Militaarsete rännakukolonnide marsruutimise optimeerimine
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2017
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Motoriseeritud rännakukolonnide optimeerimine on matemaatilise optimeerimise probleem, milles püütakse leida optimaalset marsruutimislahendust ja vastavat ajakava samaaegsetelt liikuvatele rännakukolonnidele. Käesolevas töös luuakse valik erinevatel optimeerimistehnikatel põhinevaid meetodeid, mida testides püütakse leida parimat Eesti oludele vastavat rännakukolonnide marsruutimise optimeerimismeetodit. Häid tulemusi saavutati kasutades osalise täisarvulise planeerimise mudelit koos heuristiliste täiendustega, rakendades jaga-ja-piira tehnikal põhinevat täpset algoritmi, kui ka kasutades fikseeritud järjestusega marsruutimislahendust. Lisaks töötati bakalaureusetöö koostamise käigus välja optimeerimismeetodeid kasutav rakendus, mille abil on võimalik võrrelda erinevate meetodite käitumist ja omadusi, esitada arvutuste tulemusena leitud teekondi ja ajagraafikuid ning animeerida Eesti kaardil rännakukolonnide liikumist. Töö tulemusena võib väita, et matemaatilise optimeerimise meetodid on sobivad päriseluliste rännakukolonnide optimeerimisprobleemide kiireks ja kvaliteetseks lahendamiseks ja et neid meetodeid kasutades on võimalik parandada rännakukolonnide kavandamisel tehtavate planeerimisotsuste kvaliteeti.
Convoy movement problem is a mathematical optimization problem which tries to find optimal routing and scheduling solution for concurrent military convoy movements. In this thesis several optimization methodologies are designed and tested to find best suited algorithm for solving practical convoy routing instances in Estonia. Encouraging results are obtained by using a mixed integer programming model together with simple heuristics, by creating an exact branch-and-bound methodology and by developing fixed-order based routing approach. Bachelor’s thesis also provides a complementary application to compare qualities of designed methods, to present calculated routes and schedules and to display convoy movement animations on the map of Estonia. Thesis illustrates that methods of mathematical optimization can be used to solve realworld instances of convoy movement problem fast and with quality results and hence improve decisionmaking in operational convoy planning practice.
Convoy movement problem is a mathematical optimization problem which tries to find optimal routing and scheduling solution for concurrent military convoy movements. In this thesis several optimization methodologies are designed and tested to find best suited algorithm for solving practical convoy routing instances in Estonia. Encouraging results are obtained by using a mixed integer programming model together with simple heuristics, by creating an exact branch-and-bound methodology and by developing fixed-order based routing approach. Bachelor’s thesis also provides a complementary application to compare qualities of designed methods, to present calculated routes and schedules and to display convoy movement animations on the map of Estonia. Thesis illustrates that methods of mathematical optimization can be used to solve realworld instances of convoy movement problem fast and with quality results and hence improve decisionmaking in operational convoy planning practice.