I In this paper, we propose an algorithm base on decomposition technique for solving the Mixed integer linear multiplicative-linear bilevel problems. In fact, this algorithm is an application of the algorithm given by G. K. Saharidis et al for the case in which the first level objective function is linear multiplicative. We use properties of quasi-concave of bilevel programming problems and decompose the initial problem into two subproblems named RMP and SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is less than an arbitrary tolerance. In conclusion, some numerical examples are presented in order to show the efficiency of algorithm.

IntroductionFloods, droughts, water scarcity, water contaminants, and optimal use of water resources including reservoirs and aquifers are some of the many water problems present today. These will be even more noticeable in the future. The optimal operation of reservoirs is one of the best ways in water resources management to deal with such problems and other unwanted temporal and spatial distributions of water. Optimization techniques have become increasingly important in the management and operation of complex reservoir systems over the past three decades. Some researches have provided an extensive literature review and evaluation of various optimization methods and their corresponding models. Each optimization method has its advantages and disadvantages that make them suitable for some problems. Selection of each method depends on the characteristics of the system being considered, data availability, optimization objectives, and the problem constraints.

The measure of Reactive power optimization of main power network mainly considers on-load tap changer, the optimal capacity of the capacitor, the voltage of generator under the steady load. In This paper, a multi-objective optimization methodology to the Optimal Reactive Power Flow (ORPF) problem is proposed in which the e-constrained approach is implemented for the Multi-objective Mathematical programming (MMP) formulation. The objectives functions of the proposed model include optimize the total fuel cost, the active power losses, and the system load ability. Since the control variables include discrete variables (var sources and transformer tap ratios), the ORPF is inherently a Mixed-integer nonlinear programming (MINLP) problem. The optimum tap settings of transformers are directly determined in terms of the admittance matrix of the network since the admittance matrix is constructed in the optimization framework as additional equality constraints. To show the effectiveness of proposed method the results are compared with single-objective, two-objectives and three-objectives. Finally, the method has been implemented in GAMS and solved using DICOPT solver to obtain optimal solutions. In this research, for selection of the best compromising answer among the Pareto optimal solutions has been designed a fuzzy decision-maker tool. The algorithm is tested on standard IEEE 14- bus test system. Simulation results show that the proposed algorithm is able to control reactive power flow effectively and optimize the selected objective functions.

Feature selection is an important step in data preprocessing, which helps  reducing the dimensionality of data and simplifying the models. This process not only reduces the computational complexity of models, but also improves their accuracy by eliminating irrelevant features and noise. The three most widely used approaches for feature selection are filter, wrapper and embedded methods.  In this paper, first we review some support vector machine based Mixed-integer linear programming (MILP) models and Supervised Infinite Feature Selection (Inf-FS$_s$) method.  Then, we propose three hybrid approaches based on them. The first approach involves solving the relaxed linear model of the underlying  MILP model and then solving the MILP model for those features with nonzero weights, namely a smaller MILP. In the second approach, first the Inf-FS$_s$ method is applied to rank the features. Then depending on the features costs, either chooses the top features from the ranked features until budget parameter is reached  or solves a knapsack problem to select cost effective features. The third approach applies the first approach to the top $20\%$ of features ranked by Inf-FS$_s$ method. To evaluate the proposed approaches' performance, experiments are conducted on four high-dimensional benchmark datasets for fixed and random features costs. Results demonstrate that using either of the proposed approaches can significantly reduce running time of MILP models with comparable accuracies with the original MILP models.

A two-dimensional strip packing problem is the process of packing a set of rectangular items of given dimensions into a strip of bounded width and infinite height so that the used height of the strip is minimized. In the case that only guillotine packing is permitted, the problem is called the guillotine strip packing problem (GSPP). Guillotine packing commonly arises in different industries such as glass, steel, paper and wood. Nevertheless, there is a lack of explicit mathematical models for GSPP that can globally solve the problem. In this paper, a new Mixed-integer programming model inspired by a so-called sequence sub-tour elimination technique for the traveling salesman problem (TSP) is presented as a relaxation of (non-staged) GSPP with orthogonal rotation. The proposed model is able to find good solutions (good upper bounds) for the optimal objective value and more importantly, it is a polynomial model of order $O(n^2)$, i.e. the number of decision variables (and constraints, as well) is a polynomial of order $O(n^2)$ in the number of the rectangular items ($n$). Numerical results show that the solutions obtained from the proposed model are superior to several existing heuristic algorithms in the literature.

Increased environmental pollution due to the industrial, municipal wastewaters and considerable power consumption of desalination units has increased the need of wastewater treatment technologies. Oil export quality and reduce costs of the electrostatic desalting, important issues in the upstream oil and gas. In this paper, the variety of technology packages used in the different energy levels in the upstream, regarding to the environmental costs, as a function of investment and operational cost have been compared using a Mixed integer mathematical programming models. Technology consists of four technology packages such as electrostatic desalination, industrial, municipal wastewater treatment and water desalination. Technology indexes in each package determine the superior technology timescales during the year. This model developed in Sirri Island and the priority of technology determined by the environmental conditions.

Different types of pipes are used in various industries, and linear programming of pipe production is an effective subject in this industry. Especially, efficient planning in operational level leads to reduce total cost and improves competitiveness. In this paper, the Mixed integer linear programming (MILP) approach is applied for operational planning of pipe production in different periods. To provide, moreover, a mathematical model for the manufacturing line, the model which is described in this study can choose the best supplier among a variety of suppliers. This model also optimizes the amount of raw materials acquired from suppliers as well as the amount of final product manufacturing, reducing final product and raw material inventory level in the factory. The final product inventory level, raw material inventory level, manufacturing capacity, supplier and warehouse capacity for keeping the final product and raw materials are also taken into account. The model is applied in a case study in GRP pipe production plants in Turkey.

Integrated water resources management is a systematic process for sustainable development, allocation and monitoring of water resources that is used for social, economic and environmental purposes. In this study, a multi-period Mixed-integer linear programming (MILP) model for urban water supply network management is proposed. The proposed model considers all echelons of water supply chain from supply centers to wastewater treatment centers. Also, the model optimizes the decisions such as selecting the suitable water supply centers and capacity level optimization. To verify and validate the proposed model a real case study is conducted in Urmia. The model is solved by the General Algebraic Modeling System (GAMS) software and its results have been analyzed. According to the results, the optimal water supply centers, optimal water flow, optimal water inventory, and optimal capacity levels of wastewater treatment centers in different periods are determined. Also, in case of transferring the remaining additional treated water to Urmia lake, its level is increased by about 0. 007 cm.

The technical equipment developed and used in both installation and operation processes in refineries, oil and gas pipelines, and gas booster stations has always been expensive. Hence, managers at different organizational levels are keen to find methods to control and reduce these costs. Generally speaking, the operators in a gas booster station choose the operating devices without considering the related costs. This research presents a Mixed integer nonlinear programming model designed to minimize the operational costs of gas booster stations in a main pipeline distribution network. The goal is to optimize the choice of operating devices in these stations to minimize costs while still meeting customer demands. Turbo compressors are chosen as the operating devices and the operational costs are fuel, maintenance, start-up, and penalty costs. However, the significance indexes of these costs are valued differently by the three expert managers: the executive officer, operating head, and the overhaul repairing director. Consequently, the analytical hierarchy process (AHP) method is used to calculate the overall weights of costs, and a gas transmission company in the north of Iran is considered as a case study. The model can minimize the total cost, when compared to the selections of ten experienced operators; however, the absolute weights of choosing measures and the essence of the objective function under study mean that an operator choice exists that would represent the optimum selection of turbo compressors.

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to deterministic demands. A Mixed integer linear fractional programming (MILFP) model is formulated and a solution approach for MILFP is discussed. Product distribution and allocation of different customers along with sensitivity of the key parameters and performance of the model are discussed through a numerical example. The results illustrate that profit achieved by the MILFP model is slightly higher than Mixed integer programming (MIP) model. It is observed that increase in the opening cost decreases the profit obtained by both MILFP and MIP models. If the opening cost of a location decreases or increases, the demand and capacity of the location changes accordingly. The opening cost dramatically changes the demand rather than the capacity of the product. Finally, a conclusion is drawn in favor of the MILFP model as a relevant approach in a logistic model searching for the optimum solution.