Stochastic optimization in AIMMS

Tato diplomová práce uvádí základní poznatky matematického a především stochastického programování. Navíc se zabývá použitím softwaru AIMMS při vytváření a řešení optimalizačních problémů. Naším hlavním cílem je naprogramovat v softwaru AIMMS několik metod řešení problémů stochastického programování a ukázat jejich použití a užitečnost na vybraných problémech. Jedním z problémů, který jsme si zvolili, je model spalovny. Všechny AIMMS programy, které v našem textu použijeme a popíšeme, a jejich zdrojové kódy budou přiloženy v dodatcích.This master’s thesis introduces the basic concepts of mathematical and, most importantly, stochastic programming. Moreover, it gives a description of the usage of the software AIMMS in constructing and solving various optimization problems. Our main goal is to program several methods for solving these stochastic programming problems in AIMMS and show the usage and usefulness of these methods on chosen problems. One of the problems we chose is an incineration plant model. All the AIMMS programs, that we describe and use in our text, and their source codes will be enclosed in the appendices.

Social Distancing as p-Dispersion Problem

The spread of COVID-19 and similar viruses poses new challenges for our society. There is a strong incentive towards safety measures that help to mitigate the outbreaks. Many countries have imposed social distancing measures that require a minimum distance between people in given places, such as schools, restaurants, shops, etc. This in turn creates complications for these places, as their function is to serve as many people as they were originally designed for. In this paper, we pose the problem of using the available space in a given place, such that the social distancing measures are satisfied, as a p-dispersion problem. We use recent algorithmic advancements, that were developed for the p-dispersion problem, and combine them with discretization schemes to find computationally attainable solutions to the p-dispersion problem and investigate the trade-off between the level of discretization and computational efforts on one side, and the value of the optimal solution on the other

Optimization problems in AIMMS

Tato bakalářská práce se zabývá využitím programu AIMMS při řešení a sestavování optimalizačních modelů. Po teoretickém zavedení různých typů optimalizačních úloh následuje ukázka sestavení modelu u konkrétního problému a jeho implementace do programu AIMMS. U všech konkrétních problémů jsou také vytvořeny pro koncové uživatele příjemnější grafická rozhraní, kde je možno vstupní data modelu snadno upravovat. Dále jsou přiloženy zdrojové kódy všech popsaných programů.This bachelor's thesis deals with the usage of system AIMMS for solving and creating optimization models. After the introduction to theoretical background of optimization problems there is an example of modeling a selected problem and its implementation to AIMMS. Each of the selected problems has its graphical user interface where an end user can simply modify the data of the model. All the source codes of programs described above are attached.

Circular economy implementation in waste management network design problem: a case study

The paper presents a new approach to support the strategic decision-making in the area of municipal solid waste management applying modern circular economy principles. A robust two-stage integer non-linear program is developed. The primary goal tends to reduce the waste production. The generated waste should be preferably recycled as much as possible and the resultant residual waste might be used for energy recovery. Only some waste residues are appropriate for landfilling. The aim is to propose the near-optimal waste allocation for its suitable processing as well as waste transportation plan at an operational level. In addition, the key strategical decisions on waste treatment facilities location must be made. Since waste production is very often hard to predict, it is modeled as an uncertain decision-dependent quantity. To support the circular economy ideas, advertising and pricing principles are introduced and applied. Due to the size of available real-world data and complexity of the designed program, the presented model is linearized and uncertainty is handled by a robust optimization methodology. The model, data, and algorithm are implemented in MATLAB and Julia, using the state-of-the-art solvers. The computational result is a set of decisions providing a trade-off between the average performance and the immunization against the worst-case conditions. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature

Pricing and advertising strategies in conceptual waste management planning

The paper presents a new model for integration of circular economy strategies into the municipal solid waste management. The goals are to reduce the waste produced, recycle at the highest rate as possible (material recovery) and to use the resultant residual waste for energy recovery. Such a strategy utilizes both pricing and advertising principles in the mixed integer linear programming model while accounting two criterions - assessment of greenhouse gas (GHG) and cost minimization. The aim is to design the optimal waste management grid to suggest a sustainable economy with environmental concerns. The government, municipalities and/or authorized packaging company decide about the investments to the propagation of waste prevention and to advertising of waste recycling, while investors decide about new facility location and technological parameter. The availability of waste is projected in pricing method as well as in the location of the facility. The mathematical model will consider randomness in the form of waste production. The suggested non-linear functions of pricing and advertising are replaced by piecewise linear approximation to reduce computational complexity. The proposed multi-objective model is applied in a case study for the Czech Republic in the area of waste treatment infrastructure planning to support decision-making at the micro-regional level. The integration of circular economy principles, considering also the total amount of produced GHG, revealed the existing potential in waste prevention. On the other hand, the increase of recycling is limited, landfills are not supported and the energy recovery is preferred. However, the planning of the complex system relies on the decision-maker. © 2019 Elsevier LtdCzech Republic Operational Programme Research and Development, Education, Priority 1: Strengthening capacity for quality research [CZ.02.1.01/0.0/0.0/15_003/0000456]; Operational Programme Research, Development and Education, Priority axis 1: Strengthening capacity for high-quality research [CZ.02.1.01/0.0/0.0/16 026/0008392

The L-shaped method for large-scale mixed-integer waste management decision making problems

It is without a doubt that deciding upon strategic issues requires us to somehow anticipate and consider possible variations of the future. Unfortunately, when it comes to the actual modelling, the sheer size of the problems that accurately describe the uncertainty is often extremely hard to work with. This paper aims to describe a possible way of dealing with the issue of large-scale mixed integer models (in term of the number of possible future scenarios it can handle) for the studied waste management decision making problem. The algorithm is based on the idea of decomposing the overall problem alongside the different scenarios and solving these smaller problems instead. The use of the algorithm is demonstrated on a strategic waste management problem of choosing the optimal sites to build new incineration plants, while minimizing the expected cost of waste transport and processing. The uncertainty was modelled by 5,000 scenarios and the problem was solved to high accuracy using relatively modest means (in terms of computational power and needed software)

Robust facility location problem for bio-waste transportation

The article presents an optimisation tool for bio-waste facility allocation. The quantity of bio-waste produced in individual territorial units is a key factor for the selection of localities when constructing a new facility. Bio-waste production changes over the course of the year and differs between various types of housing developments. Separation rate is a determining factor for bio-waste production. Readiness to separate the waste reflects the total quantity of bio-waste produced. Predicting the future of bio-waste production is a complex problem, and it would be suitable to consider more developed scenarios. The introduced tool takes into consideration additional possible scenarios for production and provides a robust solution from the point of view of a locality suggestion for the construction of the processing facility. The optimisation model is based on the two-stage stochastic programming approach. The decision regarding the locality for the construction of a new facility is made during the first stage. This method is called the "Here-and-Now" approach. The results are presented in a case study for a selected region in the Czech Republic. Since changes to the legislation in 2014, municipalities are now supposed to provide the possibility to collect the bio-waste of citizens. This has caused significant growth in production - about 20 % annually over the past few years. At this point, it is very complicated to estimate a future trend based on the historical data. Due to this reason, it would be appropriate to consider future bio-waste production across more scenarios. In order to enable the applicability of the tool on a large area with many nodes, it would be necessary to adapt the computation method according to its computational complexity. Copyright © 2017, AIDIC Servizi S.r.l

Optimal control of combined heat and power station operation

Combined heat and power stations have become one of the most utilized units of district heating systems. These stations usually contain several boilers for burning fossil fuels and renewable resources used for heating up steam, which can be used either for residential and commercial heating or electricity generation. To ensure efficiency, a boiler should either run continuously (for at least a given period) on a power output higher than a given threshold or switch off. The optimal control of the plant operations should combine an efficient setup for the turbine and boilers in operation, reflecting the demand for steam and the price of electricity, and a schedule that describes which boilers should be in operation at a given time. This paper proposes a method for optimal control of combined heat and power station operation for a given time horizon. The method is based on a two-level approach. The lower-level models correspond to finding the optimal setup of the combined heat and power station parameters for an hourly demand for different kinds of steam. The upper-level model corresponds to the optimal schedule of the operations of the individual boilers, which is planned for the entire time horizon. The lower-level model is modeled as a mixed-integer linear programming problem and is solved using parametric programming. A dynamic programming algorithm solves the upper-level model with a rolling horizon. The validity of the proposed method and its computational complexity for different granularity of the time horizon, different ranges of the parameters, varying demand for various kinds of steam, and varying electricity prices are investigated in a case study. The presented approach can be readily applied to other control problems with a similar structure. © 2023, The Author(s).National Technical Library in Prague; Technology Agency of the Czech Republic, TACR, (GA 20-00091Y, SS02030008); Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT, (CZ.02.1.01/0.0/0.0/16 026/0008392, FSI-S-20-6538); Grantová Agentura České Republiky, GA ČR; Univerzita Tomáše Bati ve Zlíně, (FSR FORD 5-6/2022-23/FLKŘ/001

Advanced Decomposition Methods in Stochastic Convex Optimization

Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích