Evolutionary learning and global search for multi-optimal PID tuning rules

With the advances in microprocessor technology, control systems are widely seen not only in industry but now also in household appliances and consumer electronics. Among all control schemes developed so far, Proportional plus Integral plus Derivative (PID) control is the most widely adopted in practice. Today, more than 90% of industrial controllers have a built-in PID function. Their wide applications have stimulated and sustained the research and development of PID tuning techniques, patents, software packages and hardware modules. Due to parameter interaction and format variation, tuning a PID controller is not as straightforward as one would have anticipated. Therefore, designing speedy tuning rules should greatly reduce the burden on new installation and ‘time-to-market’ and should also enhance the competitive advantages of the PID system under offer. A multi-objective evolutionary algorithm (MOEA) would be an ideal candidate to conduct the learning and search for multi-objective PID tuning rules. A simple to implement MOEA, termed s-MOEA, is devised and compared with MOEAs developed elsewhere. Extensive study and analysis are performed on metrics for evaluating MOEA performance, so as to help with this comparison and development. As a result, a novel visualisation technique, termed “Distance and Distribution” (DD)” chart, is developed to overcome some of the limitations of existing metrics and visualisation techniques. The DD chart allows a user to view the comparison of multiple sets of high order non-dominated solutions in a two-dimensional space. The capability of DD chart is shown in the comparison process and it is shown to be a useful tool for gathering more in-depth information of an MOEA which is not possible in existing empirical studies. Truly multi-objective global PID tuning rules are then evolved as a result of interfacing the s-MOEA with closed-loop simulations under practical constraints. It takes into account multiple, and often conflicting, objectives such as steady-state accuracy and transient responsiveness against stability and overshoots, as well as tracking performance against load disturbance rejection. These evolved rules are compared against other tuning rules both offline on a set of well-recognised PID benchmark test systems and online on three laboratory systems of different dynamics and transport delays. The results show that the rules significantly outperform all existing tuning rules, with multi-criterion optimality. This is made possible as the evolved rules can cover a delay to time constant ratio from zero to infinity based on first-order plus delay plant models. For second-order plus delay plant models, they can also cover all possible dynamics found in practice

Ablaufplanung bei Reihenfertigung mit mehrfacher Zielsetzung auf der Basis von Ameisenalgorithmen

In der Arbeit wird ein Permutation Flow Shop Problem mit mehrfacher Zielsetzung betrachtet. Das Problem der Reihenfolgeplanung von Aufträgen in einem Produktionssystem hat seit der Veröffentlichung des Johnson Algorithmus 1954 wesentliche Aufmerksamkeit erlangt. Dabei wurden hauptsächlich Probleme mit nur einer Zielsetzung betrachtet. In der Praxis hat sich die Reihenfolgeplanung in der Regel jedoch an mehreren Zielgrößen zu orientieren. Neben der Maximierung der Kapazitätsauslastung können z.B. auch die Minimierung der Durchlaufzeiten sowie das Einhalten von vorgegebenen Fertigstellungsterminen weitere zu berücksichtigende Ziele sein. In der vorliegenden Arbeit wird ein Zielsystem bestehend aus den Zielgrößen mittlere Durchlaufzeit, maximale Terminüberschreitung sowie der Zykluszeit betrachtet. Alle drei Zielgrößen sind zu minimieren. Es werden zwei Ameisenalgorithmen zur Ermittlung heuristisch effizienter Mengen von Auftragsfolgen vorgestellt und experimentell untersucht. Die Menge der heuristisch effizienten Auftragsfolgen ergibt sich dabei aus den von der Heuristik ermittelten heuristisch effizienten Auftragsfolgen. Bezogen auf eine Heuristik ist eine Auftragsfolge dann heuristisch effizient, wenn es keine andere von der Heuristik erzeugte und auf Effizienz überprüfte Auftragsfolge gibt, die bezüglich aller Ziele keinen schlechteren und bei mindestens einem Ziel einen besseren Zielerreichungsgrad aufweist. Daneben wird die Beurteilung der Qualität von heuristisch effizienten Mengen ausführlich betrachtet. Die bisher in der Literatur vorgestellten Maße werden kritisch diskutiert und anschließend ein System von Maßen zur Beurteilung der Qualität heuristisch effizienter Mengen entwickelt. Außerdem werden in der Arbeit allgemeine Überlegungen zur Steuerung der Suche nach Elementen der effizienten Menge angestellt. Dazu gehören Analysen zur Distanz von Auftragsfolgen im Lösungsraum, sowie die Entwicklung von Konzepten zur Definition der Nachbarschaft im Zielraum

Bus route design and frequency setting for public transit systems

Thesis (PhD)--Stellenbosch University, 2022.ENGLISH ABSTRACT: The availability of effective public transport systems is increasingly becoming an urgent problem in urban areas worldwide due to the traffic congestion caused by private vehicles. The careful design of such a transport system is important because, if well designed, such a system can increase the comfort of commuters and ensure that they arrive at their destinations timeously. A well-designed public transport system can also result in considerable cost savings for the operator of the system. The problem considered in this dissertation is that of designing three mathematical models for aiding a bus company in deciding upon efficient bus transit routes (facilitated by the first two models) and setting appropriate frequencies for buses along these routes (facilitated by the third model). The design criteria embedded in the first model (for designing bus routes) are the simultaneous pursuit of minimising the expected average passenger travel time and minimising the system operator’s cost (measuring the latter as the sum total of all route lengths in the system). The first model takes as input an origin-destination demand matrix for a specified set of bus stops, along with the corresponding road network structure, and returns as output a set of bus route solutions. The decision maker can then select one of these route sets subjectively, based on the desired trade-off achieved between the aforementioned transit system design criteria. This bi-objective minimisation problem is solved approximately in three distinct stages — a solution initialisation stage, an intermediate analysis stage and an iterative metaheuristic search stage during which high-quality trade-off solutions are sought. A novel procedure is introduced for the solution initialisation stage aimed at effectively generating high-quality initial feasible solutions. Two metaheuristics are adopted for the solution implementation, namely a dominance-based multi-objective simulated annealing algorithm and an improved non-dominated sorting genetic algorithm. The second model is a novel approach towards establishing high-quality bus routes resembling a reference set of bus routes (typically the currently operational bus routes) to varying degrees, providing the decision maker with bus route design alternatives that may be implemented incre mentally in order to limit the disruption experienced by passengers in the bus transit network. The objectives pursued in this model are the simultaneous minimisation of the expected aver age passenger travel time and the minimisation of a reference-route-to-design-route similarity measure. The second model takes the same input as the first model above, with the addition of a reference route set with which to compare alternative design routes in terms of similarity, and provides as output a set of trade-off solutions according to this model’s design criteria. The same three-stage approximate solution methodology described above is adopted for this model, and the same two metaheuristic implementations are utilised to solve instances of this new model. In the third model, high-quality bus frequencies are sought for each bus route in pursuit of min imising the expected average travel time for passengers (including waiting time, transfer time and travel time) and simultaneously minimising the total number of buses required by an operator to maintain the specified frequencies. The third model takes as input all the data required by the first model, along with a route set for which frequencies should be set, and returns as output a set of bus frequencies at which buses should operate along the various routes, based on a de sired trade-off between the aforementioned two design criteria. The solution approach adopted for this bi-objective minimisation problem again conforms to the three aforementioned distinct stages, with the exception that only a non-dominated sorting genetic algorithm is designed for solving it. The first and third models are finally applied to a special case study involving real data in order to showcase the practical applicability of the modelling approach.AFRIKAANSE OPSOMMING: Die beskikbaarheid van doeltreffende openbare vervoerstelsels word wˆereldwyd toenemend ’n dringende probleem in stedelike gebiede as gevolg van die verkeersopeenhopings wat deur private voertuie veroorsaak word. Die noukeurige ontwerp van so ’n vervoerstelsel is belangrik, want as dit goed ontwerp is, kan so ’n stelsel die gemak van pendelaars verhoog en verseker dat hul betyds by hul bestemmings aankom. ’n Goed-ontwerpte openbare vervoerstelsel kan ook aansienlike kostebesparings vir die stelseloperateur tot gevolg hˆe. Die probleem wat in hierdie proefskrif oorweeg word, is die ontwerp van drie wiskundige modelle om ’n busonderneming daartoe in staat te stel om besluite oor doeltreffende busvervoerroetes (die eerste twee modelle) en die geskikte frekwensies vir busse langs hierdie roetes (die derde model) te neem. Die ontwerpkriteria in die eerste model (vir die ontwerp van busroetes) is die gelyktydige strewe daarna om die verwagte gemiddelde reistyd van passasiers te minimeer en die koste van die stelseloperateur te minimeer (laasgenoemde gemeet as die somtotaal van alle roetelengtes in die stelsel). Die eerste model neem as toevoer ’n oorsprong-bestemming aan vraagmatriks vir ’n spesifieke stel bushaltes, tesame met die ooreenstemmende padnetwerkstruk tuur, en lewer as afvoer ’n versameling busroetestelle. Die besluitnemer kan dan een van hierdie roetestelle subjektief kies, gebaseer op die gewenste afruiling tussen die bogenoemde ontwerpkri teria. Hierdie twee-doelige minimeringsprobleem word in drie verskillende fases benaderd opgelos — ’n oplossingsinisialiseringsfase, ’n intermediˆere analise-fase en ’n iteratiewe metaheuristiese soekfase waartydens afruilingssoplossings van ho¨e gehalte gesoek word. ’n Nuwe prosedure word vir die oplossingsinisialiseringsfase daargestel wat daarop gemik is om aanvanklike haalbare oplossings van ho¨e gehalte op ’n doeltreffende wyse te genereer. Twee meteheuristieke word vir die oplossing van die model gebruik, naamlik ’n dominansie-gebaseerde meer-doelige ge simuleerde temeperingsalgoritme en ’n verbeterde nie-gedomineerde sorteer-genetiese algoritme. Die tweede model is ’n nuwe benadering om busroetes van ho¨e gehalte te vestig wat in verskil lende mates ooreenkomste met ’n verwysingstel busroetes (tipies die huidige stel operasionele roetes) toon, en bied die besluitnemer alternatiewe vir busroetes wat geleidelik ge¨ımplementeer kan word om die ontwrigting van passasiers in die busvervoernetwerk te beperk. Die doele wat in hierdie model nagestreef word, is die gelyktydige minimering van die verwagte gemiddelde passas ier se reistyd en die minimering van ’n verwysingsroete-na-ontwerp-roete ooreenkomsmaatstaf. Die tweede model neem dieselfde toevoere as die eerste model hierbo, met die byvoeging van ’n verwysingsroete waarmee alternatiewe ontwerproetestelle in terme van ooreenkoms vergelyk kan word, en bied as afvoer ’n stel afruilingsoplossings volgens die model se ontwerpkriteria. Die selfde drie-fase benaderde oplos-singsmetode hierbo beskryf, word op hierdie model toegepas, en dieselfde twee metaheuristiese implementerings word gebruik om gevalle van hierdie nuwe model op te los. In die derde model word busfrekwensies van ho¨e gehalte vir elke busroete gesoek om die verwagte gemiddelde reistyd van passasiers (insluitend wagtyd, oorklimtyd en werklike reistyd) te minimeer en terselfdertyd die totale aantal busse wat ’n operateur benodig, te minimeer terwyl die gespesifiseerde frekwensies gehandhaaf word. Die derde model neem dieselfde toevoerdata as die eerste model, tesame met ’n roete waarvoor frekwensies vasgestel moet word, en lewer as afvoer ’n stel busfrekwensies waarteen busse langs die verskillende roetes ontplooi moet word, gebaseer op ’n gewenste afruiling tussen die bogenoemde twee ontwerpkriteria. Die oplossingsbenadering wat op hierdie tweedoelige minimeringsprobleem toegepas word, volg weer die bogenoemde drie fases, met die uitsondering dat slegs ’n nie-gedomineerde sorteer-genetiese algoritme ontwerp word om dit op te los. Die eerste en derde modelle word uiteindelik op ’n spesiale gevallestudie toegepas wat op werklike data gebaseer is om sodoende die praktiese toepaslikheid van die modelleringsbenadering te illustreer.Doctora

Minimal Sets of Quality Metrics

Abstract. Numerous quality assessment metrics have been developed by researchers to compare the performance of different multi-objective evolutionary algorithms. These metrics show different properties and address various aspects of solution set quality. In this paper, we propose a conceptual framework for selection of a handful of these metrics such that all desired aspects of quality are addressed with minimum or no redundancy. Indeed, we prove that such sets of metrics, referred to as ‘minimal sets’, must be constructed based on a one-to-one correspondence with those aspects of quality that are desirable to a decision-maker.