---

The Charged System Search (CSS) is combined to chaos to solve mathematical global optimization problems. The CSS is a recently developed meta-heuristic optimization technique inspired by the governing laws of physics and mechanics. The present study introduces chaos into the CSS in order to increase its global search mobility for a better global optimization. Nine chaos-based CSS (CCSS) methods are developed, and then for each variant, the performance of ten different chaotic maps is investigated to identify the most powerful variant. A comparison of these variants and the standard CSS demonstrates the superiority and suitability of the selected variants for the benchmark mathematical optimization problems.

---

In engineering, flood routing is an important technique necessary for the solution of a floodcontrol problem and for the satisfactory operation of a flood-prediction service. A simple conceptual model like the Muskingum model is very effective for the flood routing process. One challenge in application of the Muskingum model is that its parameters cannot be measured physically. In this article we proposed imperialist competitive algorithm (ICA) for optimal parameter estimation of the linear Muskingum model. This algorithm uses imperialism and imperialistic competition process as a source of inspiration. Optimization to identify Muskingum model parameters can be considered as a suitable field to investigate the efficiency of this algorithm.

---

The Big Bang-Big Crunch (BB–BC) method is a relatively new meta-heuristic algorithm which inspired by one of the theories of the evolution of universe. In the BB–BC optimization algorithm, firstly random points are produced in the Big Bang phase then these points are shrunk to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. In this paper, the BB–BC algorithm is presented for optimal cost design of water distribution systems and employed to optimize different types of hydraulic networks with discrete variables. The results demonstrate the efficiency of the proposed method compared to other algorithms.

---

This paper presents application of an improved Harmony Search (HS) technique and Charged System Search algorithm (CSS) to estimate transport energy demand in Iran, based on socio-economic indicators. The models are developed in two forms (exponential and linear) and applied to forecast transport energy demand in Iran. These models are developed to estimate the future energy demands based on population, gross domestic product (GDP), and the data of numbers of vehicles (VEH). Transport energy consumption in Iran is considered from 1968 to 2009 as the case of this study. The available data is partly used for finding the optimal, or near optimal values of the weighting parameters (1968-2003) and partly for testing the models (2004-2009). Finally transport energy demand in Iran is forecasted up to the year 2020.

---

This article presents a comprehensive review of chaos embedded meta-heuristic optimization algorithms and describes the evolution of this algorithms along with some improvements, their combination with various methods as well as their applications. The reported results indicate that chaos embedded algorithms may handle engineering design problems efficiently in terms of precision and convergence and, in most cases they outperform the results presented in the previous works. The main goal of this paper is to providing useful references to fundamental concepts accessible to the broad community of optimization practitioners.

---

A charged system search algorithm (CSS) is applied to the optimal cost design of water distribution networks. This algorithm is inspired by the Coulomb and Gauss’s laws of electrostatics in physics. The CSS utilizes a number of charged particles which influence each other based on their fitness values and their separation distances considering the governing law of Coulomb. The well-known benchmark instances, Hanoi network, double Hanoi network, and New York City tunnel problem, are utilized as the case studies to evaluate the optimization performance of CSS. Comparison of the results of the CSS with some other meta-heuristic algorithms indicates the performance of the new algorithm.

---

The main functional purpose of a water distribution network is to transport water from a source to several domestic and industrial units while at the same time satisfying various requirements on hydraulic response. All the water distribution networks perform two basic operations: firstly the water network needs to deliver adequate amounts of water to meet specific requirements, and secondly the water network needs to be reliable therefore, the required amount of water needs to be continuously available 24 hours a day and 365 days per year. Due to the inevitable failures of some components such as pump stations, reservoirs and/or pipelines in a large-scale water distribution network, in designing a reliable network, the topological structure with low vulnerability must be achieved. Consequently, the study of connectivity, which is the key graph-theoretical notion, becomes crucial. This paper highlights some fundamental concepts from graph theory for vulnerability assessment of water distribution networks, addresses the mathematical properties of the link and node-deletion problems, and outlines some well-established results on the deterministic measures to assess the fault tolerance of networks.

---

Spillway design poses a significant challenge in effectively managing the energy within water flow to prevent erosion and destabilization of dam structures. Traditional approaches typically advocate for standard hydraulic jump stilling basins or other energy dissipators at spillway bases yet constructing such basins can be prohibitively large and costly, particularly when extensive excavation is necessary. Consequently, growing interest in cascade hydraulic structures has emerged over recent decades as an alternative for energy dissipation. These structures utilize a series of arranged steps to facilitate water flow, effectively dissipating energy as it traverses the cascade. Commonly deployed in scenarios involving high dams or steep gradients, the stepped configuration ensures efficient aeration and substantial energy dissipation along the structure, thereby reducing the size and cost of required stilling basins. Despite extensive research on hydraulic characteristics using physical and numerical models and established design procedures, construction cost optimization of step cascades remains limited but promising. This paper aims to address this gap by employing two novel gradient-based meta-heuristic optimization techniques to enhance the efficiency and cost-effectiveness of cascade stilling basin designs. Through comparative analyses and evaluations, this study demonstrates the efficacy of these techniques and offers insights for future research and applications in hydraulic structures design optimization.