Thesis (MComm)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In a ground-based air defense (GBAD) military environment, defended assets on the ground require protection from enemy aircraft entering the defended airspace. These aircraft are detected by means of a network of sensors and protection is afforded by means of a pre-deployment of various ground-based weapon systems. A fire control officer is responsible for deciding upon an assignment of weapon systems to those aircraft classified as threats. The problem is therefore to find the best set of weapon systems to assign to the threats, based on some pre-specified criterion or set of criteria. This problem is known as the weapon assignment problem. The conditions under which the fire control officer has to operate are typically extremely stressful. A lack of time is a severely constraining factor, and the fire control officer has to propose an assignment of weapon systems to threats based on his limited knowledge and intuition, with little time for analysis and no room for error. To aid the fire control officer in this difficult decision, a computerised threat evaluation and weapon assignment (TEWA) decision support system is typically employed. In such a decision support system a threat evaluation subsystem is responsible for classifying aircraft in the defended airspace as threats and prioritising them with respect to elimination, whereas a weapon assignment subsystem is responsible for proposing weapon assignments to engage these threats. The aim in this thesis is to model the weapon assignment problem as a multiobjective decision problem. A list of relevant objectives is extracted by means of feedback received from a weapon assignment questionnaire which was completed by a number of military experts. By using two of these objectives, namely the cost of assigning weapon systems and the accumulated single shot hit probability, for illustrative purposes, a bi-objective weapon assignment model is derived and solved by means of three multiobjective optimisation methodologies from the literature in the context of a simulated, but realistic, GBAD scenario. The analytic hierarchy process (AHP) is implemented by means of assessments carried out in conjunction with a military expert. The assignment of weapon systems to threats is achieved by means of a greedy assignment heuristic and an AHP assignment model. Both these methods provide plausible results in the form of high quality assignments achieving an acceptable tradeoff between the two decision objectives. However, a disadvantage of the AHP approach is that it is inflexible in the sense that a large portion of its pre-assessments have to be reiterated if the set of weapon systems and/or threats is adapted or updated. A bi-objective additive utility function solution approach to the weapon assignment problem is also developed as a result of various assessments having been carried out in conjunction with a military expert. The assignment of weapon systems to threats is again achieved by means of a greedy assignment heuristic and a utility assignment model. Both these methods again provide high quality assignments of weapon systems to threats, achieving an acceptable trade-off between the two decision objectives. However, a disadvantage of the utility function approach is that if additional weapon systems are added to the current set of weapon systems, which achieve objective function values outside the current ranges of the values employed, new utility functions have to be determined for the relevant objective function. Moreover, both the AHP and utility function approaches are also constrained by generating only one solution at a time. A final solution approach considered is the implementation of a multiobjective evolutionary metaheuristic, known as the Nondominated Sorting Genetic Algorithm II (NSGA II). This approach provides very promising results with respect to high quality assignments of weapon systems to threats. It is also flexible in the sense that additional weapon systems and threats may be added to the current sets without the need of considerable additional computations or significant model changes. A further advantage of this approach is that it is able to provide an entire front of approximately pareto optimal solutions to the fire control officer. / AFRIKAANSE OPSOMMING: In ’n militêre grond-gebaseerde lugafweeromgewing vereis bates op die grond beskerming teen vyandelike vliegtuie wat die beskermde lugruim binnedring. Hierdie vliegtuie word deur middel van ’n netwerk van sensors waargeneem en deur middel van ’n ontplooing van ’n verskeidenheid grond-gebaseerde wapenstelsels afgeweer. ’n Afvuur-beheer operateur is verantwoordelik vir die besluit om wapenstelsels aan vliegtuie wat as bedreigings geklassifiseer is, toe te wys. Die onderliggende probleem is dus om die beste stel wapens, volgens ’n voorafbepaalde kriterium of ’n stel kriteria, aan die bedreigings toe te wys. Hierdie probleem staan as die wapentoewysingsprobleem bekend. Die toestande waaronder die afvuur-beheer operateur besluite ten opsigte van wapentoewysings maak, is besonder stresvol. ’n Gebrek aan tyd is ’n uiters beperkende faktor, en die afvuurbeheer operateur moet gevolglik binne ’n tydspan wat weinige analise en geen ruimte vir foute toelaat, wapentoewysings volgens sy beperkte kennis en intuïsie maak. ’n Gerekenariseerde bedreigingsafskatting-en-wapentoekenningstelsel kan gebruik word om die operateur met besluitsteun te bedien. In sò ’n besluitsteunstelsel is ’n bedreigingsafskattingdeelstelsel verantwoordelik om vliegtuie wat die beskermde lugruim binnedring as bedreigings of andersins te klassifiseer en ten opsigte van eliminasie te prioritiseer, terwyl ’n wapentoewyingsdeelstelsel verantwoordelik is om wapentoewysings aan die bedreigings voor te stel. Die hoofdoel in hierdie tesis is om die wapentoewysingsprobleem as ’n multikriteria-besluitnemingsprobleem te modelleer. ’n Lys van relevante doelwitte is met behulp van ’n wapentoewysingsvraelys verkry wat aan militêre kenners vir voltooing uitgestuur is. Twee van hierdie doelwitte, naamlik toewysingskoste en geakkumuleerde enkelskoot-trefwaarskynlikheid, is vir illustratiewe doeleindes gebruik om ’n twee-doelwit wapentoewysingsprobleem te formuleer wat met behulp van drie multikriteria-besluitnemingsmetodologië uit die literatuur in die konteks van ’n realistiese, gesimuleerde grond-gebaseerde lugafweerscenario opgelos word. Die analitiese hiërargiese proses (AHP) is met behulp van assesserings in samewerking met ’n militêre kenner geïmplementeer. Die toewysing van wapenstelsels is met behulp van ’n gulsige toewysingsheuristiek asook aan die hand van ’n AHP-toewysingsmodel bepaal. Beide hierdie metodes is in staat om resultate van hoë gehalte te behaal wat ’n aanvaarbare afruiling tussen die twee doelwitte verteenwoordig. ’n Nadeel van die AHP is egter dat dit onbuigsaam is in die sin dat ’n groot hoeveelheid vooraf-assesserings herhaal moet word indien meer wapenstelsels en/of bedreigings by die huidige sisteem gevoeg word. ’n Twee-doelwit additiewe nutsfunksiebenadering tot die wapentoewysingsprobleem is ook met behulp van velerlei assesserings in samewerking met ’n militêre kenner ontwikkel. Die toewysings is weereens met behulp van ’n gulsige wapentoewysingsheuristiek asook ’n nutstoewysingsmodel bepaal. Beide hierdie metodes is ook in staat om resultate van hoë gehalte te behaal wat ’n aanvaarbare afruiling tussen die twee doelwitte verteenwoordig. ’n Nadeel van die nutsfunksiebenadering is egter dat indien addisionele wapenstelsels by die huidige stel wapenstelsels gevoeg word, en indien die waardes van hierdie addisionele wapenstelsels buite die grense van die doelfunksiewaardes van die huidige wapenstelsels val, daar ’n nuwe nutsfunksie vir die relevante doelwit van voor af bereken moet word. Beide die AHP- en die nutsfunksiebenaderings is verder tot die lewering van slegs een oplossing op ’n slag beperk. Laastens is ’n multikriteria evolusionêre metaheuristiek (die NSGA II) geïmplementeer wat ook goeie resultate in terme van hoë-gehalte toewysings van wapenstelsels aan bedreigings lewer. Die voordeel van hierdie benadering is dat dit buigsaam is in die sin dat die getal wapenstelsels en bedreigings in die huidige sisteem aangepas kan word sonder om noemenswaardig meer berekeninge of groot modelveranderinge teweeg te bring. ’n Verdere voordeel is dat die metaheuristiese benadering daartoe in staat is om ’n front van benaderde pareto-optimale oplossings gelyktydig te lewer.