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.     

Network capacity control using self-adjusting bid-prices

The computation of bid-prices for resources is the most popular instrument for capacity control in network revenue management. The basic task of this control includes supporting accept/reject decisions on dynamically arriving requests for products that differ in their revenues and resource demands, respectively. Within actual control, bid-prices can be used to approximate the opportunity cost of reserving resources to satisfy a request. Using this valuation, the request is accepted if the associated revenue equals or exceeds the opportunity cost. Most commonly, bid prices are computed by linear programming based on the forecasted demand with a few updates during the booking period. Due to accepted requests and variations between forecasted and real demand, the approximation of the opportunity cost becomes less accurate with time passing by, leading to inferior accept/reject decisions. Therefore, we propose the concept of self-adjusting bid-prices. The basic idea includes defining bid-prices as functions of the amount of capacity already used and of the expected demand-to-come. Coefficients for calibrating the bid-price functions are obtained by a simulation-based optimization using the metaheuristic scatter search.     

Linear program-based algorithm for the optimal design of wastewater treatment systems

This paper presents a new approach for the optimal design of distributed wastewater treatment networks with multiple contaminants. It consists of a two-stage solution strategy. In the first stage, a decomposition method is employed that replaces the general non-linear program (NLP) by a succession of linear programs, one for each treatment unit. In the second stage, the resulting network is used as a starting point for the solution of the general NLP by a local optimization solver. The decomposition process considers a specific substructure, where it is assumed that the wastewater streams go through the treatment units in sequence. To consider all combinations, the two-stage solution strategy is applied as many times as the number of possible sequences. This allows considering multiple and structurally different starting points, thus increasing the probability of finding global optimal solutions. The results have shown that the proposed approach can find better solutions than other approach reported in the literature, however with a drawback of being more demanding computationally. An erratum to this article can be found at     

A scatter search algorithm for stacking sequence optimisation of laminate composites

This paper explores the metaheuristic approach called scatter search for lay-up sequence optimisation of laminate composite panels. Scatter search is an evolutionary method that has recently been found to be promising for solving combinatorial optimisation problems. The scatter search framework is flexible and allows the development of alternative implementations with varying degree of sophistication. The main objective of this paper is to demonstrate the effectiveness of the proposed scatter search algorithm for the combinatorial problem like stacking sequence optimisation of laminate composite panels. Preliminary investigations have been carried out to compare the optimal stacking sequences obtained using scatter search algorithm for buckling load maximisation with the best known published results. Studies indicate that the optimal buckling load factors obtained using the proposed scatter search algorithm found to be either superior or comparable to the best known published results.

Later, two case studies have been considered in this paper. Thermal buckling optimisation of laminated composite plates subjected to temperature rise is considered as the first case study. The results obtained are compared with an exact enumerative study conducted on the problem to demonstrate the effectiveness and performance of the proposed scatter search algorithm. The second case study is optimisation of hybrid laminate composite panels for weight and cost with frequency and buckling constraints. The two objectives are considered individually and also collectively to solve as multi-objective optimisation problem. Finally the computational efficiency of the proposed scatter search algorithm has been investigated by comparing the results with various implementations of genetic algorithm customised for laminate composites. It was shown in this paper through numerical experiments that the scatter search is capable of finding practical solutions for optimal lay-up sequence optimisation of composite laminates and results are comparable and sometimes even superior to genetic algorithms.     

Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times

This paper is concerned with the production smoothing problem that arises in the context of just-in-time manufacturing systems. The production smoothing problem can be solved by employing a two-phase solution methodology, where optimal batch sizes for the products and a sequence for these batches are specified in the first and second phases, respectively. In this paper, we focus on the problem of selecting optimal batch sizes for the products. We propose a dynamic programming (DP) algorithm for the exact solution of the problem. Our computational experiments demonstrate that the DP approach requires significant computational effort, rendering its use in a real environment impractical. We develop three meta-heuristics for the near-optimal solution of the problem, namely strategic oscillation, scatter search and path relinking. The efficiency and efficacy of the methods are tested via a computational study. The computational results show that the meta-heuristic methods considered in this paper provide near-optimal solutions for the problem within several minutes. In particular, the path relinking method can be used for the planning of mixed-model manufacturing systems in real time with its negligible computational requirement and high solution quality.     

离散需求下的多产品二级分销网络优化模型

构建了一个不确定需求下的多产品二级分销网络模型,以成本最小化为目标考虑了建设成本、配送成本、库存成本、缺货成本以及惩罚成本;以实际情况为背景考虑了工厂的产能约束、最小和最大转运量约束、最小配送量等约束。针对模型的复杂性,设计了禁忌搜索算法对模型进行求解,并通过一个算例验证了模型的正确性。通过遗憾值系数的变化找到了算例的最优鲁棒解,并且应用该算法求解模型耗时不到15 s,证明了算法的有效性和可行性,并具有一定的实际应用意义。     

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.     

An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. The iterative local search along with a shift strategy is developed and applied to the heuristic to balance the exploitation and exploration tasks in the solution space without the tuning of any parameters. The experimental results on many scales of packing problems show that this approach can produce high-quality solutions for most of the benchmark datasets, especially for large-scale problems, within a reasonable duration of computational time.     

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.     

基于性能曲线的冷水机组配置和运行优化

在设计中引入简单有效的计算手段,对冷水机组配置和运行的优化进行节能分析是必要的,本文分析了与冷水机组节能相关的因素,介绍了常用冷水机组典型性能特征,举例分析常用冷水机组COP-PLRC-tc曲线,提出了基于性能曲线的冷水机组配置和优化运行方法,阐述了运用该方法对进行冷水机组配置和运行优化的步骤,最后为采用该方法的应用实例。     

A modification of threshold accepting and its application to the quadratic assignment problem

In this paper we propose a modification of the threshold accepting heuristic by Dueck and Scheuer. Instead of using discrete threshold values a threshold function similar to the cooling schedule of simulated annealing is used. Furthermore, the number of iterations during each step of the heuristic is a function of the current and the initial threshold value. Using this scheme, we investigate the trade-off between solution quality and convergence speed on different instances of the well known quadratic assignment problem. In a second set of experiments the results of a multistart-version of TA are compared with the results of unique long runs at identical CPU-requirements to identify the better optimization strategy. Since, generally, in the literature the number of starting solutions for QAP-heuristics appears to be chosen on a rather arbitrary basis, we also highlight how varying this number influences the TA-results.This article was processed by the author using the LAT_EX style filepljour2 from Springer-Verlag.     

High dimension dynamic programming model for water resources expansion projects

An optimization model for High Dimension Dynamic Programming (HDDP) was developed to determine the optimal size of water resources projects within a planning period. The model uses Objective Space Dynamic Programming (OSDP) technique to determine the size of the projects and a Mixed Integer Programming (MIP) formulation to overcome the ‘inner’ and ‘outer’ problems of OSDP and to check for the global optimality of the solution. The model is applied to determine the optimal capacity of proposed desalination plants needed to satisfy a number of demand points from different cities, during a planning period of 20 years in Egypt. The model’s speed towards the optimal solution depends on the objective space bounds and search method for these bounds. The integration of OSDP and MIP is shown to be an efficient approach for solving optimization problems. Results show that the model is well suited for solving large-scale water resources expansion problems.     

A TWO-PHASE NETWORK DESIGN HEURISTIC FOR MINIMUM COST WATER DISTRIBUTION SYSTEMS UNDER A RELIABILITY CONSTRAINT

This paper presents a two-phase design and optimization procedure for constructing a pipe network water distribution system having a built-in degree of reliability. The first phase is comprised of an algorithm called TREESEARCH which iteratively constructs a tree pipe network. Starting with a shortest-path based tree, the procedure employs a linear programming subproblem to systematically modify this tree by adding and deleting one link at a time, with the aim of reducing the cost of the network while satisfying the flow continuity, energy balance, and pressure head requirement constraints. The second phase of the algorithm, called REDUNDANCY, is concerned with the issue of reliability. In this phase, the tree network constructed by the algorithm TREESEARCH is augmented through the addition of links so that there are at least two arc-disjoint paths from each source node to every demand node it serves. This augmentation is performed through the use of a set covering problem which recommends the links to be added, and a Hardy-Cross solver for redesigning the perturbed network to ensure feasibility, while attempting to minimize the overall design cost. The two phases are coordinated by applying algorithm REDUNDANCY to several candidate solutions presented by TREESEARCH. Two example problems from the literature, one involving a single source and the other a multiple source network, are solved using the proposed procedure. The solutions obtained have a smaller cost than those previously obtained by other researchers.