Mixed-integer Linear Programming Optimization Problem Research Articles

Diesel genset optimization in remote microgrids

In this paper, a new model is proposed for the real-time diesel genset optimal dispatch and unit commitment in remote microgrids. The objective is to reduce fuel consumption, while taking into account several constraints, such as maintenance considerations and prime power ratings, specific to gensets. The model described in this work is deterministic in nature and is a mixed-integer linear programming optimization problem. In order to demonstrate the correct behavior of the model, four case studies were chosen to illustrate the activation of different constraints under certain conditions. The results show that the model properly reproduces the intended behavior, and that it could have permitted to reduce fuel consumption by 4.3 % when compared to the actual dispatch during those 2 days. Finally, it was shown that the performance of the model solved with CPLEX and Gurobi is adequate for real-time optimization in remote microgrids, and that the economic gain of using a baseload strategy instead of a load sharing strategy is negligible compared to the increase of complexity in implementing this baseload strategy.

Optimal Planning of Residential Energy Hubs Considering Customer Desire Function

This paper proposes an optimal residential energy hub (REH) design framework where the desired tradeoff between maximizing the satisfaction level of residential user energy usage and minimizing the overall costs is obtained by establishing a customer desire function (CDF). Considering the major household appliances, the REH demands are categorized into several groups, and CDFs are formulated and applied to each group of loads. The developed mathematical model results in a mixed-integer linear programming optimization problem. Simulations were carried out on a residential building as a case study. Numerical results confirmed the presented framework effectiveness in improving the end-user convenience level and enhancing the investment benefits. They also demonstrated the significance of various energy networks and the optimal configuration of REH components on the financial and technical of the REH.

The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession

The traditional machine-part cell formation problem simultaneously clusters machines and parts in different production cells from a zero–one incidence matrix that describes the existing interactions between the elements. This manuscript explores a novel alternative for the well-known machine-part cell formation problem in which the incidence matrix is composed of non-binary values. The model is presented as multiple-ratio fractional programming with binary variables in quadratic terms. A simple reformulation is also implemented in the manuscript to express the model as a mixed-integer linear programming optimization problem. The performance of the proposed model is shown through two types of empirical experiments. In the first group of experiments, the model is tested with a set of randomized matrices, and its performance is compared to the one obtained with a standard greedy algorithm. These experiments showed that the proposed model achieves higher fitness values in all matrices considered than the greedy algorithm. In the second type of experiment, the optimization model is evaluated with a real-world problem belonging to Human Resource Management. The results obtained were in line with previous findings described in the literature about the case study.

Application of the microsoft excel solver tool in the optimization of distillation sequences problems

AbstractDistillation is a very important operation for purification and separation in Chemical Engineering field. The determination of the optimal distillation sequence is key to minimize the total investment and operating cost and it can be posed as a mixed integer‐linear programming (MILP) problem. To solve them and due to the high number of variables and equations, it is required the use of specific software, for example, General Algebraic Modeling System or A Mathematical Programming Language. However, these software involve long training for the student to adequately harness them. The use of non‐specialized, widespread and easy to access software programs is a good opportunity to tackle the teaching of some typical optimization problems. One of them is the Microsoft Excel Solver Tool, accessible by any engineering student who usually learn its use in the first years of their degree, so that MS‐Excel is already known when students deal with optimization problems. Additionally, it is scarcely known that Microsoft Excel Solver may tackle both real and binary variables, so it is possible to leverage it for solving MILP problems. This paper presents an example of distillation sequences problem aimed to separate a mixture comprising four different compounds with a minimal operational cost (which constitutes a MILP optimization problem indeed) solved using Excel Solver tool. This methodology was taught successfully to the students of the Master of Chemical Engineering of Rey Juan Carlos University and Autónoma University of Madrid.

Wireless energy efficient occupancy-monitoring system for smart buildings

Rationalizing energy consumption in smart buildings is considered in this paper, and a wireless monitoring system based on Passive Infrared sensors (PIRs) is proposed. The proposed system is pervasive and can be integrated in existing buildings without any complicated wiring or setting. Realistic constraints are considered for this purpose such as sensing-hole, battery limitation, user comfort, etc. To ensure maximum coverage in presence of holes, the optimal placement of PIRs is formulated as a mixed integer linear programming optimization problem (MILP). Experimentations have been carried out to quantify the effects of the holes on the detection accuracy and to demonstrate the impact of the optimal PIRs placement on energy consumption. To facilitate installation and integration without complicated settings, notably in existing buildings, the system is designed to be battery operated. Therefore, energy efficiency will not be limited to optimize energy consumption in buildings, but also to optimize consumption in the components of the system (sensors and actuators). Duty cycling is inevitable to extend the network lifetime of such components, but the setting of this cycle yields a trade-off in optimizing the energy consumption i) at the building level, vs., ii) that consumed by sensors and actuators. Reducing energy consumption (duty cycle) of sensors/actuators will delay non-occupancy detections and thus will increase the building energy wastage, and vice-versa. Duty cycling the radios is dealt with and modeled as a cooperative game, which allows to derive a Nash Bargaining as the optimal balancing cycle. The proposed approach is analytically investigated using realistic parameters of the existing hardware and users’ comfort. The results demonstrate that the system can survive for more than 6 years without battery replacement.

Probabilistic Under Frequency Load Shedding Considering RoCoF Relays of Distributed Generators

The activation of under frequency load shedding (UFLS) is the last automated action against the severe frequency drops in order to rebalance the system. In this paper, the setting parameters of a multistage load shedding plan are obtained and optimized using a discretized model of dynamic system frequency response. The uncertainties of system parameters including inertia time constant, load damping, and generation deficiency are taken into account. The proposed UFLS model is formulated as a mixed-integer linear programming optimization problem to minimize the expected amount of load shedding. The activation of rate-of-change-of-frequency relays as the anti-islanding protection of distributed generators is considered. The Monte Carlo simulation method is utilized for modeling the uncertainties of system parameters. The results of probabilistic UFLS are then utilized to design four different UFLS strategies. The proposed dynamic UFLS plans are simulated over the IEEE 39-bus and the large-scale practical Iranian national grid.

Mixed-Integer Linear Programming-Based Splitting Strategies for Power System Islanding Operation Considering Network Connectivity

An efficient splitting strategy is important for the islanding operation of power systems. In this paper, a mixed-integer linear programming (MILP)-based splitting method is proposed. First, the graph theory is employed to transform the splitting problem into a graph partition problem. Then, the graph partition problem is modeled as an MILP optimization problem with consideration to the network connectivity of all subgraphs. The MILP-based splitting strategy can be efficiently computed with existing commercial solvers, and the multiple optimal solutions can be captured with the recursive process. Compared with the splitting methods in the literature, the proposed method is more flexible and efficient, such that the users can select the optimal solution from multiple solutions with different interests and heuristic splitting rules (e.g., with the minimum amount of switched lines). Finally, the effectiveness of the proposed method has been verified with IEEE 30-, 118-, and 300-bus test systems.

Hybrid simulated annealing and mixed integer linear programming algorithm for optimal planning of radial distribution networks with distributed generation

This paper presents a hybrid simulated annealing (SA) and mixed integer linear programming (MILP) approach for static expansion planning of radial distribution networks with distributed generators (DGs). The expansion planning problem is first modeled as MILP optimization problem with the goal of minimizing the investment cost, cost of losses, cost of customer interruptions due to failures at the branches and at DGs and the cost of lost DG production due to failures at branches. In order to reduce the complexity of planning problems the decomposition of the original problem is proposed into a number of sequences of sub-problems (local networks) that are solved using the MILP model. The decomposition and solution process is iteratively guided and controlled by the proposed SA algorithm that employs the proper intensification and diversification mechanism to obtain the minimum total cost solution.

Fast Model Predictive Control for Urban Road Networks via MILP

In this paper, an advanced control strategy, i.e., model predictive control (MPC), is applied to control and coordinate urban traffic networks. However, due to the nonlinearity of the prediction model, the optimization of MPC is a nonlinear nonconvex optimization problem. In this case, the online computational complexity becomes a big challenge for the MPC controller if it is implemented in a real-life traffic network. To overcome this problem, the online optimization problem is reformulated into a mixed-integer linear programming (MILP) optimization problem to increase the real-time feasibility of the MPC control strategy. The new optimization problem can be very efficiently solved by existing MILP solvers, and the global optimum of the problem is guaranteed. Moreover, we propose an approach to reduce the complexity of the MILP optimization problem even further. The simulation results show that the MILP-based MPC controllers can reach the same performance, but the time taken to solve the optimization becomes only a few seconds, which is a significant reduction, compared with the time required by the original MPC controller.

APPLICATION OF MIXED INTEGER LINEAR PROGRAMMING IN THE GENERATION OF VECTORS WITH MAXIMUM DATAPATH COVERAGE FOR COMBINATIONAL LOGIC CIRCUITS

In this paper, we present a novel methodology for vector generation that maximizes the metric of datapath coverage for a given combinational logic circuit. The proposed methodology is based on Mixed Integer Linear Programming (MILP). The search of input vectors based on the datapath coverage metric is a satisfiability (SAT) problem. In order to obtain maximum coverage vectors, we use a novel model for the Boolean logic gates to translate the original SAT problem into an MILP optimization problem. Next, the new problem is solved following the MILP optimization environment and an exhaustive search strategy. We compare our proposed methodology with the exhaustive search algorithm. Experimental results and performance comparisons based on the large set of MCNC'91 suite of benchmark circuits are presented. They show significant speedups of MILP methodology against the exhaustive search algorithm for the complex circuits.

Design of Multi-echelon Supply Chain Networks under Demand Uncertainty

We consider the design of multiproduct, multi-echelon supply chain networks. The networks comprise a number of manufacturing sites at fixed locations, a number of warehouses and distribution centers of unknown locations (to be selected from a set of potential locations), and finally a number of customer zones at fixed locations. The system is modeled mathematically as a mixed-integer linear programming optimization problem. The decisions to be determined include the number, location, and capacity of warehouses and distribution centers to be set up, the transportation links that need to be established in the network, and the flows and production rates of materials. The objective is the minimization of the total annualized cost of the network, taking into account both infrastructure and operating costs. A case study illustrates the applicability of such an integrated approach for production and distribution systems with or without product demand uncertainty.