AN INTEGER PROGRAMMING MODEL FOR LAYOUT DESIGN OF WATER DISTRIBUTION NETWORKS

A model for the layout optimization of water distribution networks under single loadings is presented. The model uses zero-one integer programming to select the links that should form the network, while still satisfying looping, redundancy, and hydraulic requirements. This solution constitutes a starting solution to any network component optimization model. A network component optimization step, using well established design models, is then applied to this solution to refine the pipe sizes and pressure heads, thus giving a layout and component optimal solution. The model is demonstrated by application to an example.     

Optimal cost design of water distribution networks using harmony search

This study presents a cost minimization model for the design of water distribution networks. The model uses a recently developed harmony search optimization algorithm while satisfying all the design constraints. The harmony search algorithm mimics a jazz improvisation process in order to find better design solutions, in this case pipe diameters in a water distribution network. The model also interfaces with a popular hydraulic simulator, EPANET, to check the hydraulic constraints. If the design solution vector violates the hydraulic constraints, the amount of violation is considered in the cost function as a penalty. The model was applied to five water distribution networks, and obtained designs that were either the same or cost 0.28–10.26% less than those of competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing and tabu search under similar or less favorable conditions. The results show that the harmony search-based model is suitable for water network design.     

A Novel Continuous-Time Modeling and Optimization Framework for Well Platform Planning Problems

The long-term planning problem for integrated gas field development is investigated. The key decisions involve both design of the production and transportation network structure and operation of the gas fields over time. A novel continuous-time modeling and optimization approach is proposed, which introduces the concept of event points and allows the well platforms to come online at potentially any time within the continuous horizon under consideration. A two-level formulation and solution framework is developed to take into account complicated economic calculations and results in mixed-integer nonlinear programming (MINLP) problems. As compared with the discrete-time model, the proposed approach leads to more compact mathematical models and significant reduction of the size of the resulting MINLP problems. Even though, the proposed approach in its current form cannot guarantee convergence to the optimal solution, computational results show that this approach can reduce the computational efforts required substantially and solve problems that are intractable for the discrete-time model.     

Optimization models for operative planning in drinking water networks

The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (Burgschweiger et al. in ZIB Report ZR-05-31, Zuse Institute Berlin, 2005), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.     

Application of a max–min ant system to joint layout and size optimization of pipe networks

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.     

Reformulation linearization technique based branch-and-reduce approach applied to regional water supply system planning

A regional water supply system design problem that determines pipe and pump design parameters and water flows over a multi-year planning horizon is considered. A non-convex nonlinear model is formulated and solved by a branch-and-reduce global optimization approach. The lower bounding problem is constructed via a three-pronged effort that involves transforming the space of certain decision variables, polyhedral outer approximations, and the Reformulation Linearization Technique (RLT). Range reduction techniques are employed systematically to speed up convergence. Computational results demonstrate the efficiency of the proposed algorithm; in particular, the critical role range reduction techniques could play in RLT based branch-and-bound methods. Results also indicate using reclaimed water not only saves freshwater sources but is also a cost-effective non-potable water source in arid regions. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/0305215X.2015.1016508.     

AN OPTIMIZATION METHOD TO DESIGN HYDRAULIC NETWORKS

Nonlinear programming is applied to the solution of hydraulic network problems. The significant differences between the proposed optimization method and other conventional methods are that this method can solve problems with mixed unknowns (e.g. pipe sizes, discharges and pressures), it can optimize solutions involving unknowns defined by inequalities (e.g. specifled minimum discharge and pressure values), it can handle network control problems such as required valve adjustments or in-line booster pump needs, and it may solve problems of networks with continuous discharge distribution along the pipes.     

Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design—determining well placement, number of fracturing stages, and fracture lengths—is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.     

A manufacturing network design model based on processor and worker capabilities

This paper presents an optimization methodology to design networks of manufacturing facilities producing several products under deterministic demand. The bill of materials and the operations for each product are taken into account through the use of a product-state graph. Starting from the current state of the manufacturing network, the approach considers a multi-period planning horizon. For each period it specifies the facilities to open within the set of current and potential facilities, the mission for each of the centres in the selected facilities, the equipment to be used for producing the goods, and the structure of the network. Taking human resource competencies into account, the approach selects the type of workers to use for executing the manufacturing tasks. The transfer of resources between plants is also considered. A multi-period mixed integer linear programming model is formulated, a solution method based on the addition of specialized cuts is proposed and computational results are presented.     

Normative Models for Some Warehouse Sizing Problems

The problem examined is the determination of the optimum size for a warehouse used to store products over a finite planning horizon. Both fixed and changeable warehouse size problems are treated under conditions of deterministic and probabilistic storage demand. The latter is formulated as a linear programming problem and transformed via duality theory into an equivalent network flow problem for efficient solution. Costs considered are those due to warehouse construction, storage of products within the facility, and storage demand not satisfied by storage in the warehouse.     

An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Recent years witness a great deal of interest in artificial intelligence (AI) tools in the area of optimization. AI has developed a large number of tools to solve the most difficult search-and-optimization problems in computer science and operations research. Indeed, metaheuristic-based algorithms are a sub-field of AI. This study presents the use of the metaheuristic algorithm, that is, water cycle algorithm (WCA), in the transportation problem. A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull distribution. Since the parameters are stochastic, the corresponding constraints are probabilistic. They are converted into deterministic constraints using the stochastic programming approach. In this study, we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization problems. WCA is influenced by the water cycle process of how streams and rivers flow toward the sea (optimal solution). WCA is applied to the stochastic transportation problem, and obtained results are compared with that of the new metaheuristic optimization algorithm, namely the neural network algorithm which is inspired by the biological nervous system. It is concluded that WCA presents better results when compared with the neural network algorithm.     

Optimizing water tanks in water distribution systems by combining network reduction,mathematical optimization and hydraulic simulation

In the last two decades, water consumption in Germany has been decreasing, which causes the water tanks and pipes in water distribution systems to work inefficiently. This paper proposes a method that supports the planning process for tanks in water distribution systems. The method uses a combination of network reduction, mathematical optimization and hydraulic simulation. The mathematical optimization model is a non-convex Mixed Integer Quadratically Constrained Program (MIQCP) that is solved by a piecewise linearization. As this may lead to many binary variables and therefore high computing times, the size of the water distribution system model is reduced before building the optimization model. After applying several network reduction techniques and using a piecewise approximation of the original model, there may be some hydraulic differences between the original network model and the reduced network model. To make sure that the solution obtained in the optimization process is feasible in the original water distribution system model, the solution is verified by a hydraulic simulation. If the solution is not feasible, the reduced model has to be modified and solved again until the hydraulic simulation verifies a solution as feasible. In this paper, each of these processes is described and the results indicate the usefulness of each of them.     

Cost-effective selection and multi-period scheduling of pavement maintenance and rehabilitation strategies

An optimization methodology is developed for determining the most cost-effective maintenance and rehabilitation (M&R) activities for each pavement section in a highway pavement network, along an extended planning horizon. A multi-dimensional 0–1 knapsack problem with M&R strategy-selection and precedence-feasibility constraints is formulated to maximize the total dollar value of benefits associated with the selected pavement improvement activities. The solution approach is a hybrid dynamic programming and branch-and-bound procedure. The imbedded-state approach is used to reduce multi-dimensional dynamic programming to a one-dimensional problem. Bounds at each stage are determined by using Lagrangian optimization to solve a relaxed problem by means of a sub-gradient optimization method. Tests for the proposed solution methodology are conducted using typical data obtained from the Texas Department of Transportation.     

A QUANTIFIED ASSESSMENT OF THE RELATIONSHIP BETWEEN THE RELIABILITY AND ENTROPY OF WATER DISTRIBUTION SYSTEMS

Several researchers have suggested that it might be possible to use entropy as a general performance indicator for water distribution systems. It has several advantages over other performance and reliability indices, for example, it is extremely rapid and far easier to calculate than other measures, has minimal data requirements and lends itself to direct incorporation into design optimization frameworks.

This paper summarises the first proper attempt to investigate the apparent relationship between the entropy and reliability of water distribution systems. A maximum entropy-constrained approach was used to generate designs for a sample water distribution system which, along with traditional minimum-cost designs, formed the basis of this study. By varying the layout, number of loops and links and reversing the direction of flow in some pipes, it is shown statistically that the correlation between entropy and reliability is strong. Based on the results, a new method for sizing the pipes of water distribution systems is proposed. It is quick, easy to implement, finds optimal pipe sizes, does not require non-linear programming and always guarantees a high level of reliability.     

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.     

Using 0/1 mixed integer linear programming to solve a reliability-centered problem of power plant preventive maintenance scheduling

The problem of power plant preventive maintenance scheduling is studied in this paper. A reliability perspective is considered. This problem consists of ascertaining which generating units must halt production to be examined regularly for safety. It is very important because a failure in a power station may cause a general breakdown in an electric network. The main consequence is that the electricity demand of customers will not be satisfied in such cases. Therefore, reliability is the key point used in the methodology presented. The problem is approached under the operations research perspective as an optimization issue. 0/1 mixed integer linear programming is used to solve the model reached. An application study is included. The model is put to use in a real power plant setting, representative of the Spanish one. The result obtained is a schedule that allows the efficient organization of preventive maintenance over a specific time horizon.     

Optimization of municipal pressure pumping station layout and sewage pipe network design

Accelerated urbanization places extraordinary demands on sewer networks; thus optimization research to improve the design of these systems has practical significance. In this article, a subsystem nonlinear programming model is developed to optimize pumping station layout and sewage pipe network design. The subsystem model is expanded into a large-scale complex nonlinear programming system model to find the minimum total annual cost of the pumping station and network of all pipe segments. A comparative analysis is conducted using the sewage network in Taizhou City, China, as an example. The proposed method demonstrated that significant cost savings could have been realized if the studied system had been optimized using the techniques described in this article. Therefore, the method has practical value for optimizing urban sewage projects and provides a reference for theoretical research on optimization of urban drainage pumping station layouts.     

An uncertain optimization method for overall ballistics based on stochastic programming and a neural network surrogate model

A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.     

A strategic model for exact supply chain network design and its application to a global manufacturer

This paper presents a comprehensive model that captures significant strategic decisions involved in designing or redesigning high-performance supply chains from the perspective of the manufacturer. The problem considers deterministic demand by multiple clients, for multiple products, over the periods of a long-term horizon. The design decisions involve selection of suppliers, establishment or resizing of production facilities and distribution centres, possible subcontracting of related activities, and selection of transportation modes and routes. The problem is formulated by a Mixed Integer Linear Programming model. Its objective is to minimise the overall costs associated with procurement, production, inventory, warehousing, and transportation over the design horizon. Appropriate constraints model the complex relationships among the links of the supply chain. The proposed model has been applied to a large case study of a global manufacturing firm, providing valuable insights into the transformation of the firm’s current supply chain network, as well as into the potential of the proposed approach.     

基于JITD的服务备件二级分销网络集成研究

从供应链集成的角度出发,使用双层规划建立了服务备件二级分销网络的设施选址-运输路线安排-库存控制问题(CLRIP)模型,确定了分销中心的位置、车辆的运输路线等。该模型充分考虑决策部门和顾客双方的利益,针对服务备件的价值高以及服务水平要求高的特点,将按需拉动的准时制配送策略（JITD）应用于分销网络设计中,在降低系统成本的同时,可以大幅度提高配送的准时性和稳定性。设计了该模型的启发式算法,通过算例验证了模型和算法的有效性。研究结果有助于优化服务备件分销网络结构、提高配送准时性和降低物流成本。