Optimal cost design of water distribution networks using a decomposition approach

Water distribution network decomposition, which is an engineering approach, is adopted to increase the efficiency of obtaining the optimal cost design of a water distribution network using an optimization algorithm. This study applied the source tracing tool in EPANET, which is a hydraulic and water quality analysis model, to the decomposition of a network to improve the efficiency of the optimal design process. The proposed approach was tested by carrying out the optimal cost design of two water distribution networks, and the results were compared with other optimal cost designs derived from previously proposed optimization algorithms. The proposed decomposition approach using the source tracing technique enables the efficient decomposition of an actual large-scale network, and the results can be combined with the optimal cost design process using an optimization algorithm. This proves that the final design in this study is better than those obtained with other previously proposed optimization algorithms.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

A jazz-based approach for optimal setting of pressure reducing valves in water distribution networks

This study presents a model for valve setting in water distribution networks (WDNs), with the aim of reducing the level of leakage. The approach is based on the harmony search (HS) optimization algorithm. The HS mimics a jazz improvisation process able to find the best solutions, in this case corresponding to valve settings in a WDN. The model also interfaces with the improved version of a popular hydraulic simulator, EPANET 2.0, to check the hydraulic constraints and to evaluate the performances of the solutions. Penalties are introduced in the objective function in case of violation of the hydraulic constraints. The model is applied to two case studies, and the obtained results in terms of pressure reductions are comparable with those of competitive metaheuristic algorithms (e.g. genetic algorithms). The results demonstrate the suitability of the HS algorithm for water network management and optimization.     

Improved mine blast algorithm for optimal cost design of water distribution systems

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms.     

An adaptive heuristic cross-entropy algorithm for optimal design of water distribution systems

The optimal design problem of a water distribution system is to find the water distribution system component characteristics (e.g. pipe diameters, pump heads and maximum power, reservoir storage volumes, etc.) which minimize the system's capital and operational costs such that the system hydraulic laws are maintained (i.e. Kirchhoff's first and second laws), and constraints on quantities and pressures at the consumer nodes are fulfilled. In this study, an adaptive stochastic algorithm for water distribution systems optimal design based on the heuristic cross-entropy method for combinatorial optimization is presented. The algorithm is demonstrated using two well-known benchmark examples from the water distribution systems research literature for single loading gravitational systems, and an example of multiple loadings, pumping, and storage. The results show the cross-entropy dominance over previously published methods.     

A diversity-enriched variant of discrete PSO applied to the design of water distribution networks

The design of water distribution networks (WDNs) is addressed by using a variant of the particle swarm optimization (PSO) algorithm. This variant, which makes use of a discrete version of PSO already considered by the authors, overcomes one of the PSO's main drawbacks, namely its difficulty in maintaining acceptable levels of population diversity and in balancing local and global searches. The performance of the variant proposed here is investigated by applying the model to solve two standard benchmark problems: the Hanoi new water distribution network and the New York Tunnel water supply system. The results obtained show considerable improvements in both convergence characteristics and the quality of the final solutions, and near-optimal results are consistently achieved at reduced computational cost.     

On the use of graphical analysis for the design of batch water networks

This paper presents a series of graphical analyses for the design of batch water networks to process systems characterized by fixed flow rate operations. Water integration is carried out by exploiting all water reuse opportunities, with which both freshwater consumption and wastewater generation can be reduced at the same time. Throughout the analyzing procedure, the minimum freshwater consumption is first identified. Under the already set freshwater target, the follow-up analyses are continued to cut down the number of storage tanks for the simplification of the network complexity. The resultant network structure is finally obtained with the corresponding storage policy. After water integration to the literature case study, more than 54 and 63% of savings in freshwater, with more than 61 and 72% of reductions in wastewater are reported for the single and cyclic batch productions, respectively, compared to the base case without water reuse.     

Mathematical programming synthesis of non-isothermal water networks by using a compact/reduced superstructure and an MINLP model

The synthesis problems of non-isothermal water networks, combining heat exchanger network and water network (WN), usually consist of a significant number of constraints and variables, namely, flow rates, contaminant concentrations, temperatures and a large number of non-linear terms. In most cases, solving medium and large-scale synthesis problems is computationally too expensive and challenging. In order to circumvent that problem, we propose a compact superstructure and mixed-integer non-linear programming model for the simultaneous synthesis of non-isothermal WNs. The proposed superstructure includes heat integration stages enabling direct and indirect heat exchanges with a manageable number of hot and cold streams. This reduces the models size enabling easier solutions of the synthesis problems using local solvers. In addition, a superstructure reduction strategy is proposed making the superstructure flexible and adaptable for different types of problems, namely, pinched and threshold, and providing additional reduction of connections within the proposed superstructure. The proposed model is solved using a two-step solution strategy including initialisation and design steps. The model is applied to the examples of different complexities including single and multiple contaminant problems, and water-using and wastewater treatment units. Using the proposed iterative strategy, the improved locally optimal solutions are identified for most examples, minimising the total annual cost of the overall network.     

Estimations of production yields for selection of a practical optimal optical coating design

Modern design approaches enable one to construct a series of theoretical designs with excellent spectral properties for almost all optical coating design problems. Selection of a practical optimal design among a variety of possible theoretical designs becomes a key issue. We demonstrate how preproduction estimations of expected production yields can be used for selection of a practical optimal design. The question of reliability of such estimations is also addressed.     

Reliability-based optimal structural design by the decoupling approach

A decoupling approach for solving optimal structural design problems involving reliability terms in the objective function, the constraint set or both is discussed and extended. The approach employs a reformulation of each problem, in which reliability terms are replaced by deterministic functions. The reformulated problems can be solved by existing semi-infinite optimization algorithms and computational reliability methods. It is shown that the reformulated problems produce solutions that are identical to those of the original problems when the limit-state functions defining the reliability problem are affine. For nonaffine limit-state functions, approximate solutions are obtained by solving series of reformulated problems. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, thus allowing flexibility in the choice of the optimization algorithm and the reliability computation method.     

Development of a MINLP model for the optimization of a large industrial water system

This paper presents the design of a large water system within the production and packaging areas of a brewery. In order to accomplish the task, mathematical models were developed based on a Mixed Integer Nonlinear Programming (MINLP) formulation from the open literature. These models enable the investigation of several integration options: a) direct water re-use between batch and semi-continuous consumers operating within the same time interval and b) regeneration re-use options, by designing and scheduling an on-site wastewater treatment system. A multilevel strategy was applied for this large-scale industrial problem, which firstly decomposes design problem into several smaller integration problems concerning water consumers within each section of the brewery. At the following level, water re-use and regeneration re-use opportunities between the brewhouse and the packaging areas were explored for each working day. Finally, the design of an integrated water system was performed over the entire working week by fixing identified intra-daily matches between sections. An optimum water integration scheme is proposed based on the results obtained.     

On the optimal design of river fishways

A river fishway is a hydraulic structure enabling fish to overcome stream obstructions such as dams in hydroelectric power plants. The main aim of this paper is to present an application of mathematical modeling and optimal control theory to an ecological engineering problem related to preserve and enhance natural stocks of fish migrating between saltwater and freshwater. Particularly, we improve the optimal shape design of a fishway. This problem is formulated within the framework of the optimal control of partial differential equations, approximated by a discrete optimization problem, and solved by using both a gradient method (a Spectral Projected-Gradient algorithm) and a derivative-free method (the Nelder-Mead algorithm). Finally, numerical results are compared and analyzed for a standard real-world situation.     

On the imaginative constructivist nature of design: a theoretical approach

Most empirical accounts of design suggest that designing is an activity where objects and representations are progressively constructed. Despite this fact, whether design is a constructive process or not is not a question directly addressed in the current design research. By contrast, in other fields such as Mathematics or Psychology, the notion of constructivism is seen as a foundational issue. The present paper defends the point of view that forms of constructivism in design need to be identified and integrated as a foundational element in design research as well. In fact, a look at the literature reveals at least two types of constructive processes that are well embedded in design research: first, an interactive constructivism, where a designer engages a conversation with media, that allows changing the course of the activity as a result of this interaction; second, a social constructivism, where designers need to handle communication and negotiation aspects, that allows integrating individuals’ expertise into the global design process. A key feature lacking these well-established paradigms is the explicit consideration of creativity as a central issue of design. To explore how creative and constructivist aspects of design can be taken into account conjointly, the present paper pursues a theoretical approach. We consider the roots of constructivism in mathematics, namely the Intuitionist Mathematics, in order to shed light on the original insights that led to the development of a notion of constructivism. Intuitionists describe mathematics as the process of mental mathematical constructions realized by a creative subject over time. One of the most original features of intuitionist constructivism is the introduction of incomplete objects into the heart of mathematics by means of lawless sequences and free choices. This allows the possibility to formulate undecided propositions and the consideration of creative acts within a formal constructive process. We provide an in-depth analysis of intuitionism from a design standpoint showing that the original notion is more than a pure constructivism where new objects are a mere bottom-up combination of already known objects. Rather, intuitionism describes an imaginative constructivist process that allows combining bottom-up and top-down processes and the expansion of both propositions and objects with free choices of a creative subject. We suggest that this new form of constructivism we identify is also relevant in interpreting conventional design processes and discuss its status with respect to other forms of constructivism in design.     

Incorporating reliability in optimal design of water distribution networks—review and new concepts

Much of the effort in optimal design of water distribution networks (WDNs) has focussed so far on minimizing cost alone, with little emphasis on reliability or on investigating the tradeoff between cost and reliability. This is a consequence of the difficulty in defining reliability measures which are meaningful and appropriate, while still of a form which can be incorporated directly into optimization models. This paper will deal with these issues. It contains three parts: (1) conceptual discussion of reliability definitions from different points of view (system versus consumers), (2) a literature survey of existing techniques to incorporate reliability in the optimal design of WDNs, and (3) a new concept for explicitly including reliability in the optimal design of WDNs.     

Field services design and management of natural gas distribution networks: a class of vehicle routing problem with time windows approach

Service operations management of metropolitan gas networks at operational level implies the optimisation of decisions related to logistic activities, taking into account multi-objectives and operational constraints. This paper proposes a metaheuristic approach for the operational planning of the daily logistic activities based on vehicle routing with time window model. Experimental results for a real planning case in a gas distribution network demonstrate the approach effectiveness.     

Dynamic programming approach to optimal feedback-feed-forward controller design

Summary A new derivation of the parametric expansion of the dynamic programming algorithm for optimal feedback-feed-forward controller design is presented. Matrix methods are employed to give clarity to the results first offered by Merriam. The advantages of the optimal design technique for multivariable problems are readily apparent. A unique technique is given for easily solving the design equations for the case of time invariant systems with gaussian load disturbance.     

The optimum design of fluid distribution networks with particular reference to low pressure gas distribution networks

This paper is concerned with the development of a computational algorithm to find the optimal solution to the fluid network distribution design problem. The problem is formulated as a non-linear mathematical optimization problem and is solved using a sequential unconstrained minimization technique. Illustrative examples are included and the design solutions obtained compared with the solutions obtained using a parametric method.     

Applying tabu search and simulated annealing to the optimal design of sewer networks

Optimizations of sewer network designs create complicated and highly nonlinear problems wherein conventional optimization techniques often get easily bogged down in local optima and cannot successfully address such problems. In the past decades, heuristic algorithms possessing robust and efficient global search capabilities have helped to solve continuous and discrete optimization problems and have demonstrated considerable promise. This study applied tabu search (TS) and simulated annealing (SA) to the optimization of sewer network designs. For a case study, this article used the sewer network design of a central Taiwan township, which contains significantly varied elevations, and the optimal designs from TS and SA were compared with the original official design. The results show that, in contrast with the original design's failure to satisfy the minimum flow-velocity requirements, both TS and SA achieved least-cost solutions that also fulfilled all the constraints of the design criteria. According to the average performance of 200 trials, SA outperformed TS in both robustness and efficiency for solving sewer network optimization problems.     

Path entropy method for multiple-source water distribution networks

Over the past decade, one of the key research areas for water distribution networks has been the quantification of network reliability. An interesting approach in this research topic is the use of informational entropy as a surrogate measure for the reliability of water distribution network. Research on water distribution network entropy has progressed to the stage where practical applications are possible, but the actual meaning of the network entropy has never been fully elucidated. Recently, an alternative approach to calculate network entropy was proposed, which was termed the path entropy method (PEM). This alternative method was shown to be useful for the case of single-source water distribution networks. The purpose of this article is to explore the use of the PEM on multiple-source networks. A two-source and two-demand water distribution network is analysed to gain insight into the differences between single-source and multiple-source networks in terms of maximum-entropy flow distribution. This leads to the formal proof of the principle governing maximum-entropy flow ratios in multiple-source water distribution networks.