Quantum-Driven Optimisation in Agent-Based Transport Models: Early Lessons from Applying QUBO to Freight Logistics

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE Quan um-D i en Op imisa ion in Agen -Based T anspo Models: Ea ly Lessons om Applying QUBO o F eigh Logis ics Si i Fa iya School o Social Sciences He io -Wa Uni e si y Edinbu gh, Uni ed Kingdom [email p o ec ed] Dhanan Sa wo U omo School o Social Sciences He io -Wa Uni e si y Edinbu gh, Uni ed Kingdom [email p o ec ed] Abs ac — This pape p esen s a concep ual amewo k o in eg a ing quan um-d i en op imisa ion in o agen -based anspo models (ABMs) o add ess conges ion managemen challenges in eigh logis ics. Focusing on a busy oll-on/ oll-o (Ro-Ro) ga eway in Sou heas England, we o mula e he a ic low op imisa ion p oblem as a MaxCu Quad a ic Uncons ained Bina y Op imisa ion (QUBO) p oblem. Using ORCA Compu ing’s PT-Se ies pho onic quan um ha dwa e, we apply quan um sol e s o p edic conges ion s a es ac oss c i ical po zones. These QUBO ou pu s a e hen embedded in o an ABM o dynamically adjus ehicle ou ing and zone capaci ies, c ea ing a hyb id quan um-classical wo k low. We sha e ea ly lessons om his in eg a ion, including insigh s in o p oblem o mula ion, sol e in e p e a ion, and sys em coupling. This wo k p o ides ounda ional unde s anding and p ac ical guidance o applying quan um-inspi ed me hods o eal-wo ld anspo sys ems and ou lines u u e di ec ions owa d scalable, eal- ime hyb id logis ics op imisa ion. Keywo ds— Quan um op imisa ion, QUBO, MaxCu , agen - based modelling, eigh logis ics, a ic low, quan um-classical in eg a ion, conges ion managemen , pho onic quan um compu ing, hyb id wo k lows I. INTRODUCTION The eigh logis ics sec o is unde inc easing p essu e o imp o e ope a ional e iciency, minimise conges ion, and mee ambi ious deca bonisa ion a ge s. Roll-on/ oll-o (RoRo) e minals in Sou heas England play a pi o al ole in UK-EU ade, handling as lows o ucks, passenge ehicles, and e ies. Howe e , hei ope a ions a e highly sensi i e o dis up ions, pa icula ly du ing peak pe iods when demand su ges and in as uc u e cons ain s collide. T adi ional app oaches o op imising po and e minal ope a ions, such as heu is ics, me aheu is ics, and ule-based me hods, ha e p o ided aluable insigh s bu ace limi a ions when con on ed wi h he complex, dynamic, and high- dimensional na u e o eal-wo ld anspo sys ems. This has led o ising in e es in ad anced compu a ional pa adigms ha can add ess hese challenges mo e e ec i ely. Among hese, quan um op imisa ion, speci ically h ough Quad a ic Uncons ained Bina y Op imisa ion (QUBO) o mula ions, has appea ed as a p omising ool. By ansla ing complex decision p oblems in o a ma hema ical o ma ha can be p ocessed by quan um ha dwa e, QUBO-based app oaches open new possibili ies o ackling combina o ial and dynamic p oblems ha ha e adi ionally been challenging. Building on insigh s om he Quan um Technology Access P og amme (QTAP) Digi al Ca apul in Uni ed Kingdom, a 6-mon h inno a ion p og amme gi ing inno a o and companies hands-on access o quan um ha dwa e, simula o s, and expe suppo o explo e eal-wo ld use cases and assess he po en ial o quan um echnologies. This pape ocuses on in eg a ing QUBO op imisa ion ou pu s in o an agen -based anspo model (ABM), esul ing in a hyb id quan um-classical wo k low ailo ed o Ro-Ro e minal ope a ions in Sou heas England. We apply QUBO-d i en ehicle alloca ion s a egies o educe conges ion and imp o e h oughpu . Ou con ibu ions: 1. We demons a e he p ac ical se in o QUBO-based quan um op imisa ion wi hin de ailed ABMs o eigh logis ics. 2. We p o ide ea ly insigh s in o scalabili y, model ansla ion, and eal- ime in eg a ion challenges aced by hyb id wo k lows. This wo k o e s ounda ional lessons o deploying quan um op imisa ion in eal-wo ld anspo sys ems, placing he g oundwo k o u u e ad ancemen s in quan um-assis ed logis ics planning. II. LITERATURE REVIEW The e olu ion o global supply chains and he ise o con aine isa ion ha e signi ican ly inc eased he ope a ional demands on po s and e minals [1]. In esponse, he ield o ope a ions esea ch has de eloped a wide ange o op imisa ion echniques, pa icula ly o con aine e minals and RoRo ope a ions, including heu is ic and me aheu is ic app oaches [2]. While hese me hods ha e yielded no able imp o emen s, hey o en all sho when add essing he in ica e, s ochas ic, and la ge-scale na u e o mode n anspo sys ems, especially unde peak demand condi ions. In ecen yea s, he e has been g owing a en ion o quan um op imisa ion, which o e s a undamen ally di e en compu a ional pa adigm. The QUBO o mula ion has become cen al, enabling he mapping o many NP-ha d op imisa ion p oblems on o quan um ha dwa e [3]. Sol ing NP-ha d p oblems wi h adi ional op imisa ion me hods is o en compu a ionally in ensi e, as he solu ion space g ows exponen ially wi h p oblem size. This leads o long compu a ion imes o he need o heu is ic app oaches, which may only deli e app oxima e solu ions. Ea ly s udies ha e shown p omising applica ions in logis ics and anspo con ex s. Fo example, Neuka e al. [4] applied quan um 2 anneale s o op imise a ic low, highligh ing po en ial ad an ages o e classical app oaches. Ajageka e al. [5] de eloped hyb id quan um-classical app oaches o la ge- scale disc e e–con inuous p oblems in chemical enginee ing, demons a ing he e sa ili y o quan um me hods ac oss domains. Ven u elli e al. [6] explo ed spin-glass models using quan um op imisa ion, p o iding aluable insigh s in o algo i hmic scalabili y and pe o mance on complex combina o ial p oblems. Using he QUBO o mula ion, quan um app oaches can explo e la ge solu ion spaces in pa allel and escape local minima mo e e ec i ely, o e ing po en ial ad an ages o e classical me hods o ackling NP- ha d p oblems. Despi e hese ad ances, li le esea ch has explo ed how quan um op imisa ion can be meaning ully embedded wi hin simula ion amewo ks such as agen -based models (ABMs). ABMs a e powe ul ools o simula ing he beha iou s o he e ogeneous agen s, such as ehicles, ope a o s, and in as uc u e and o cap u ing eme gen sys em-le el dynamics. In eg a ing QUBO-op imised decisions in o ABMs o e s po en ial o eal- ime, adap i e logis ics managemen , ye his in e sec ion emains la gely unexplo ed. To add ess his gap, he p esen s udy p oposes a concep ual and compu a ional amewo k o embedding QUBO-based op imisa ion wi hin an agen -based anspo model o RoRo e minal ope a ions. In doing so, i con ibu es o he eme ging ield o hyb id quan um-classical wo k lows o eigh logis ics, o e ing p ac ical insigh s o esea che s and p ac i ione s aiming o apply quan um echnologies in anspo sys ems. III. METHODOLOGY This wo k p esen s a concep ual amewo k o in eg a ing quan um-d i en op imisa ion in o anspo ABMs o explo e conges ion managemen s a egies in eigh logis ics. The app oach combines a QUBO o mula ion o he a ic low p oblem, quan um sol e execu ion, and in eg a ion o sol e ou pu s in o an agen - based simula ion. A. G aph-Based Sys em Rep esen a ion We ep esen he Ro-Ro e minal as a g aph, whe e nodes co espond o key ope a ional zones (e.g., bu e a ea, UK bo de con ol, andom checks, check-in poin s, eigh queue, ou is queue) and edges ep esen he di ec connec ions be ween zones. This g aph s uc u e cap u es he spa ial and unc ional ela ionships be ween sys em componen s and se es as he basis o de ining conges ion in e ac ions. Figu e 1. G aph ep esen a ion o he Ro-Ro e minal sys em. In Figu e 1. nodes ep esen key ope a ional zones, and edges ep esen physical o ope a ional connec ions be ween hem. This g aph o ms he basis o de ining he QUBO conges ion minimisa ion p oblem. B. QUBO Fo mula ion The objec i e is o minimise conges ion and imp o e h oughpu ac oss key po zones, including bu e a eas, inspec ion poin s, and check-in ga es. We de ine bina y decision a iables xi o each zone i, whe e xi=1 indica es conges ion and xi = 0 indica es smoo h low. The QUBO objec i e unc ion seeks o pa i ion he g aph o minimise conges ion p opaga ion, wi h he gene al o m: min ∑₍ᵢ,ⱼ₎∈𝐸 𝑤ᵢⱼ 𝑥ᵢ𝑥ⱼ + ∑ᵢ 𝑏ᵢ𝑥ᵢ, (1) Whe e xᵢ is a bina y decision a iable (1 i node i is p edic ed conges ed, 0 o he wise), wᵢⱼ is he in e ac ion weigh be ween connec ed nodes i and j, and bᵢ is he node-speci ic bias o penal y e m. We implemen ed he QUBO o mula ion in Py hon, using lib a ies such as ne wo kx and numpy o build he adjacency ma ix and de ine in e ac ion e ms. C. Quan um Sol e Execu ion We p epa ed The QUBO p oblem was submi ed o ORCA Compu ing’s PT-Se ies pho onic quan um ha dwa e, using hei Bina y Bosonic Sol e . The PT-Se ies is a ype o quan um compu e ha uses pho ons (pa icles o ligh ) o compu a ion; i ’s ORCA Compu ing’s b anded pla o m designed o ackle op imisa ion and machine lea ning p oblems. The Bina y Bosonic Sol e (BBS) is an algo i hm de eloped by ORCA Compu ing o sol e bina y op imisa ion p oblems, especially hose o mula ed as QUBO (Quad a ic Uncons ained Bina y Op imisa ion) p oblems, using hei pho onic quan um ha dwa e. The sol e e u ns bina y solu ions ep esen ing p edic ed conges ion pa e ns ac oss he e minal ne wo k. To add ess a iabili y inhe en in cu en nea - e m quan um de ices, mul iple sol e uns we e pe o med, and he solu ion landscape was analysed ac oss di e en con igu a ions. Figu e 2 shows he con e gence beha iou o ou sol e con igu a ions (con ig1 - con ig4) o e 80 upda es. The y-axis ep esen s he objec i e unc ion alue, while he x-axis shows he upda e s eps. Figu e 2. Objec i e unc ion e olu ion ac oss quan um sol e con igu a ions. This illus a es a iabili y be ween uns and highligh s he impo ance o mul i- un analysis o iden i y s able, high- quali y solu ions. 3 D. Pos p ocessing Following quan um sol e execu ion, a pos p ocessing phase ansla es he bina y ou pu ec o in o ac ionable sys em pa ame e s o he anspo ABMs. This in ol es mapping bina y a iables (e.g., conges ion/no-conges ion pe zone) in o ou ing p io i ies, lane capaci ies, o ope a ional adjus men s. The agen -based model (ABM) simula es indi idual agen s, such as eigh ehicles, passenge ca s, and con ol in as uc u e, each wi h de ined objec i es, o example, minimising a el ime, ollowing op imal ou es, o managing a ic low. This s ep is essen ial o b idge he quan um solu ion laye wi h he mic o-le el ABM en i onmen , ensu ing ha agen s ope a e wi hin ealis ic, in e p e able sys em s a es. E. Agen -Based Model In eg a ion The ABMs simula es he de ailed, mic o-le el beha iou s o indi idual ehicle agen s, including eigh ucks, passenge ca s, and e ies, ope a ing wi hin he Ro-Ro e minal sys em. The ABM cap u es how agen s make decisions abou lane choice, queueing, and p ocessing a checkpoin s, while in e ac ing dynamically wi h bo h he physical in as uc u e and o he agen s. Figu e 3. Concep ual wo k low o in eg a ing QUBO-based quan um op imisa ion in o an agen -based anspo model. The in eg a ion o he QUBO-de i ed conges ion ou pu s in o he ABM is designed as a concep ual coupling laye whe e op imisa ion esul s in luence bo h agen beha iou s and sys em-le el pa ame e s. Speci ically, he in eg a ion ope a es ac oss h ee in e connec ed pa hways: • In o ming agen ou ing decisions. The QUBO sol e p o ides bina y p edic ions o conges ion s a es ac oss he ne wo k, whe e each node (e.g., bu e zone, check-in, inspec ion poin ) is ma ked as conges ed o ee- lowing. In he ABM, hese conges ion signals a e used o bias agen decision-making, s ee ing ehicles away om p edic ed bo lenecks when al e na i e ou es o lanes a e a ailable. Fo example, ucks app oaching a conges ed bu e lane may be p obabilis ically eassigned o neighbou ing, less conges ed lanes, o ca s may be e ou ed owa d unde used check-in boo hs. • Adjus ing sys em-le el pa ame e s Beyond indi idual agen decisions, he QUBO ou pu s also in o m mac o-le el sys em adjus men s, such as p ocessing capaci ies a ce ain checkpoin s can be dynamically educed i he sol e p edic s a conges ion buildup, e lec ing ealis ic slowdowns unde hea y load. Al e na i ely, addi ional esou ces (e.g., ac i a ing backup lanes, opening ex a boo hs) can be simula ed when conges ion ho spo s a e de ec ed, modelling ope a ional esponses. These adjus men s allow he ABM o explo e how quan um-op imised in e en ions a ec sys em pe o mance a mul iple scales. • Explo ing eme gen sys em dynamics. Th ough unning compa a i e ABM simula ions unde baseline (no quan um inpu ) and quan um- in o med scena ios, he amewo k enables concep ual explo a ion o how quan um-guided in e en ions eshape a ic pa e ns and queue dis ibu ions. Speci ically, i examines whe he conges ion is e ec i ely mi iga ed sys em-wide o me ely shi ed o o he zones, and how local quan um-in o med decisions p opaga e h ough he ne wo k o in luence agg ega e pe o mance indica o s, such as a e age wai ing imes, h oughpu , and queue leng hs. The p ima y aim is no o compa e he compu a ional speed o quan um e sus classical sol e s, bu a he o assess he quali y and op imali y o he solu ions in imp o ing sys em pe o mance. F. Feedback Loop A e he ABM simula ion, sys em pe o mance is e alua ed using key indica o s such as h oughpu , wai ing imes, and queue leng hs. This analysis helps iden i y a eas whe e he QUBO-de i ed solu ions we e oo igid o lacked de ail. Insigh s om hese esul s a e hen used o e ine he QUBO o mula ion, adjus p oblem a iables, o in oduce addi ional objec i es, c ea ing an i e a i e p ocess ha imp o es solu ion quali y and sys em pe o mance. The mos ad anced hyb id wo k low ope a es as a con inuous QUBO - ABM – QUBO - ABM loop, whe e quan um op imisa ion and agen -based simula ion epea edly in o m and imp o e each o he . This in eg a ion se es as an ea ly-s age p oo o concep o hyb id quan um-classical wo k lows in anspo logis ics, p o iding me hodological insigh s in o coupling s a ic quan um ou pu s wi h dynamic agen -based simula ions. While cu en ly explo a o y, he app oach o e s a pa hway o u u e esea ch in o eal- ime, scalable, and gene alisable quan um-assis ed anspo managemen sys ems. Figu e 3 summa ises his hyb id wo k low, illus a ing he end- o-end pipeline om sys em ep esen a ion, QUBO o mula ion, and quan um sol e execu ion, h ough o pos p ocessing and in eg a ion wi hin he ABM simula ion. IV. EARLY LESSONS AND LEARNING EXPERIENCE The in eg a ion o quan um-d i en op imisa ion in o an anspo ABMs o e s aluable ea ly insigh s in o he design 4 and po en ial o hyb id quan um-classical wo k lows o eigh logis ics. While his wo k is concep ual, se e al impo an lessons we e iden i ied du ing he p ocess. A. Pos p ocessing o Quan um Ou pu s One o he key lessons is he impo ance o meaning ul pos p ocessing o he aw ou pu s om he quan um sol e . The QUBO solu ion p o ides bina y alues o each node, indica ing p edic ed conges ion s a es. Howe e , hese ou pu s a e no immedia ely usable by he ABM. They mus be ansla ed in o ope a ional signals, such as adjus ing zone capaci ies, modi ying agen ou ing p e e ences, o ac i a ing al e na i e lanes. Wi hou ca e ul pos p ocessing, he in eg a ion isks ei he o e eac ing o noisy quan um ou pu s o unde u ilising hei insigh s. B. Hyb id Wo k low Complexi y Coupling a s a ic op imisa ion laye (quan um sol e ) wi h a dynamic, ime-e ol ing agen -based simula ion in oduces me hodological complexi y. Fo example: • The QUBO o mula ion e lec s a snapsho o he sys em bu does no accoun o empo al dynamics. • The ABM mus decide how equen ly o upda e i s pa ame e s based on quan um ou pu s and how o econcile possible misma ches be ween he quan um model and he simula ion scale. • This hyb id design equi es hough ul in e acing be ween he wo componen s o ensu e consis en and in e p e able ou comes. C. Va iabili y and S abili y Cu en nea - e m quan um de ices, such as pho onic quan um p ocesso s, a e inhe en ly s ochas ic and sensi i e o p oblem scaling. • Mul iple sol e uns a e o en needed o s abilise he ou pu s and iden i y consis en conges ion pa e ns. • This aises ques ions abou how o design obus agg ega ion s a egies o pos selec ion me hods o il e meaning ul signals om noisy quan um solu ions. D. Concep ual Oppo uni ies Despi e hese challenges, he s udy e eals p omising oppo uni ies: • Quan um ou pu s can se e as an addi ional decision laye , complemen ing adi ional agen heu is ics wi h global sys em-le el op imisa ion insigh s. • Hyb id wo k lows enable expe imen a ion wi h new o ms o adap i e, da a-in o med con ol in anspo sys ems. • The app oach has he po en ial o gene alise beyond a single po se ing, o e ing insigh s o ai po s, in e modal hubs, and u ban a ic ne wo ks. E. Limi a ions This wo k is explo a o y and concep ual; i does no ye p o ide quan i a i e pe o mance benchma ks o claim ope a ional ad an ages o e classical op imisa ion me hods. Scalabili y, eal- ime in eg a ion, and gene alisabili y emain open esea ch challenges ha u u e wo k mus add ess. V. CONCLUSION AND FUTURE WORKS This s udy o e s one o he i s concep ual explo a ions o in eg a ing quan um op imisa ion, speci ically MaxCu - based QUBO o mula ions, in o anspo ABMs o eigh logis ics. The hyb id quan um-classical app oach in oduces a p omising new pa adigm, combining global sys em-le el op imisa ion insigh s om quan um sol e s wi h mic o-le el beha iou al de ail om ABMs. One key akeaway is ha quan um ou pu s alone a e no su icien ; meaning ul in eg a ion equi es ca e ul design o in e aces be ween he quan um and classical laye s. T ansla ing bina y conges ion p edic ions in o ac ionable simula ion adjus men s in ol es bo h pos p ocessing and domain knowledge. Mo eo e , he QUBO o mula ion necessa ily simpli ies eal-wo ld sys em dynamics o i cu en quan um ha dwa e limi s, meaning some ope a ional nuances a e abs ac ed away. The s ochas ic na u e o nea - e m quan um de ices, such as he pho onic quan um p ocesso used in his wo k, aises ques ions abou solu ion a iabili y and obus ness. While epea ed uns and pos selec ion s a egies can mi iga e noise, hey also inc ease wo k low complexi y. Finally, he app oach aises b oade me hodological ques ions: • How equen ly should s a ic quan um op imisa ions be ecompu ed o in o m dynamic sys ems? • How do we econcile misma ches in imescales, esolu ions, and model assump ions ac oss he quan um and classical laye s? • How scalable is he app oach when mo ing om small sys em ep esen a ions o eal-wo ld, high- esolu ion anspo ne wo ks? The key con ibu ion o his wo k is me hodological: p o iding ea ly insigh s and design p inciples o coupling quan um op imisa ion wi h dynamic simula ion models in logis ics. While his s udy does no claim compu a ional ad an age o epo pe o mance benchma ks, i o e s ounda ional lessons o u u e quan um-assis ed anspo applica ions. Fu u e wo k will ocus on se e al c i ical di ec ions: • Scaling he QUBO o mula ions o la ge , mo e complex ne wo ks. • Explo ing eal- ime o nea - eal- ime in eg a ion be ween quan um sol e s and ABMs. • In es iga ing gene alisabili y ac oss di e en anspo domains, such as u ban a ic managemen o in e modal logis ics hubs. • Inco po a ing iche agen beha iou s and ope a ional cons ain s in o he hyb id modelling amewo k. • Explo ing how ABM ou pu s (e.g., conges ion pa e ns o agen in e ac ions) can se e as adap i e inpu s o upda e he QUBO o mula ion, enabling a con inuous closed-loop op imisa ion sys em. As quan um ha dwa e and hyb id algo i hmic me hods con inue o ad ance, we belie e his line o esea ch has he 5 po en ial o eshape op imisa ion and decision-making in complex, da a-d i en anspo sys ems. REFERENCES [1] T. E. No eboom and J.-P. 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