposed method is considerably more accurate than the conventional algorithm and more efficient than existing improved methods of dynamic simulation. [ABSTRACT FROM AUTHOR]

A novel cellular-automata approach is developed in this article for the optimal solution of large-scale reservoir-operation problems. The aim of this article is to show how cellular automata can be used for the solution of reservoir-operation problems, and, more importantly, to demonstrate that the method is extraordinarily more efficient and effective than heuristic-search methods. Both penalized and non-penalized versions of the method are proposed and formulated for the solution of water-supply and hydropower reservoir-operation problems. The cells are defined as the discrete points chosen on the operation horizon of the problem and storage volumes are taken as the cell states. The optimization objective functions of the problems are used to derive the updating rule of the problems. In the non-penalized method, the problems constraints are satisfied explicitly by limiting the change in the cell states between one iteration and the next. In the penalized version, however, a penalty method is used to modify the updating rules so that the constraints are automatically satisfied. The proposed methods are used to optimally solve the problem of water supply and hydropower operation of the Dez reservoir in Iran over short, medium, and long operation periods, and the results are presented and compared with those obtained using three heuristic-search methods (genetic algorithms, Ant Colony Optimization algorithms, and Particle Swarm Optimization algorithms). The results show that the cellular-automata method is much more efficient and effective than most powerful search methods for both of the problems considered in this work. Application of the method to multi-reservoir systems is underway, with encouraging early results. [ABSTRACT FROM AUTHOR]

Stochastic search methods, such as the particle swarm optimization (PSO) algorithm, are primarily directed by two main features - exploration and exploitation. Exploration is the ability of the algorithm to broadly search through the solution space for new quality solutions, whereas exploitation is responsible for refining the search in the neighborhood of the good solutions found previously. Proper balance between these features is sought, to obtain good performance of these algorithms. An explorative mechanism is introduced in this paper to improve the performance of the PSO algorithm. The method is based on introducing artificial exploration into the algorithm by randomly repositioning the particles approaching stationary status. A velocity measure is used to distinguish between flying and stationary particles. This can be sought as a sudden death followed by a rebirth of these particles. Two options are tested for the rebirthing mechanism, which are (i) clearing and (ii) keeping the memory of rebirthing particles. The global best particle is exempted from rebirthing process so that the most useful of the swarm’s past experiences is not lost. The method is applied to a benchmark storm water network design problem and the results are presented and compared with those of the original algorithm and other methods. The proposed method, though simple, is shown to be very effective in avoiding local optima, leading to an improved version of the algorithm at no extra computational effort. Les méthodes de recherche stochastiques telles que l’algorithme d’optimisation par essaim de particules (« PSO ») sont gérées principalement par deux caractéristiques majeures, l’exploration et l’exploitation. L’exploration est la capacité de l’algorithme à rechercher l’espace de solution de manière grossière pour trouver de nouvelles solutions de qualité alors que l’exploitation est responsable de préciser la recherche dans l’entourage des bonnes solutions trouvées précédemment. Un bon équilibre entre ces caractéristiques est nécessaire pour assurer le bon rendement de ces algorithmes. Un mécanisme exploratoire est présente dans cet article afin d’améliorer le rendement de l’algorithme d’optimisation par essaim de particules. La méthode est basée sur l’introduction, dans l’algorithme, d’une exploration artificielle en repositionnant aléatoirement les particules s’approchant de l’état stationnaire. Une mesure de la vitesse sert à distinguer entre les particules volantes et stationnaires. Cela peut se présenter comme une mort subite suivie d’une re-naissance de ces particules. Deux options de mécanisme de re-naissance sont vérifiées : (i) effacer et (ii) conserver la mémoire des particules en re-naissance. La meilleure particule globale est exemptée du processus de re-naissance afin que les parties les plus utiles des expériences passées de l’essaim ne soient pas perdues. La méthode est utilisée dans un problème d’évaluation de la conception de réseaux d’eaux pluviales; les résultats sont présentés et comparés à ceux de l’algorithme original et à ceux obtenus par d’autres méthodes. La méthode proposée, bien que simple, s’est avérée très efficace pour éviter l’optimum local, permettant ainsi d’améliorer l’algorithme sans demande computationnel additionnelle. [ABSTRACT FROM AUTHOR]

A penalty adapting ant algorithm is presented in an attempt to eliminate the dependency of ant algorithms on the penalty parameter used for the solution of constrained optimization problems. The method uses an adapting mechanism for determination of the penalty parameter leading to elimination of the costly process of penalty parameter tuning. The method is devised on the basis of observation that for large penalty parameters, infeasible solutions will have a higher total cost than feasible solutions and vice versa. The method therefore uses the best feasible and infeasible solution costs of the iteration to adaptively adjust the penalty parameter to be used in the next iteration. The pheromone updating procedure of the max-min ant system is also modified to keep ants on and around the boundary of the feasible search space where quality solutions can be found. The sensitivity of the proposed method to the initial value of the penalty parameter is investigated and indicates that the method converges to optimal or near-optimal solutions irrespective of the initial starting value of the penalty parameter. This is significant as it eliminates the need for sensitivity analysis of the method with respect to the penalty factor, thus adding to the computational efficiency of ant algorithms. Furthermore, it is shown that the success rate of the search algorithm in locating an optimal solution is increased when a self-adapting mechanism is used. The presented method is applied to a benchmark pipe network optimization problem in the literature and the results are presented and compared with those of existing algorithms. [ABSTRACT FROM AUTHOR]

Application of an ant colony optimization algorithm (ACOA) for simultaneous layout and size optimization of tree-like pipe networks is described in this paper using two different formulations. In the first formulation, each link of the base graph is considered as the decision point of the problem. Each decision point is considered in turn and the ants are then required to choose any of the available options at the current decision point. The list of available pipe diameters with the null option included for each link constitutes the available options in this formulation. In the second approach, the network nodes are considered as the decision points of the problem. The available options in this formulation are represented by the list of allowable pipe diameters for all plausible links such that the resulting network is a tree network. The plausible links at each decision point are provided by a tree-growing algorithm. This formulation leads to a very small search space compared with the first algorithm, as each ant is now forced to create a feasible solution regarding the layout geometry of the network. This approach fully exploits the sequential nature of the ACOA in building solutions, which is believed to be one of the main advantages of these algorithms compared with other general metaheuristics. The proposed methods are applied to find the optimal layout of two benchmark examples in the published literature and the results are presented and compared with the existing results. [ABSTRACT FROM AUTHOR]

The application of a max–min ant algorithm to the layout and size optimization of pipe networks is described in this paper. The formulation conventionally used for the pipe size optimization of networks with fixed layout is extended to account for the layout determination of the networks. This is achieved by including new constraints regarding the reliability of the network and modifying some of the constraints of the optimization problem. A deterministic concept of reliability is used in which the number of independent paths from source nodes to each of the demand nodes is considered as a measure of reliability. The method starts with a predefined layout which includes all possible links. The method is capable of designing the layout and pipe sizes of water distribution networks of predefined reliability including tree-like and looped networks. It is also shown that a layout optimization of a network followed by size optimization does not lead to an optimal or a near-optimal solution. This emphasizes the need for simultaneous layout and size optimization of networks if an optimal or near-optimal solution is desired. The performance of the method for layout and pipe size optimization of pipe networks is tested against two benchmark examples in the literature and the results are presented. The first example is considered to show the necessity of joint layout and size optimization even for the simple tree networks while the second example is considered to illustrate the efficiency of the proposed method for layout and size optimization of real-world networks with different levels of reliability. [ABSTRACT FROM AUTHOR]

A model is developed for the optimal design of storm water networks. The model uses a genetic algorithm (GA) as the search engine and the TRANSPORT module of the US Environmental Protection Agency storm water management model version 4.4H (SWMM4.4H) as the hydraulic simulator. Two different schemes are used to formulate the problem with varying degrees of success in reaching a near-optimal solution. In the first scheme, the nodal elevations and pipe diameters are selected as the decision variables of the problem which were determined by the GA to produce the trial solutions. In the second scheme, only nodal elevations are optimized by the GA, and determination of pipe diameters is left to the TRANSPORT SWMM module. Simulation of the trial solutions in both methods is carried out by the TRANSPORT module of SWMM4.4H. The proposed model is applied to some benchmark examples, and the results are presented and compared with the existing results in the literature. [ABSTRACT FROM AUTHOR]

Ant algorithms are now being used more and more to solve optimization problems other than those for which they were originally developed. The method has been shown to outperform other general purpose optimization algorithms including genetic algorithms when applied to some benchmark combinatorial optimization problems. Application of these methods to real world engineering problems should, however, await further improvements regarding the practicality of their application to these problems. The sensitivity analysis required to determine the controlling parameters of the ant method is one of the main shortcomings of the ant algorithms for practical use. Premature convergence of the method, often encountered with an elitist strategy of pheromone updating, is another problem to be addressed before any industrial use of the method is expected. It is shown in this article that the conventional transition rule used in ant algorithms is responsible for the stagnation phenomenon. A new transition rule is, therefore, developed as a remedy for the premature convergence problem. The proposed transition rule is shown to overcome the stagnation problem leading to high quality solutions. The resulting ant algorithms are also found to be less sensitive to the sensitivity indexes, requiring less computational effort for the determination of these parameters. The efficiency and effectiveness of the proposed rule and the resulting algorithm is tested on some pipe network optimization benchmark problems and the results are compared with the existing results using ant algorithms and other evolutionary methods. [ABSTRACT FROM AUTHOR]

In this paper, a Cellular Automata based simulation-optimization approach is proposed for the optimal design of household sewer networks. A two-phase CA is used as the optimization tool while the EPA's storm water management model (SWMM) is used as the simulator. A splitting method is first used to redefine the sewer network design problem in terms of two simpler sub-problems with diameters and nodal elevations of each pipe as decision variables which are iteratively solved using CA methods in two-stage manner until convergence is achieved. Each CA uses a separate ad-hoc local rule to update the cell state of the corresponding problem derived using engineering judgment and the hydraulic principles of the sewer flow. The proposed method is applied to some benchmark sewer networks and the results are presented and compared to those of the existing methods. Results indicates the efficiency and effectiveness of the proposed methods compared to the existing methods. [ABSTRACT FROM AUTHOR]