KŮDELA, J. Stochastická optimalizace v programu AIMMS [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2014.

Posudek vedoucího

Popela, Pavel

The aim of the thesis was to study and then efficiently implement two-stage stochastic programming models and related decomposition-based algorithms in the AIMMS software system and apply them to the selected engineering problem based on the real-world data. The presented text folows and significantly extends the original ideas that the author has developed in his bachelor thesis. The new challenge for the author was to work in three different directions and combine the obtained results. The goal has been successfully achieved. The author has proven his deep knowledge of decomposition techniques of stochastic programming by their implementation and useful application. He has also learned the advanced optimization software AIMMS and developed the original general implementation of advanced decomposition techniques. The important application problem of the optimal incinerator design has been originally reduced and modelled by aforementioned stochastic programming approach and then solved by using the original implementation of the L-shaped method. The thoughtful use of AIMMS visualization possibilities will help with advantageous intepretation of results for practice. The resulting text is written in a compact and straightforward way starting from the preface to the conclusions. So, instead of flooding thesis by many formal paragraphs on complicated theme of decomposition, the author focused on readability of thesis, utilized many convenient references, and hence, successfully balanced between requirements on precision and clarity. However, as the supervisor, I still have to emphasize that quite a lot of realised work remains hidden for interested reader cf. more than one hundred pages of the source codes in appendices and reduced theoretical overview and application related details. For the uninformed reader, I would like to emphasize that the author has successfully utilized his experience from his one year study of mathematics abroad in Italy. The author has worked systematically and independently, consulting only the key ideas with his supervisor. Author's English is enjoyable for reading and only a few misprints remain after several correcting stages. The text is well organized and formatted. It is also suitably divided in parts by the following chapters. Chapter 1 introduces basic concepts and gradually leads to the description of scenario-based two-stage stochastic linear programs (SBTSLP). The author already shows his understanding to the topic, e.g., by making a useful difference between optimization programmes and software programs. Literature references are correctly placed, the author successfully combines several resources for the theoretical overview. The introduction of complicated topics in Sections from 1.3 to 1.7 is precise and readable. Especially, advanced topics as L-shaped method, progressive hedging algorithm, and sample average approximation are introduced without extra formalism or numerical examples and details but still precisely and clearly. Chapter 2 introduces the AIMMS software in the way of a short crash course for the beginner. Future readers interested in optimization tools may appreciate a short remark on program licences and useful comments on GAMS and Excel interfaces. The chapter ends with insightful comments on GMP possibilities. Chapter 3 describes author's original results related to the SBTSLP user interface in AIMMS and coding of studied decomposition and sampling techniques in the related programming language. Details on L-shaped algorithm implementation are presented and whole code is tested by instance of the modified farmer's example (see Birge-Louveaux book). The results of the initial computational study on limits of usability of author's implementation are discussed and illustrated by graphs. Chapter 4 shows the applicability of the previous chapters. The problem of incinerator optimal design has been consulted by the author with specialists from Institute of Process and Environmental Engineering who supported him with real-world data. As the promising theme for the future research, it has also been included in the application of the Czech-Norwegian project. The author originally modified the modelling idea developed with his supervisor (see also MATLAB results). So, he shows how the studied complex strategical decision making problem can be approximated by the significantly reduced, and so, visually tractable SBTSLP model that can help engineers (cf. usefulness of the known pinch approach in process engineering). In addition, the author's AIMMS code can be used for explanatory graphs, cost forecasts, and decomposed computations for enlarged models without approximations. So, I recommend the proposed thesis for defence in front of the committee.

Posudek oponenta

Mrázková, Eva

Diplomová práce se zabývá řešením úloh stochastické optimalizace v programu AIMMS. Jsou zde uvedeny základní poznatky především z teorie stochastického programování se zaměřením na dvoustupňovou lineární úlohu. Tato teoretická část zahrnuje i popis několika metod, které jsou vhodné pro řešení optimalizačních úloh s neurčitostí a které autor implementoval do programu AIMMS. Následuje přehledná kapitola o vlastnostech optimalizačního programu AIMMS. Těžiště práce leží v praktické implementaci obecné dvoustupňové lineární úlohy stochastického programování, pro níž autor vytvořil grafické rozhraní, které umožňuje uživateli snadno formulovat a řešit jakoukoli úlohu tohoto typu. Využití tohoto rozhraní je ukázáno na klasické farmářově úloze. Autorův program umožňuje provést také citlivostní analýzu vzhledem k parametrům náhodného rozdělení. K řešení této obecné úlohy je využita metoda již obsažená v programu AIMMS. Navíc se ale autor rozhodl samostatně naprogramovat několik dalších metod řešení včetně Bendersovy dekompozice a to mu umožnilo provést zajímavé srovnání různých metod řešení. Poslední kapitola práce ukazuje, že výše zmíněná obecná úloha neslouží jen k teoretickému zkoumání „školních“ úloh, ale že ji lze využít i pro řešení optimalizačních úloh z reálného života (zde je to úloha týkající se spalovny). Z formálního hlediska je důležité zmínit kvalitní sazbu práce v prostředí LaTeX. V práci se vyskytuje jen poměrně malé množství překlepů. Autor v předložené práci splnil požadavky zadání. Celkově považuji práci za velmi kvalitní, hodnotím ji stupněm A a doporučuji k obhajobě.

eVSKP id 68776