APPLICATION OF OFFICE INFORMATION TECHNOLOGIES TO SOLVE THE PROBLEMS OF OPTIMAL STRUCTURAL RESERVATION OF SYSTEMS

Problem statement. The problems of optimal structural redundancy of systems are usually formulated as a nonlinear problem of mathematical programming with integer variables, and to solve them, usually, various optimization methods are used, which requires the development of special algorithms and appropriate software. However, in the case of clarifying the original task of optimal redundancy, there is often a need to adjust the developed algorithms and software. All this greatly complicates obtaining the desired results. Another approach to solving problems of optimal redundancy of systems is the use of office information technology, the tool environment of which is adapted to solve mathematical problems, including optimization problems. This approach does not require the development of special algorithms and software. However, issues related to the effectiveness of the information technology used to solve this problem require further scientific and practical study. This article formulates a model of optimal design of redundant systems according to the criterion of minimum cost while ensuring the required level of reliability during a given time. This model is written in terms of a nonlinear problem of mathematical programming with integer variables and is numerically implemented in the operating environment of an Excel spreadsheet when the main object of the designed system consists of 6 elements. The optimal options for reserving this object according to the schemes of "hot" and "cold" redundancy are obtained. The purpose of the article is to show the effectiveness and efficiency of the MS Excel spreadsheet to solve problems of optimal structural redundancy of systems. Conclusions. This article discusses issues related to the problem of solving problems of optimal design of redundant systems in the tool environment of the MS Excel spreadsheet. Examples of solving the problems of separate "hot" and separate "cold" redundancy of a 6-element object prove the effectiveness and efficiency of the MS Excel spreadsheet to solve this problem. In addition, the developed optimization model can be successfully used in practical tasks to ensure the reliability of technical systems in the early stages of their design.

Road Safety Resource Allocation Using Interactive Multiobjective Optimization

A model is proposed for allocating safety resources to various hazard sites. Due to budget constraints, allocation of resources for necessary countermeasures is a critical issue in safety improvement programs. Therefore, the Decision Maker needs a tool that can prioritize the identified countermeasures looking at several objectives, the most important of which are: reducing the number of accidents and minimizing the costs. A number of countermeasures could be implemented simultaneously in the same location and this was considered, so that the solution that best optimizes the objectives was selected. Since the considered objectives are not commensurable, a new methodology with interactive multi-objective optimization in the case of 0-1 integer variables was proposed, based on the application of a logical preference model built using dominance-based Rough Set Approach (IMO-DRSA). Finally, an application of the methodology is presented considering a sample of Italian urban intersections and a set of mutually exclusive alternatives at each location.

Minimum Spillage from Reservoirs using Mixed Integer Linear Programming

The use of the traditional linear programming is not possible when an if-condition is to be imposed on the model unless some modifications are made. The difficulty arises due to the fact that the inclusion of if-condition to the generic formulation of the linear programming and its mechanism called "simplex method" is not a trivial task. The mixed integer linear programming seems to be a good candidate to achieve this goal. However, two issues should be satisfied beforehand if one would like to minimize the spill. 1. the reservoir should be full up to the spillway crest level in order for the spillage to occur. 2. the next state of the reservoir after the spill has been occurred should be full as well. Adding binary integer variables to the model helps in achieving the optimal solution in terms of minimum sum of spillage without violating any of the underlying constraints. When the input to the model being altered, the results showed that the model can cope with the uncertainty inherent in any natural inflow process in terms of spillage minimization.

Counterfactual Explanations for Optimization-Based Decisions in the Context of the GDPR

The General Data Protection Regulations (GDPR) entitle individuals to explanations for automated decisions. The form, comprehensibility, and even existence of such explanations remain open problems, investigated as part of explainable AI. We adopt the approach of counterfactual explanations and apply it to decisions made by declarative optimization models. We argue that inverse combinatorial optimization is particularly suited for counterfactual explanations but that the computational difficulties and relatively nascent literature make its application a challenge. To make progress, we address the case of counterfactual explanations that isolate the minimal differences for an individual. We show that under two common optimization functions, full inverse optimization is unnecessary. In particular, we show that for functions of the form of the sum of weighted binary variables, which includes frameworks such as weighted MaxSAT, a solution can be found by solving a slightly modified version of the original optimization model. In contrast, the sum of weighted integer variables can be solved with a binary search over a series of modifications to the original model.

Unit commitment using complementarity

A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.

Unit commitment using complementarity

A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.

Planning of Aircraft Fleet Maintenance Teams

This paper addresses a support information system for the planning of aircraft maintenance teams, assisting maintenance managers in delivering an aircraft on time. The developed planning of aircraft maintenance teams is a computer application based on a mathematical programming problem written as a minimization one. The initial decision variables are positive integer variables specifying the allocation of available technicians by skills to maintenance teams. The objective function is a nonlinear function balancing the time spent and costs incurred with aircraft fleet maintenance. The data involve technicians’ skills, hours of work to perform maintenance tasks, costs related to facilities, and the aircraft downtime cost. The realism of this planning entails random possibilities associated with maintenance workload data, and the inference by a procedure of Monte Carlo simulation provides a proper set of workloads, instead of going through all the possibilities. The based formalization is a nonlinear integer programming problem, converted into an equivalent pure linear integer programming problem, using a transformation from initial positive integer variables to Boolean ones. A case study addresses the use of this support information system to plan a team for aircraft maintenance of three lines under the uncertainty of workloads, and a discussion of results shows the serviceableness of the proposed support information system.

Bifurcations in 2D Spatiotemporal Maps

In this work, we give theoretical and numerical analyses for local bifurcations of 2D spatiotemporal discrete systems of the form [Formula: see text] where [Formula: see text] is a real nonlinear function, [Formula: see text] and [Formula: see text] are two independent integer variables, representing respectively a spatial coordinate and the time. On the basis of the spectral theory, we derive the conditions under which the local bifurcations such as flip and fold occur at the fixed points for some parameter values. As a case-study, a quite complex system, [Formula: see text]D spatiotemporal dynamic given by two coupled logistic maps, named [Formula: see text]D logistic coupled maps ([Formula: see text]D-LCM) is considered. The proposed map provides a reliable experimental and theoretical basis for identifying some cases of local bifurcations.

MINLP Model for Operational Optimization of LNG Terminals

Liquefied natural gas (LNG) is a clear and promising fossil fuel which emits less greenhouse gas (GHG) and has almost no environmentally damaging sulfur dioxide compared with other fossil fuels. An LNG import terminal is a facility that regasifies LNG into natural gas, which is supplied to industrial and residential users. Modeling and optimization of the LNG terminals may reduce energy consumption and GHG emission. A mixed-integer nonlinear programming model of the LNG terminal is developed to minimize the energy consumption, where the numbers of boil-off gas (BOG) compressors and low-pressure (LP) pumps are considered as integer variables. A case study from an actual LNG terminal is carried out to verify the practicality of the proposed method. Results show that the proposed approach can decrease the operating energy consumption from 9.15% to 26.1% for different seasons.