Model abstraction for discrete-event systems by binary linear programming with applications to manufacturing systems

Model abstraction for finite state automata is helpful for decreasing computational complexity and improving comprehensibility for the verification and control synthesis of discrete-event systems (DES). Supremal quasi-congruence equivalence is an effective method for reducing the state space of DES and its effective algorithms based on graph theory have been developed. In this paper, a new method is proposed to convert the supremal quasi-congruence computation into a binary linear programming problem which can be solved by many powerful integer linear programming and satisfiability (SAT) solvers. Partitioning states to cosets is considered as allocating states to an unknown number of cosets and the requirement of finding the coarsest quasi-congruence is equivalent to using the least number of cosets. The novelty of this paper is to solve the optimal partitioning problem as an optimal state-to-coset allocation problem. The task of finding the coarsest quasi-congruence is equivalent to the objective of finding the least number of cosets. Then the problem can be solved by optimization methods, which are respectively implemented by mixed integer linear programming (MILP) in MATLAB and binary linear programming (BLP) in CPLEX. To reduce the computation time, the translation process is first optimized by introducing fewer decision variables and simplifying constraints in the programming problem. Second, the translation process formulates a few techniques of converting logic constraints on finite automata into binary linear constraints. These techniques will be helpful for other researchers exploiting integer linear programming and SAT solvers for solving partitioning or grouping problems. Third, the computational efficiency and correctness of the proposed method are verified by two different solvers. The proposed model abstraction approach is applied to simplify the large-scale supervisor model of a manufacturing system with five automated guided vehicles. The proposed method is not only a new solution for the coarsest quasi-congruence computation, but also provides us a more intuitive understanding of the quasi-congruence relation in the supervisory control theory. A future research direction is to apply more computationally efficient solvers to compute the optimal state-to-coset allocation problem.

Binary Linear Programming as a Tool of Cost Optimization for a Water Supply Operator

The problem of scheduling pumps is widely discussed in the literature in the context of improving energy efficiency, production costs, emissions, and reliability. In some studies, the authors analyze the available case studies and compare the results; others present their own computational methods. In the paper, a problem of pump scheduling in regular everyday operations of a water supply operator is considered. The issues of water production optimization and energy savings are part of the topic of sustainable development. The objective of the article is the minimization of the cost of electric power used by the pumps supplying water. It is achieved thanks to the variability of both the demand for water and the price of electric power during the day combined with the possibility of storing water. The formulation of an existing electric power cost optimization problem as a binary linear programming problem was improved. An essential extension of the above mathematical model, which enables more flexible management of the pump system, was also proposed. An example containing real-world input data was successfully solved using Microsoft Excel with a free OpenSolver add-in.

Joint 2D SSA with GSVD and binary linear programming based image super-resolution

This paper proposes a joint two dimensional (2D) singular spectrum analysis (SSA) with the generalized singular value decomposition (GSVD) and the binary linear programming based method for performing the super-resolution. For a given low resolution image, first both the upsampling operation and a lowpass filtering are applied on each column of the image to obtain an enlarged image. Second, apply the 2D Hankelization to both the low resolution image and the enlarged image to obtain their corresponding trajectory matrices. Third, both the GSVD and the 2D de-Hankelization are applied to these two trajectory matrices to obtain their corresponding sets of the de-Hankelized 2D SSA components. Here, it is proved that the exact perfect reconstruction is achieved. In order to enhance the high frequency contents of the enlarged image, the selection of the de-Hankelized 2D SSA components is formulated as a binary linear programming problem. Computer numerical simulation results show that the proposed method outperforms the state of art methods.

Metode Pemrograman Linier Biner untuk Penjadwalan Kelas Tambahan

This project discusses the methods of binary linear programming with an application of scheduling problem for students and teachers in an addi-tional class program. This topic was inspired by the the problems faced by several schools, which in preparing students for exams, often need to or-ganize additional class programs. Such a program is certainly efficient, because it can save teaching load, but is quite complicated in terms of scheduling. The desired schedule must fit the student learning times and teacher availability. Using mathematical modeling, conditions and regula-tions are expressed in the form of mathematical equations and or inequali-ties, which act as constraints. Next, formulating the problem in the stand-ard form, allow us to implement the integer linear programming tools available in Matlab. The output we obtained, were in the form of a binary matrix, directly representing the student learning schedule, as well as the teacher's teaching schedule.

Optimization of knowledge transferring costs in designing product portfolio: a fuzzy binary linear programming model

Purpose The success of any organization in a knowledge-based economy depends on effective knowledge transferring and then proper use of the transferred knowledge. As is known, optimizing the knowledge transferring costs in a product portfolio plays an important role in improving productivity, competitive advantage and profitability of any organization. Therefore, this paper aims to determine an optimal product portfolio by minimizing the konlwedge transferring costs. Design/methodology/approach Here, a fuzzy binary linear programming model is used to select an optimal product portfolio. The model is capable of considering the knowledge transferring costs while taking into account the human-hours constraints for each product by a fuzzy approach. Using fuzzy ranking functions, a reasonable solution of the model can be achieved by classical or metaheuristic algorithms. Findings Numerical experiments indicate that the proposed fuzzy model is practically effective. Originality/value The contributions of this work essentially consist of considering knowledge transferring costs in selecting an optimal product portfolio and using the fuzzy data which make the model more realistic.

SCHEDULING OF REPETITIVE CONSTRUCTION PROCESSES WITH CONCURRENT WORK OF SIMILARLY SPECIALIZED CREWS

The highest degree of construction works harmonization can be achieved when planning a repetitive project with processes replicated many times in work zones of identical size. In practice, structural considerations affect the way of dividing the object under construction into zones differing in terms of scope and quantity of works. Due to this fact, individual processes are being allotted to different non-identical zones. Most methods intended for scheduling repetitive processes were developed with the assumption that the work zones are identical and that a particular process cannot be concurrently conducted. To address this gap, the authors put forward a mathematical model of the problem of scheduling of repetitive processes that are repeated in different work zones with the following assumption: several crews of the same type are available, thus particular process can run simultaneously in different locations. The aim of optimization is minimizing the idle time of all crews under the constraint of not exceeding the contractual project duration. The proposed mixed binary linear programming model can be solved using software available in the market or developed into a dedicated system to support decisions. To illustrate the benefits of the model, an example of scheduling interior finishing works was provided.

A Mixed Binary Linear Programming Model for Optimal Energy Management of Smart Buildings

Efficient alternatives in energy production and consumption are constantly being investigated and conducted by increasingly strict policies. Buildings have a significant influence on electricity consumption, and their management may contribute to the sustainability of the electricity sector. Additionally, with growing incentives in the distributed generation (DG) and electric vehicle (EV) industries, it is believed that smart buildings (SBs) can play a key role in sustainability goals. In this work, an energy management system is developed to reduce the power demands of a residential building, considering the flexibility of the contracted power of each apartment. In order to balance the demand and supply, the electrical power provided by the external grid is supplemented by microgrids such as battery energy storage systems (BESS), EVs, and photovoltaic (PV) generation panels. Here, a mixed binary linear programming formulation (MBLP) is proposed to optimize the scheduling of the EVs charge and discharge processes and also those of BESS, in which the binary decision variables represent the charging and discharging of EVs/BESS in each period. In order to show the efficiency of the model, a case study involving three scenarios and an economic analysis are considered. The results point to a 65% reduction in peak load consumption supplied by an external power grid and a 28.4% reduction in electricity consumption costs.