Least-cost Design Research Articles

Thermal System and Net-Zero-Carbon Least-Cost Design Optimization of New Detached Houses in Canada

This study focused on optimizing a model house for different locations and types of thermal systems to understand better how heating system type affects thermal envelope design, operational greenhouse gas emissions, and life-cycle cost. The study investigated six different thermal system configurations in separate optimizations for five locations. Optimization implies reducing energy consumption, minimizing greenhouse gas emissions (GHG), lowering operational costs, ensuring regulatory compliance, enhancing resilience, and improving occupant comfort and health. The Pareto front, multi-objective optimization, is used to identify a set of optimal solutions, considering multiple goals that may conflict with each other. In determining the least-cost building design envelope, the design balances costs with other goals, such as energy efficiency and environmental impact. The optimizations determine the life-cycle cost versus operational GHG emissions for a single-detached house in Canadian locations with varying climates, emissions factors, and energy costs. Besides natural gas, the study evaluated four electricity-heated options: (a) an air-source heat pump, (b) a ductless mini-split heat pump, (c) a ground-source heat pump, and (d) an electric baseboard. A net-zero-carbon design with grid-tied photovoltaics was also optimized. Results indicate that the heating system type influences the optimal enclosure design. In each location, at least one all-electric kind of design has a lower life-cycle cost than the optimized gas-heated model, and such designs can mitigate the majority of operational GHG emissions from new housing in locations with a low carbon electricity supply.

Optimal pipe-sizing design of water distribution networks using modified Rao-II algorithm

ABSTRACT Several evolutionary algorithms (EAs) have been suggested in the last three decades for the least-cost design of water distribution networks (WDNs). EAs generally worked well to identify the global/near-global optimal solutions for small- to moderate-size networks in a reasonable time and computational effort. However, their applications to large-size networks are still challenging due to large computational effort. Recent developments in EAs are towards parameter-less techniques that avoid fine-tuning of case-specific parameters to reduce the computational effort. Further, several self-adaptive penalties and search-space reduction methodologies have been suggested to reduce the computational effort. A fast, efficient, and parameter-less Rao-II algorithm has been used earlier with penalty-based approaches for the optimal design of WDNs. In this study, the application of a Rao-II algorithm is further explored with three self-adaptive penalty approaches to compare the convergence characteristics. The Rao-II algorithm is observed to converge at an infeasible solution in cases that the applied penalty to an infeasible solution is not so substantial to make it inferior to the feasible solutions. Modifications are suggested to improve the Rao-II algorithm, named the modified Rao-II algorithm. The modified Rao-II algorithm with the self-adaptive penalty methods resulted in better solutions than those obtained earlier.

Optimal Sizing and Life-cycle Cost Modelling of Hydraulic Capsule Pipelines

Estimation of the total cost is essential for the planning and the designing of pipelines in a cost-effective way. As a result, the total cost modelling could go beyond the established objectives of least-cost design and optimization. This study incorporates a design methodology for pipelines transporting spherical capsules, which have variant sizes and densities. A methodology has been developed to determine the optimal size and lifetime of pipelines transporting solid–liquid mixtures (Capsule Flow). The methodology includes a model for the prediction of various life-cycle costs. The methodology provides a closed form solution to predict the optimal pipe diameter corresponding to the least total cost. Such solutions are obtained for different life-cycle costs, of which the one associated with minimum annual total cost provides the lifetime. The developed methodology has been used to obtain the optimal diameter of a pipeline for a practical case. The study reveals the interrelationship between the optimal pipe diameter and the corresponding minimum total cost.

Designing reinforced HSC rectangular beams using optimization techniques

AbstractThe current work discusses optimizing the structural design of reinforced high strength concrete rectangular sections under design loads. Using a least-cost design criterion and minimal design variables, an analytical approach to the problem is devised. A nonlinear mathematical programming format for the formulation of the problem is among the things that are demonstrated. To demonstrate how the formulation can be used in line with the ACI 318-08 standard, several typical cases are given. The outcomes are compared to those obtained from existing design practice. The ideal solution demonstrates unequivocally that significant reductions in the anticipated absolute costs of the building materials to be employed are possible and without making significant changes, this method may be expanded to address other portions.

Design Optimization Methodology for Diversion Structure with Concrete Cofferdam Using Risk-Based Least-Cost Design Method

The optimal size of a diversion structure should be carefully studied to ensure economic viability and safety during construction. In practice, to determine the size of a diversion structure, design flood frequency is selected as the suggested return period presented by the design standard, which is presented differently. This study proposes a methodology for the design of a diversion structure with a concrete cofferdam adopting risk analysis to reflect the more practical hazard and risk of diversion structure during dam construction. The proposed methodology is based on a risk-based least-cost design process and risk analysis. The optimization result is presented as the lowest expected monetary value, which accounts for construction cost, reconstruction cost, and delay liquidated damage with the failure probability and recovery cost with the overflow probability. This methodology was applied to the case study of the Gulpur hydropower project in Pakistan. The results showed that the optimal design flood frequency is 1 year for a recovery cost of USD 0.5 mil. and 1~2 years for a recovery cost of USD 1.0~2.0 mil. with 3, 4, and 5 years of the usage period of the diversion structure. Furthermore, 2~10 years is the optimal value for a recovery cost of USD 3.0~4.0 mil. These results indicated that the optimal design flood frequency increases as the recovery cost and usage period of the diversion structure increase. The results of the study reveal that the recovery cost and the period of use of the diversion structure affect the design flood frequency of the diversion structure. From a design perspective, the period of use is determined by the construction period of the project or the construction method, whereas the recovery cost depends on the countermeasure method. Therefore, after preparing a proactive plan and estimating the recovery cost, the design flood frequency for the diversion structure should be determined.

Optimization of Water Distribution Networks Using Genetic Algorithm Based SOP–WDN Program

Water distribution networks are vital hydraulic infrastructures, essential for providing consumers with sufficient water of appropriate quality. The cost of construction, operation, and maintenance of such networks is extremely large. The problem of optimization of a water distribution network is governed by the type of water distribution network and the size of pipelines placed in the distribution network. This problem of optimal diameter allocation of pipes in a distribution network has been heavily researched over the past few decades. This study describes the development of an algorithm, ‘Smart Optimization Program for Water Distribution Networks’ (SOP–WDN), which applies genetic algorithm to the problem of the least-cost design of water distribution networks. SOP–WDN demonstrates the application of an evolutionary optimization technique, i.e., genetic algorithm, linked with a hydraulic simulation solver EPANET, for the optimal design of water distribution networks. The developed algorithm was applied to three benchmark water distribution network optimization problems and produced consistently good results. SOP–WDN can be utilized as a tool for guiding engineers during the design and rehabilitation of water distribution pipelines.

The Study of Subsurface Land Drainage Optimal Design Model

This paper focused on choosing the best design of subsurface land drainage systems in semiarid areas. The study presented three different soil layers with different hydraulic conductivity and permeability, all layers are below the drain level, and the permeability is increasing with depth. A mathematical model was formulated for the horizontal and vertical drainage optimal design. The result was a nonlinear optimization problem with nonlinear constraints, which required numerical methods for its solution. The purpose of the mathematical model is to find the best values of pipes and tubewells spacing, groundwater table drawdown, and pumps operating hours which leads to a minimum total cost of the subsurface drainage design. A computer code was developed in MATLAB environment and applied to the case study. Results show that the vertical drainage was economically better for the case study drainage network design. And the main factor affecting the mathematical model for both pipe and well drainage was the distance between pipes and tubewells. In addition, considering the lifespan of vertical drainage project, the optimal design involves the minimum possible duration of pumping stations. It is hoped that the proposed optimal mathematical model will present a design methodology by which the costs of all alternative designs can be compared so that the least-cost design is selected.

A Head Formulation for the Steady-State Analysis of Water Distribution Systems Using an Explicit and Exact Expression of the Colebrook–White Equation

Steady-state demand-driven water distribution system (WDS) solution is the bedrock for much research conducted in the field related to WDSs. WDSs are modeled using the Darcy–Weisbach equation with the Swamee–Jain equation. However, the Swamee–Jain equation approximates the Colebrook–White equation, errors of which are within 1% for ϵ/D∈[10−6,10−2] and Re∈[5000,108]. A formulation is presented for the solution of WDSs using the Colebrook–White equation. The correctness and efficacy of the head formulation have been demonstrated by applying it to six WDSs with the number of pipes ranges from 454 to 157,044 and the number of nodes ranges from 443 to 150,630. The addition of a physically and fundamentally more accurate WDS solution method can improve the quality of the results achieved in both academic research and industrial application, such as contamination source identification, water hammer analysis, WDS network calibration, sensor placement, and least-cost design and operation of WDSs.

Analytical Optimization Approach for Simultaneous Design and Operation of Water Distribution–Systems Optimization

AbstractThis paper presents an analytical algorithm for simultaneous least-cost design and operation of looped water distribution systems (WDSs). This method could be used to replace evolutionary m...

Route map for renewable energy sources implementation for household in Bulgaria

This paper is concerned with the design of a hybrid household system, located in the city of Sofia with the possibility of grid connection. It is comprised of photovoltaic (PV) arrays, wind generator and battery energy storage devices. A multi-objective, non-derivative optimisation is considered in this residential application; the primary objective is the system cost minimisation. The commercial software, HOMER Pro, is utilised to identify the least-cost design among hundreds of options. This paper discusses suitability of renewable energy (RE) applied in one-family household according socio-economic situation in Bulgaria. Finally, a route map of RES implementation options is presented, and economic indicators such as Total net presents cost (NPC), Cost of Energy (COE) and RES fraction are assessed.

A Two-Stage LP-NLP Methodology for the Least-Cost Design and Operation of Water Distribution Systems

This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, a reformulated linear programming (LP) method is used to find the least cost design of a WDS for a given set of flow distribution. In the second stage, a non-linear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the WDS design obtained in stage one. The following features of the proposed two-stage method make it more appealing compared to other methods: (1) the reformulated LP stage can consistently reduce the penalty cost when designing a WDS under multiple loading conditions; (2) robustness as the number of loading conditions increases; (3) parameter tuning is not required; (4) the method reduces the computational burden significantly when compared to meta-heuristic methods; and (5) in oppose to an evolutionary “black box” based methodology such as a genetic algorithm, insights through analytical sensitivity analysis, while the algorithm progresses, are handy. The efficacy of the proposed methodology is demonstrated using two WDSs case studies.

A New Optimization Approach for the Least-Cost Design of Water Distribution Networks: Improved Crow Search Algorithm

Due to large number of decision variables and several hydraulic constraints, optimal design of water distribution networks (WDNs) is considered as one of the most complex optimization problems. This paper introduces and applies a new optimization approach, improved crow search algorithm (ICSA), based on the improvement of original crow search algorithm (CSA) by adding an operator parameter. Both approaches (i.e., CSA and ICSA) were applied to two case studies (i.e., Two-Reservoir and Khorramshahr City networks) by linking the hydraulic simulator (e.g., EPANET 2.0). The proposed ICSA saved the total construction cost by 2.16% and 1.79% for the Two-Reservoir and Khorramshahr City networks compared to the original CSA based on optimal network design, respectively. Results revealed that the proposed ICSA provided outstanding design for the both WDNs compared to previous studies and original CSA.

Optimization of Pressurized Tree-Type Water Distribution Network Using the Improved Decomposition–Dynamic Programming Aggregation Algorithm

Pressurized tree-type water distribution network (WDN) is widely used in rural water supply projects. Optimization of this network has direct practical significance to reduce the capital cost. This paper developed a discrete nonlinear model to obtain the minimum equivalent annual cost (EAC) of pressurized tree-type WDN. The pump head and pipe diameter were taken into account as the double decision variables, while the pipe head loss and flow velocity were the constraint conditions. The model was solved by using the improved decomposition–dynamic programming aggregation (DDPA) algorithm and applied to a real case. The optimization results showed that the annual investment, depreciation and maintenance cost (W1) were reduced by 22.5%; however, the pumps’ operational cost (p) increased by 17.9% compared to the actual layout. Overall, the optimal EAC was reduced by 15.2% with the optimized pump head and optimal diameter distribution of the network. This method demonstrated an intrinsic trade-off between investment and operational cost, and provided an efficient decision support tool for least-cost design of pressurized tree-type WDN.

Testing evolutionary algorithms for optimization of water distribution networks

Water distribution networks (WDNs) are one of the most important elements of urban infrastructure and require large investment for construction. Design of WDNs is classified as a large combinatorial discrete nonlinear optimization problem. The main concerns associated with the optimization of such networks are the nonlinearity of the discharge-head loss relationships for pipes and the discrete nature of pipe sizes. Due to these issues, this problem is widely considered to be a benchmark problem for testing and evaluating the performance of nonlinear and heuristic optimization algorithms. This paper compares different techniques, all based on evolutionary algorithms (EAs), which yield optimal solutions for least-cost design of WDNs. All of these algorithms search for the global optimum starting from populations of solutions, rather than from a single solution, as in Newton-based search methods. They use different operators to improve the performance of many solutions over repeated iterations. Ten EAs, four of them for the first time, are applied to the design of three networks and their performance in terms of the least cost, under different stopping criteria, are evaluated. Statistical information for 20 executions of the ten algorithms is summarized, and Friedman tests are conducted. Results show that, for the two-loop benchmark network, the particle swarm optimization gravitational search and biology and bioinformatics global optimization algorithms efficiently converge to the global optimum, but perform poorly for large networks. In contrast, given a sufficient number of function evaluations, the covariance matrix adaptation evolution strategy and soccer league competition algorithm consistently converge to the global optimum, for large networks.

Design of a Hybrid AC/DC Microgrid Using HOMER Pro: Case Study on an Islanded Residential Application

This paper is concerned with the design of an autonomous hybrid alternating current/direct current (AC/DC) microgrid for a community system, located on an island without the possibility of grid connection. It is comprised of photovoltaic (PV) arrays and a diesel generator, AC loads, and battery energy storage devices for ensuring uninterruptible power supply during prolonged periods of low sunshine. A multi-objective, non-derivative optimisation is considered in this residential application; the primary objective is the system cost minimisation, while it is also required that no load shedding is allowed. Additionally, the CO2 emissions are calculated to demonstrate the environmental benefit the proposed system offers. The commercial software, HOMER Pro, is utilised to identify the least-cost design among hundreds of options and simultaneously satisfy the secondary objective. A sensitivity analysis is also performed to evaluate design robustness against the uncertainty pertaining to fuel prices and PV generation. Finally, an assessment of the capabilities of the utilised optimisation platform is conducted, and a theoretical discussion sheds some light on the proposal for an enhanced design tool addressing the identified issues.

A framework for optimal reliability-based storm sewer network design in flat areas

This paper presents a framework for the optimal design of a storm sewer network in flat areas where there is insufficient energy from gravity for runoff drainage. A reliability index based on nodal partial flooding is introduced as a performance criterion and utilizes the intrinsic storage capacity of the sewer network. The Storm Water Management Model is used for hydraulic simulation of the sewer system. This model is coupled with an adaptive genetic algorithm to obtain the least-cost design of the network. The model offers numerous design alternatives with various levels of reliability. The model was successfully applied to the Kianpars storm sewer network, a flat district of the city of Ahvaz in Iran. The proposed model is useful for managing the budget and technical limitations of sewer system design in flat areas as well as efficiently deriving an optimum trade-off between design cost and reliability.

Joint Consideration of Layout and Pipe Sizes for Water Distribution Network Design with Reliability

In a looped water distribution network (WDN) alternate paths are available for supply in case a pipe fails and isolated from the network. The provision of minimum size or minimum flow carrying capacity of each pipe in a least-cost design of WDNs, or deciding layout of a looped WDN such that at least two-pipes are connected at each node may assure connectivity but not sufficient capacity of the network to meet demands during failure of any pipe. Reliability of looped network increases with increase in number of pipes at each node, or increase in pipe sizes; however, the cost also increases. Thus, reliability-based design should consider both layout and pipe sizes optimization. Methodologies based on entropy have been suggested for selection of layout and design to consider reliability [1,2]. A new methodology, based on flow uniformity in the network, is attempted for the selection of network layout. The flow-uniformity is assessed through variance of flow-series. It is observed that in a branched network, the variance of pipe-flows is maximum; and the reliability of the network increases as the variance decreases by adding loop-forming links. A heuristic methodology is suggested to obtain a layout with minimum variance. The layout so selected is optimally designed using linear programming. The methodology is applied to a simple problem and cost and reliability values are compared. Further, a network from the literature [3] is considered. The reliability consideration is observed to have a layout with more number of pipes as compared to that obtained for minimum cost design.

Serious Gaming for Water Systems Planning and Management

Water systems planning and management share the same roots with gaming, as they rely on concepts in systems analysis, operations research and decision sciences. This paper focuses on Serious Games (those used for purposes other than mere entertainment), with applications in the area of water systems planning and management. A survey of published work on gaming is carried out with particular attention given to applications of Serious Gaming to water systems planning and management. The survey is also used to identify the principal criteria for the classification of Serious Gaming for water related applications, including application areas, goals, number and type of players, user interface, type of simulation model used, realism of the game, performance feedback, progress monitoring and game portability. The review shows that game applications in the water sector can be a valuable tool for making various stakeholders aware of the socio-techno-economic issues related to managing complex water systems. However, the critical review also indicates a gap that exists in the Serious Game application area with the lack of water distribution system games. A conceptually simple, but computationally elaborate new game for water distribution system analysis, design and evaluation (SeGWADE) is presented in this paper. It has a main goal of finding a least-cost design for a well-known benchmark problem, for which the game environment takes the computational and visualisation burden away from the simulation tool and the player. The game has been evaluated in a classroom environment in which a high degree of player engagement with the game was observed, due to its basic game ingredients and activities, i.e., challenge, play and fun. In addition, a clear improvement in learning has been observed in how players attempted to identify solutions that satisfy the pressure criterion with players readily identifying the proximity of the better solutions to the starting, infeasible configuration. Through applications of Serious Gaming such as this, decision makers can learn about the complexity of the water distribution system design problem, experiment safely using a computer model of a real system, understand conflicting objectives (i.e., minimization of cost and satisfaction of minimum pressure) and develop strategies for coping with complexity without being burdened by the limitations of the ICT technology at their disposal.

Least-Cost Robust Design Optimization of Water Distribution Systems under Multiple Loading

AbstractLeast-cost design of water distribution system is a well-known problem in the literature. The formulation of the least-cost design problem started by deterministic modeling and later by more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. Recently, a new nonprobabilistic modeling, titled the robust counterpart (RC) approach, has been developed for the least-cost design problem to incorporate the uncertainty without the need for full stochastic information. These nonprobabilistic methods, developed in the field of robust optimization, were shown to be advantageous over classical stochastic methods in the following aspects: tractability and computation time, nonnecessity of full probabilistic information, and the ability to integrate correlation of uncertain parameters aspects without adding complexity. Former studies have considered the RC approach for a special case of the least-cost problem with a single load demand uncertainty, and single gravi...

Optimal Management of Water Distribution Networks with Simulated Annealing: The C-Town Problem

AbstractSustainability is a major issue for water companies, who have to provide high quality services at achievable costs. In this context, water loss control and energy efficiency are two great challenges water companies have to face. Water loss represents both higher service cost (real losses) and loss of revenue (apparent losses), while the energy bill from treatment plants and pumping stations represents a significant part of the service cost. The Battle of Background Leakage Assessment for Water Networks (BBLAWN) was a competition dedicated to this subject: water distribution network (WDN) optimal management. Teams/individuals from academia, consulting firms, and utilities were invited to propose methodologies for solving the C-Town WDN problem: minimize operational and capital costs and background leakages. This paper presents one of the methodologies proposed at BBLAWN. The methodology proposed here to solve the C-Town WDN problem comprises two optimization models: a least-cost design model to ide...