Utafiti huu umeunda modeli ya uboreshaji wa njia ya viwango viwili inayolenga kupunguza wastani wa umbali wa kutembea kutoka jamii ambako wazee wanaishi hadi vituo vya basi huku ikidumisha urefu wa njia na vikwazo vya uendeshaji. Katika kiwango cha juu, jamii hugawiwa kwenye kituo hai kilicho karibu zaidi; katika kiwango cha chini, njia inayotekelezeka inayounganisha vituo vilivyochaguliwa hubainishwa. Mbinu kuu ya utatuzi ni genetic algorithm; mbinu nne za uanzishaji—random, greedy, simulated annealing na Quantum Approximate Optimization Algorithm—zililinganishwa. Uanzishaji wa QAOA ulizalisha population inayotekelezeka kikamilifu katika generation ya sifuri katika scenario zote, uliweka suluhisho za mwanzo katika wastani wa Hamming distance wa bits 6,14 kutoka kwenye suluhisho bora la mwisho, na ulihifadhi structural diversity kubwa zaidi kuliko greedy au simulated annealing initialization. Hata hivyo, njia zote za mwisho zilipatikana kwa genetic algorithm ya kawaida, QAOA iliendeshwa kwenye AerSimulator ya kawaida badala ya quantum hardware halisi, na quantum computational advantage haikuonyeshwa.

Modeli ilijaribiwa katika scenario tatu za njia za nafasi na tolerance za \(\delta=1{,}2\), \(1{,}4\) na \(1{,}6\), zinazoruhusu %20, %40 na %60 ya urefu wa ziada ukilinganishwa na urefu wa njia asili. Katika Case 1 wastani wa umbali wa kutembea ulipungua kutoka mita 146,0 hadi mita 27,9, katika Case 2 kutoka mita 364,1 hadi mita 162,9, na katika Case 3 kutoka mita 194,9 hadi mita 82,0. Katika Case 1 faida ya accessibility ilifikia saturation baada ya \(\delta=1{,}4\), wakati katika scenario nyingine mbili route flexibility ya ziada iliendelea kupunguza walking distance. Kinyume chake, katika hali kali zaidi ya Case 2, njia iliyoripotiwa inazidi kikomo chake cha urefu wa njia. Utafiti pia hauna maelezo muhimu ya reproducibility kama chanzo cha route data, uundaji wa pedestrian na driving networks, simulated annealing settings, lower-level solver iliyotumika na code sharing.

Kwa mtazamo wa Türkiye: Mbinu hii inaweza kuchunguzwa nchini Türkiye kwa upangaji wa njia za basi za manispaa za miji mikubwa na wilaya, access kwa elderly care centers, viunganisho vya hospitali na family health centers, public transport access kwa maeneo ya vijijini, na kutathmini upya njia zilizopo kwa malengo ya social equity. Kabla ya matumizi, validation inapaswa kufanywa kwa kutumia data halisi za vituo, njia, ratiba, barabara na pedestrian networks nchini Türkiye; pamoja na kuzingatia sidewalk continuity, slope, pedestrian crossings, signalling, safe crossing, transfer needs na real walking speeds za wazee. Mitandao mikubwa kama Istanbul, Ankara au Izmir inapaswa kujaribiwa tofauti na njia za wilaya ndogo na vijijini; matokeo ya optimization yanapaswa kuunganishwa na cost, vehicle, service frequency na driver working constraints za manispaa. Kwa kuwa utafiti haukutekelezwa kwenye manispaa, bus operator au passenger group yoyote nchini Türkiye, haiwezi kuhitimishwa moja kwa moja kwamba local routes zitapata accessibility gain, runtime au feasible-solution ratio ileile.

Tatizo ambalo utafiti unajaribu kutatua

Katika bus route design, njia fupi na ya moja kwa moja inaweza kuwa na faida kwa operator. Kwa upande mwingine, kuweka vituo mbali na maeneo ambako wazee wanaishi kunaweza kuwalazimisha abiria kutembea umbali mrefu. Kuongeza vituo karibu na jamii za wazee au kupeleka njia katika maeneo haya kunaweza kuongeza total route length, idadi ya turns na operational complexity.

Utafiti unawakilisha mvutano huu kwa viwango viwili vya maamuzi:

• Kiwango cha strategic accessibility: Kugawa kila jamii ya wazee kwenye kituo cha basi kilichochaguliwa na kupunguza wastani wa walking distance.
• Kiwango cha operational routing: Kuunganisha vituo vilivyochaguliwa kwa route ya basi iliyo continuous na inayokidhi limits za urefu na stop spacing.

Muundo huu ni bilevel optimization problem ambapo uamuzi mmoja unategemea matokeo ya mwingine. Hata kama upper level inachagua kituo inachotaka, kama lower level haiwezi kujenga feasible route kwa vituo hivyo, suluhisho halikubaliki.

Swali la utafiti

Swali kuu ni kama accessibility-oriented constrained bus-route search inakuwa efficient zaidi wakati initial population ya genetic algorithm inaundwa na solutions zenye taarifa kuhusu structure ya problem.

Hasa, mbinu nne zifuatazo za initialization zililinganishwa:

1. Initialization ambapo decision bits hutengenezwa kwa kiasi kikubwa kwa random,
2. Greedy initialization inayotoa priority kwa vituo vilivyo karibu na jamii,
3. Simulated annealing initialization inayokubali local changes chini ya temperature control,
4. QAOA-based initialization inayobadilisha upper-level objective na constraints kuwa QUBO energy.

Dai kuu la watafiti si kwamba QAOA inapata final optimum bora kuliko classical methods. Kulingana na utafiti, mchango wa QAOA ni kusogeza solution distribution ambayo genetic algorithm inaanzia kwenye regions zenye feasibility na quality nzuri.

Modeli ya viwango viwili iliundwaje?

Kiwango cha juu: Access ya jamii kwenda vituoni

Kila elderly community \(k\) hugawiwa kwenye selected stop \(i\). Upper-level objective function inapunguza wastani wa walking distance:

\[ \min_{z_{ki}} \frac{1}{m} \sum_{k=1}^{m} \sum_{i=1}^{n} d_{ki}z_{ki}. \]

Hapa:

• \(m\), ni idadi ya elderly communities.
• \(n\), ni idadi ya candidate stops.
• \(d_{ki}\), ni umbali kati ya community \(k\) na stop \(i\).
• \(z_{ki}=1\), ikiwa community \(k\) imegawiwa kwa stop \(i\); vinginevyo ni 0.

Kila community lazima igawiwe kwa stop moja tu, stop hiyo lazima iwe kwenye active route, na distance lazima isiwe zaidi ya mita 400. Katika utafiti \(d_{\mathrm{walk}}=400\) mita.

Katika explanatory text, decision maker wa upper level anaelezwa kuwa wazee, wakati katika Figure 2 ameonyeshwa kama “Government”. Kwa hiyo haiko consistent kwenye narrative kama wazee ni direct decision makers au target group ya public planning.

Kiwango cha chini: Route kati ya selected stops

Lower level inapunguza total route length inayounganisha selected stops:

\[ \min_{x_{ij}} \sum_{i\neq j}d_{ij}x_{ij}. \]

\(x_{ij}=1\) ikiwa basi linasafiri moja kwa moja kutoka stop \(i\) kwenda \(j\), huchukua thamani 1. Modeli inalenga kwamba:

• Kila selected stop iwe na incoming link moja na outgoing link moja,
• Subtours zilizotenganishwa na route zisijitokeze,
• Original stops zihifadhiwe,
• Idadi ya selected stops isiwe chini ya idadi ya initial stops,
• Total route length isizidi \(\delta d_0\),
• Consecutive stops ziwe katika range ya mita 100–400,
• Start na end stops zichaguliwe kwa lazima

.

Route-length constraint ni:

\[ L\leq \delta d_0 \]

ambapo \(d_0\) ni original route length na \(\delta\) ni allowed expansion factor. \(\delta=1{,}2\) inawakilisha route yenye urefu usiozidi %20 zaidi ya original route; \(\delta=1{,}6\) inawakilisha hadi %60 zaidi.

Uncertainty ya kimbinu katika definitions za distance

Katika mathematical model section, distances kati ya stops na communities zinasemekana kukokotolewa kwa Haversine formula. Katika greedy initialization section, community–stop distances hukokotolewa kwenye pedestrian network kwa truncated single-source Dijkstra algorithm. Katika result metrics, route length inafafanuliwa kama shortest-path distance kwenye driving network.

Vipimo hivi vitatu si kitu kilekile:

• Haversine distance ni great-circle straight-line distance kati ya coordinates mbili.
• Pedestrian-network distance hufuata walkable links.
• Driving-network distance hufuata road ambayo vehicle inaweza kutumia.

Kwa kuwa utafiti haujatenganisha kikamilifu ni distance matrix gani ilitumika katika table au experiment gani, reproducibility inakuwa ngumu. Hasa, ni lazima kufafanuliwa kama 400-meter accessibility limit ilitumika kwa Haversine distance au pedestrian-network distance.

Genetic algorithm inatafuta maamuzi gani?

Kila individual inafafanuliwa na chromosome inayowakilisha community–stop assignments na selected stops:

\[ \chi_j= \left( \mathbf{z}^{(j)},\mathbf{y}^{(j)} \right). \]

Lower-level connection variables \(\mathbf{x}\) hazijaongezwa moja kwa moja kwenye chromosome. Baada ya genetic algorithm kutengeneza stop selection, lower-level problem hutatuliwa tena ili kubainisha best route inayolingana na selection hiyo. Kama lower level si feasible, individual hupewa large penalty.

Separation hii inahifadhi bilevel structure kinadharia. Hata hivyo utafiti hauelezi ni software gani, exact solver gani au repair heuristic gani ilitumika kweli kutatua lower-level problem katika experiments. Maandishi yanasema exact solver au approximate heuristic inaweza kutumika, lakini hayajaeleza ni ipi ilitumika.

Genetic algorithm settings

Katika method description, crossover imeitwa “order-preserving”, lakini equation na parameter table zinaonyesha one-point crossover. Mutation equation inaeleza swap ya stop bits mbili, wakati parameter table inaandika bit-flip kwa kila gene. Kwa kuwa details hizi zinaweza kutoa matokeo tofauti katika software implementation, actual operation haiwezi kubainishwa bila code.

Jinsi mikakati minne ya initialization inavyofanya kazi

Random initialization

Bits za candidate stops ziliwekwa active au inactive kwa probability ya takribani 0,5. Original stops kisha ziliwekwa active kwa lazima na reference individual yenye original stops pekee ikaongezwa kwenye population.

Mbinu hii huchunguza decision space kwa upana; lakini kwa kuwa route length, connectivity na lower-level constraints nyingine hazilazimishwi wakati wa initialization, sehemu kubwa ya initial population inaweza kuwa infeasible.

Greedy initialization

Kila candidate stop ilipewa score ifuatayo kulingana na ukaribu wake na communities:

\[ s_i= \sum_{k\in K} \frac{1}{1+d_{ki}}. \]

Stops zenye distance ndogo hupata score kubwa. Optional stops zenye scores za juu zaidi zilichaguliwa na population ikatengenezwa kwa mabadiliko ya bits chache kutoka main template hii.

Mbinu hii ni ya haraka; lakini haizingatii route connectivity na length limit wakati wa scoring. Pia, ingawa maximum optional-stop count inayoitwa \(K_{\max}\) imetumika katika mbinu, parameter table inaeleza kwamba total active-stop limit haikutekelezwa.

Simulated annealing initialization

Simulated annealing ilitumia neighborhood moves zinazobadilisha activity bit ya stop moja au kubadilisha active stop na candidate nyingine. Probability ya kukubali suluhisho baya zaidi ilifafanuliwa kama:

\[ P(\mathrm{kabul})= \begin{cases} 1, & R(y')<R(y),\\ \exp\left[-\frac{R(y')-R(y)}{T}\right], & \text{aksi durumda} \end{cases} \]

Temperature ilipunguzwa kwa geometric schedule:

\[ T_{t+1}=\alpha T_t. \]

Katika temperature kubwa, acceptance ya worse solutions inalenga kutoka kwenye local minima; katika temperature ndogo, search inalenga zaidi good solutions.

Licha ya umuhimu wake kwa comparison ya utafiti, initial temperature, cooling coefficient, minimum temperature, iteration count, idadi ya independent SA runs na size ya selected elite pool hazijatolewa.

QAOA-based initialization

QAOA haibadilishi genetic algorithm yote. Stop na assignment decisions za upper level zilibadilishwa kuwa Quadratic Unconstrained Binary Optimization, QUBO, na QAOA ikatumika kusample low-energy bit strings kutoka energy function hii.

Upper-level QUBO imeandikwa katika utafiti kama:

\[ Q_{\mathrm{ULM}}(z,y)= \sum_{k=1}^{m}\sum_{i=1}^{n} \frac{d_{ki}}{m}z_{ki} + \lambda_1 \sum_{k=1}^{m} \left( \sum_{i=1}^{n}z_{ki}-1 \right)^2 \]

\[ + \lambda_2 \sum_{k=1}^{m} \left( \sum_{i=1}^{n}d_{ki}z_{ki}-d_{\mathrm{walk}} \right)^2 + \lambda_3 \sum_{k=1}^{m}\sum_{i=1}^{n} z_{ki}(1-y_i). \]

Term ya kwanza inalenga kuwakilisha walking distance, ya pili assignment ya kila community kwenye stop moja, ya tatu walking limit, na ya nne kuhakikisha assignments zinafanywa kwenye active stops pekee.

Term ya tatu ina tatizo muhimu la mathematical interpretation. Original constraint ni inequality:

\[ \sum_i d_{ki}z_{ki}\leq d_{\mathrm{walk}} \]

lakini katika QUBO imeandikwa kama:

\[ \left( \sum_i d_{ki}z_{ki}-d_{\mathrm{walk}} \right)^2 \]

Square penalty hii bila slack variable inaweza kuvuta distance kuelekea mita 400 badala ya kuhakikisha tu kwamba iko chini ya mita 400. Kwa mfano, stop halali yenye umbali wa mita 30 pia hupata penalty kwa sababu iko mbali sana na mita 400. Kwa hiyo haijaonyeshwa kwamba QUBO katika umbo lililoandikwa inawakilisha original inequality kikamilifu.

Muundo wa QAOA circuit

Binary variables zilibadilishwa kuwa Ising Hamiltonian kwa Pauli-\(Z\) operators:

\[ x_i=\frac{1-Z_i}{2}. \]

Mwanzoni Hadamard gates huunda equal superposition ya bit strings zote. Kisha cost na mixer layers hutumika kwa kubadilishana:

\[ |\psi(\boldsymbol{\gamma},\boldsymbol{\beta})\rangle = U_M(\beta_p)U_P(\gamma_p) \cdots U_M(\beta_1)U_P(\gamma_1) |\psi_0\rangle. \]

Cost unit \(U_P\) huongeza phase kulingana na QUBO energy. Mixer unit \(U_M\) huwezesha exploration kati ya bit strings tofauti. Katika utafiti:

• Circuit depth \(p=3\),
• Classical parameter optimizer COBYLA,
• Optimization iterations 40,
• Measurement count 2000 shots,
• Matrix-product-state bond dimension \(\chi=20\)

zilitumika.

Figure 1 inaonyesha general QAOA circuit, na Figure 5 compiled \(p=3\) circuit yenye Hadamard, \(ZZ\) interaction, \(RX\) mixing na measurement layers. Figure 6 inaonyesha \(\gamma\) parameters zikibadilika zaidi katika iterations za mwanzo, huku \(\beta\) values zikiconverge kwa utaratibu zaidi. Figure 7 inaonyesha QUBO energy yenye oscillations kali kati ya takribani −10.000 na 45.000. Figure 8 inaonyesha sampled energy distribution ikiwa imejikita kwenye low-energy region lakini ikiwa na right tail inayofika takribani 50.000.

Je, quantum computer halisi ilitumika?

Hapana. QAOA experiments zote zilifanywa kwenye classical AerSimulator. Thamani zilizoitwa “noisy” energy katika utafiti hazitokani na gate errors za quantum hardware halisi, \(T_1/T_2\) decay au crosstalk.

Maandishi yanataja kama effective noise sources:

• MPS truncation approximation yenye bond dimension 20,
• Sampling uncertainty kutokana na 2000 shots,
• Gate twirling na dynamic decoupling configurations

. Hata hivyo techniques mbili za mwisho zina athari ndogo kwenye simulator isiyo na real hardware errors. Finite-shot uncertainty pia ni statistical uncertainty inayotokana na kukadiria measurement probabilities kwa sample chache, badala ya physical CPTP channel inayobadilisha quantum state.

Kwa hiyo utafiti hauonyeshi kwamba \(p=3\) circuit kwenye NISQ device halisi itatoa energy na feasible-solution distribution ileile.

Scenario tatu za route

Figure 3 inawasilisha maps tatu. Alama ya nyumba inaonyesha facility au community ambako wazee wanaishi, bus icons zinaonyesha candidate au selected stops, blue lines zinaonyesha route, na dashed circles zinaonyesha 400-meter accessibility area.

Imeelezwa kwamba scenarios zinawakilisha hali tofauti kama sparse coverage, complex road geometry na overlapping service areas. Hata hivyo:

• Chanzo cha geographic data,
• Utambulisho wa original bus line,
• Jinsi candidate stops zilivyotengenezwa,
• Ni version ya tarehe gani ya road na pedestrian network ilitumika,
• Kama community population au elderly count ziliwekewa weights

hazijaelezwa. Kila demand area kwenye maps inaonekana kuwa na uzito sawa.

Route flexibility ilibadilishaje accessibility?

Katika Case 1, kutoka \(\delta=1{,}2\) hadi \(1{,}4\) kuliongeza route length kwa mita 236,0 huku walking distance ikipungua kwa mita 118,1. Kuongeza hadi \(\delta=1{,}6\) hakukuleta faida mpya. Katika scenario hii, route flexibility ya kutosha kwa accessibility ilifikia saturation katika kiwango cha kati.

Katika Case 2, walking distance ilipungua kwa utaratibu route ilipozidi kuwa ndefu, na access score ikaongezeka kutoka 0,090 hadi 0,593. Hata hivyo katika row ya \(\delta=1{,}2\), route ya mita 3587,2 inazidi limit ya mita 3409,4 kwa mita 177,8. Hii inaashiria kwamba ama infeasible solution iliingia kwenye results table, au route limit ilitumika kama penalty badala ya hard constraint. Utafiti haujaeleza tofauti hii.

Katika Case 3, walking distance ilipungua kutoka mita 194,9 hadi mita 82,0 huku turn count ikibaki 14. Hii inaonyesha kwamba accessibility improvement ilitokana zaidi na route na stops kupanuliwa kuelekea demand area kuliko na kuongeza turns.

Walking time na access score

Average walking time ilikokotolewa kwa:

\[ \bar{T}_m= \frac{\bar{W}_m}{v_w} \]

na fixed walking speed ya \(v_w=1{,}4\) m/s ikakubaliwa kwa passengers wote. Ingawa utafiti unalenga elderly access, haukutumia speeds tofauti kulingana na age, mobility limitation, walking aid, road slope au intersection waiting time.

Access score ya kila community ilifafanuliwa kama:

\[ A_k= \max \left( 0, 1-\frac{d_k}{d_{\mathrm{walk}}} \right) \]

Stop ikiwa karibu kabisa na community, score ni 1; distance ikifikia mita 400, score inakaribia 0. Score hii inawakilisha distance pekee; service frequency, fare, vehicle accessibility, safe pedestrian path au number of transfers hazijaingizwa.

Mbinu za initialization zilifikiaje feasible solution kwa haraka?

Katika Figures 12–14, QAOA initialization ilionyesha feasible-solution ratio ya 1,0 kuanzia generation ya sifuri katika scenarios zote tatu na values zote za \(\delta\). SA initialization kwa kawaida ilianza na feasibility ya juu, huku random na greedy methods zikiwa na infeasible individuals katika generations za mwanzo.

Hata hivyo, katika Mann–Whitney analysis ya “time to first feasible solution”, tofauti ya ndani ya GA kati ya QAOA na random initialization haikuwa significant:

\[ p=0{,}400,\qquad r=-0{,}073. \]

Tofauti kati ya QAOA na greedy initialization pia haikuwa significant baada ya Bonferroni correction:

\[ p=0{,}052,\qquad r=0{,}168. \]

Matokeo haya yanaonyesha kwamba ingawa QAOA ilizalisha feasible population katika generation ya sifuri, absolute differences katika time metric iliyotumiwa zilikuwa ndogo sana.

Matokeo yakijumuisha initialization cost

SA ni mojawapo ya mbinu zinazoconverge kwa haraka zaidi katika genetic-algorithm stage; lakini preprocessing time yake ni takribani orders mbili za ukubwa juu kuliko mbinu nyingine. Katika full wall-clock comparison, gharama hii ilifuta advantage ya high-quality initialization ya SA.

Haiko wazi kama reported QAOA initialization times za 2–4 milliseconds zinajumuisha COBYLA iterations 40, 2000-shot sampling na circuit compilation zote. Kama operations hizi zilifundishwa mara moja tofauti na kutumika tena katika GA runs mbalimbali, time comparison kati ya QAOA na mbinu nyingine inaweza kuwa inapima scopes tofauti.

Population diversity

Hamming distance kati ya chromosomes mbili ni idadi ya bits zinazotofautiana:

\[ d_{ij}= \sum_{k=1}^{N} \left| y_k^{(i)}-y_k^{(j)} \right|. \]

Kwa kuwa utafiti una candidate stops 40, random decision strings mbili zinatarajiwa kuwa na tofauti ya takribani bits 20.

QAOA ilitoa pairwise diversity takribani %60 kubwa zaidi kuliko SA. Greedy initialization ilizalisha individuals zinazofanana sana na hivyo kuongeza risk ya premature convergence.

Initial distance to final best solution

Katika comparison hii, QAOA initial population ndiyo ilikuwa karibu zaidi kimuundo na best stop selection iliyopatikana baadaye. Hata hivyo, kwa kuwa “final best solution” ilibainishwa mwishoni mwa experiments hizo hizo, metric hii haionyeshi distance to independent, unknown true optimum; inaonyesha distance to reference solution iliyopatikana na algorithm yenyewe.

Tatizo katika quality–diversity indicator

Utafiti uliifafanua quality–diversity indicator kama:

\[ QD= \frac{\text{normalize edilmiş ortalama amaç}} {\text{ortalama ikili Hamming uzaklığı}} \]

na ukaeleza kwamba value ndogo ni bora.

Kulingana na definition, lowest na hivyo “best” QD value ni ya random initialization. Watafiti wanaeleza kwamba random method inapata hii kwa kusambaza poor-quality solutions kwenye space pana sana na hivyo haitoi meaningful balance. Ingawa interpretation hii inaeleweka, indicator yenyewe haipenalize poor quality vya kutosha. Kwa hiyo QD ratio haiwezi ku-rank mbinu nne kwa uaminifu ikiwa inatumiwa peke yake.

Katika Table 10 SA diversity imetolewa kama 7,17, na katika Table 12 kama 6,89. Pia maandishi yanayodai kwamba QAOA diversity ni mara 2,9 kubwa kuliko SA si sahihi kihesabu kwa value yoyote kati ya hizo; ratio ni takribani mara 1,6–1,7.

Tathmini ya takwimu

Time metrics zililinganishwa kwa pairwise Mann–Whitney U tests kwa observations 90 kwa kila method, zikiunganisha independent seeds 10, values tatu za \(\delta\) na scenarios tatu. Kwa pairwise comparisons sita, Bonferroni-corrected threshold:

\[ \alpha^*=0{,}008 \]

ilitumika, na effect size ikaripotiwa kwa rank-biserial correlation \(r\).

Baadhi ya matokeo muhimu ni:

• QAOA ni faster kuliko random initialization katika total within-GA time: \(p=0{,}001\), \(r=-0{,}294\).
• Tofauti ya within-GA total time kati ya QAOA na greedy initialization si significant: \(p=0{,}101\).
• SA ilifikia within-GA convergence faster kuliko QAOA: \(p<0{,}001\), \(r=0{,}536\).
• Initialization cost ikiongezwa, SA ni slower sana kuliko structured methods zote.
• Hakukuwa na significant difference katika within-GA first-feasible-solution times kati ya QAOA na random initialization: \(p=0{,}400\).

Kuchanganya measurements kutoka scenarios tatu tofauti na constraint levels tatu katika distribution moja kunaweza kuficha scenario-dependent effects. Pia, conditions tofauti za \(\delta\) za method ileile zimechukuliwa kama independent. Hakuna separate statistical model iliyotumika ku-account repeated au hierarchical experimental structure.

Utafiti unasema mara kadhaa kwamba final route objective values hazikutofautiana statistically kati ya methods. Hata hivyo Table 9 ina time metrics pekee; between-method test results za final objective value, walking distance au access score hazijatolewa.

Nguvu za utafiti

• Accessibility na operational efficiency zimechukuliwa katika bilevel decision structure badala ya weighted sum moja.
• Mbinu nne za initialization zimejaribiwa kulinganishwa chini ya genetic-algorithm settings zilezile.
• Si final objective value pekee; first feasible solution, convergence, total time na initialization cost zilitathminiwa kando.
• Kutenganisha within-GA time na full wall-clock time kulifanya real cost ya SA preprocessing ionekane.
• Initial populations zilichunguzwa kwa Hamming distance, closeness to optimum na quality–diversity.
• Independent runs kumi na bootstrap confidence intervals zilitumika.
• Jukumu la QAOA halikuwasilishwa kama quantum advantage, bali limewekewa mipaka kama structured initialization sampler.
• Spatial geometries tatu na route-flexibility levels tatu zililinganishwa.
• Scenarios zilionyesha kwamba route flexibility inaweza kuleta saturation au continued improvement katika accessibility gain.

Mapungufu ya utafiti

• Utafiti haujapitiwa na wahakiki.
• Real quantum hardware haikutumika.
• Ni spatial examples tatu ndogo tu zilizotathminiwa.
• Hakuna field validation kwa real passenger, schedule au operational data.
• Ukubwa wa elderly population, need level au community weights hazijaelezwa.
• 400-meter threshold imetumika kwa communities zote kama value moja.
• Fixed speed ya 1,4 m/s imechukuliwa kwa kila mtu katika walking time.
• Road slope, sidewalk, pedestrian crossings, intersection waiting time na safety hazijatathminiwa.
• Service frequency, capacity, operating cost, vehicle na personnel constraints hazijaingizwa kwenye modeli.
• Actual implementation ya lower-level route solver haijaelezwa.
• Haversine, pedestrian-network na driving-network distances hazijatenganishwa kwa consistency katika method yote.
• SA hyperparameters hazijatolewa.
• Exact values za QUBO penalty coefficients zilizotumika katika experiments hazijatolewa.
• QUBO walking inequality imebadilishwa kuwa squared equality penalty bila slack variable.
• Haijaelezwa ni bit strings ngapi zilichukuliwa kutoka QAOA na ngapi ziliingizwa kwenye GA population.
• Haiko wazi kama QAOA times zinajumuisha circuit training kikamilifu.
• Case 2 inazidi route-length limit.
• Namba za Case 3 text na Table 5 hazilingani.
• Kuna internal method inconsistencies kuhusu mutation, crossover na supported strategies.
• Quality–diversity indicator inaonyesha random initialization kuwa best kulingana na definition yake yenyewe.
• Objective-value tests zinazounga mkono equality ya final solutions hazijatolewa.
• Code, data, network file, random-seed list na reproducibility package hazijashirikiwa.

Utafiti unaunga mkono nini?

• Initial distribution ya genetic algorithm inaweza kuathiri feasible-solution ratio katika early generations.
• QAOA samples zinazoongozwa na QUBO energy zinaweza kuzalisha feasible initial candidates chini ya classical simulator conditions.
• QAOA initialization inaweza kuweka initial population karibu zaidi na final solution kuliko random na greedy initialization.
• QAOA inaweza kuhifadhi structural diversity kubwa zaidi kuliko greedy na SA initialization.
• SA inaweza kutoa high-quality initialization; lakini preprocessing time inaweza kudhoofisha total performance.
• Greedy method inaweza kufikia first feasible solution kwa cost ndogo sana, lakini ika-concentrate population karibu na template nyembamba.
• Ongezeko dogo la route length linaweza kupunguza walking distance kwa kiasi kikubwa katika baadhi ya spatial structures.
• Route flexibility zaidi si lazima itoe accessibility gain ya ziada katika kila hali.

Utafiti hauthibitishi nini?

• Haudhibitishi kwamba QAOA inatoa quantum computational advantage dhidi ya classical algorithms.
• Hauonyeshi kwamba real quantum device itatoa initial quality na time ileile.
• Hauonyeshi kwamba QAOA inafanya final route kuwa bora kuliko mbinu nyingine.
• Hauonyeshi kwamba QAOA inatoa wall-clock time fupi kuliko greedy initialization.
• Hauonyeshi kwamba modeli inaweza ku-scale kwa maelfu ya stops na routes nyingi katika city kubwa.
• Haithibitishi kwamba mita 400 ni accessibility threshold inayofaa na salama kwa wazee wote.
• Hauonyeshi kwamba routes zilizotengenezwa zitapendwa na passengers.
• Hauonyeshi kwamba routes mpya zinapunguza cost, travel time, emissions au vehicle requirement.
• Haithibitishi kwamba routes zinazopendekezwa kwenye maps zinaweza kuendeshwa katika field conditions.
• Hautoi success rate au cost advantage kwa public-transport network ya Türkiye.

Maana kwa kuzingatia jana, leo na kesho

Traditional route optimization mara nyingi huzingatia final route cost na single solution algorithm. Utafiti huu unapima initial-population geometry kando na hivyo unaelekeza attention si tu kwenye “matokeo gani yalipatikana”, bali pia “search ilianzia wapi katika solution space”.

Kutokana na limitations za quantum hardware ya sasa, kutumia QAOA kama small structured initializer badala ya tool inayotatua transport problem yote kunaweza kuwa hybrid approach inayotekelezeka zaidi. Kwa kuwa ushahidi wa utafiti unatokana na simulation badala ya real hardware, mchango huu unapaswa kutathminiwa zaidi kama algorithmic initialization design kuliko quantum advantage.

Katika siku zijazo, experiments kwenye networks kubwa zaidi, real quantum hardware, QUBO inequality transformations tofauti na fully specified classical comparisons zinaweza kubainisha kwa uaminifu zaidi mchango halisi wa QAOA sampling. Framework hiyo hiyo ikipanuliwa kwa multiple bus lines, transfers, service frequency, vehicle capacity na operating budget, representation ya social accessibility na operational decisions inaweza kuwa realistic zaidi.

Mbinu na Matokeo ya Utafiti

Technical research design

Evaluation metrics

Key quantitative findings

• QAOA initial populations zilifikia feasibility ratio 1,0 katika generation ya sifuri katika scenarios na tolerance zote.
• Mean pairwise Hamming distance ya random initialization ni ya juu zaidi kwa 19,84, na greedy ni ya chini zaidi kwa 4,12.
• Pairwise Hamming distance ya QAOA ni 11,47, ya SA ni 7,17.
• Initial distance ya QAOA kwenda final best solution ni mean 6,14; SA 7,73; greedy 9,63; random 18,72.
• Normalized initial objective value ya QAOA ni ya chini zaidi kwa 0,791, na random method ni ya juu zaidi kwa 1,000.
• SA ni faster kuliko QAOA katika within-GA convergence time; lakini preprocessing cost ya sekunde 0,24–0,29 ilifanya method hiyo kuwa slowest katika full time.
• Greedy ndiyo method inayofikia first feasible solution kwa haraka zaidi katika full wall-clock time.
• QAOA ni significantly faster kuliko random initialization katika within-GA total time na statistically similar na greedy initialization.
• Katika Case 1 walking distance ilipungua kutoka mita 146,0 hadi mita 27,9 na route flexibility ya ziada haikutoa gain baada ya \(\delta=1{,}4\).
• Katika Case 2 walking distance ilipungua kutoka mita 364,1 hadi mita 162,9; lakini result ya \(\delta=1{,}2\) ilizidi route limit.
• Katika Case 3 walking distance ilipungua kutoka mita 194,9 hadi mita 82,0 huku turn count ikibaki 14.

Scientific function ya visuals

Taarifa zinazohitajika lakini hazipo kwa reproducibility

• Geographic coordinates na network files za scenario tatu,
• Stop na route lists za original lines,
• Candidate-stop generation method,
• Pedestrian na driving network data source na dates,
• Lower-level route solver iliyotumika,
• Actual QUBO matrix size na experimental coefficients,
• Values za \(\lambda_1\), \(\lambda_2\) na \(\lambda_3\),
• Idadi ya individuals zilizochaguliwa kutoka QAOA samples kwenda population,
• Qiskit na AerSimulator versions,
• COBYLA starting parameters na random seeds,
• SA initial temperature, cooling coefficient na iteration count,
• Actual crossover na mutation operations zilizotumika,
• Ni calculations zipi zinajumuishwa kwenye QAOA initialization time,
• Statistical tests za final objective values,
• Source code na runtime environment.

Technical conclusion

Matokeo ya utafiti yanaonyesha kwamba hata kama genetic algorithm inaweza kufikia final route quality ileile, initial population inaweza kuwa na athari kubwa kwenye feasibility, diversity na convergence stability. QAOA-based initialization ilizalisha low-energy samples zenye constraint information kwenye classical simulator; kwa kiasi fulani ikasawazisha infeasible exploration ya random method na narrow population ya greedy method.

Hata hivyo, haijatenganishwa kwa experiments maalumu kama matokeo yanatokana na QAOA yenyewe, penalty structure iliyowekwa kwenye QUBO, classical COBYLA optimization au filtering na repair ya samples baadaye. Direct comparisons na energy-based classical samplers zinazofanana, QUBO relaxations au advanced diversity-preserving heuristics zinahitajika.

Maelezo ya Chanzo na Mbinu

Jina kamili asili la utafiti: A Hybrid Quantum-Classical Framework for Accessibility-Oriented Bus Route Design: QAOA-Based Initialization for Bilevel Optimization

Waandishi: Daniel Udekwe, Ruimin Ke na Qian-Wen Guo.

Mpangilio wa waandishi: Mpangilio wa sasa wa rekodi ya SSRN umehifadhiwa.

Mwandishi wa mawasiliano: Qian-Wen Guo ameonyeshwa kama corresponding author katika rekodi ya sasa ya SSRN.

Co-first author au equal contribution: Hakuna taarifa ya co-first authorship au equal contribution.

Taarifa ya waandishi katika faili: Toleo lililopakiwa halina full author and affiliation block, na footers zinatumia “First Author et al.”. Utambulisho wa waandishi umethibitishwa kupitia official current SSRN record.

Taasisi 1: SSRN record inaonyesha Florida State University kwa Daniel Udekwe. Current institutional biography inamwonyesha kama doctoral student katika Florida State University, Department of Civil and Environmental Engineering.

Taasisi 2: SSRN record haijaonyesha institution kwa Ruimin Ke. Current institutional profile ina affiliation na Rensselaer Polytechnic Institute, Civil and Environmental Engineering.

Taasisi 3: Current institutional affiliation ya Qian-Wen Guo ni Florida A&M University–Florida State University College of Engineering, Department of Civil and Environmental Engineering.

DOI:10.2139/ssrn.6997069

Official source link:Current SSRN record page

Publication platform: SSRN.

Publication date: 25 Juni 2026.

Publication year: 2026.

Page count: 28.

Previous version: Kuna rekodi ya zamani ya SSRN ya title ileile ya 5 Juni 2026 yenye DOI 10.2139/ssrn.6883134. Utafiti uliopakiwa ni current version namba 6997069.

Jarida: Faili iliyopakiwa ina kauli “Preprint submitted to Elsevier”; lakini hakuna specific journal name au acceptance decision.

Mchapishaji: Preprint inasambazwa kupitia SSRN platform. Specific peer-reviewed journal publisher haijathibitishwa kupitia version hii.

Aina ya chanzo: Modeling-based preprint research article yenye bilevel optimization, classical quantum-circuit simulation na genetic-algorithm comparison.

Hali ya mapitio ya rika: Utafiti huu ni preprint na haujapitiwa na wahakiki.

Michango ya waandishi: Hakuna separate CRediT au task-based author contribution statement katika version hii.

Ufadhili: Hakuna funding organization, project name au grant number katika version hii.

Mgongano wa maslahi: Waandishi wamesema hakuna known financial interest au personal relationship inayoweza kuathiri utafiti.

Data access: Hakuna open data repository, map network, coordinate list au data-access statement iliyotolewa.

Code access: Hakuna source code au reproducibility package ya genetic algorithm, lower-level solver, SA na QAOA implementation iliyotolewa.

Quantum implementation limit: QAOA circuit haikuendeshwa kwenye real quantum hardware; ilisimuliwa kwa njia ya classical kwenye AerSimulator. Utafiti hauonyeshi quantum computational advantage.

Model consistency warning: Result ya Case 2 kwa \(\delta=1{,}2\) inazidi route-length limit. Explanatory text ya Case 3 na namba za Table 5 hazilingani. Walking-distance inequality katika QUBO imebadilishwa kuwa squared equality penalty bila slack variable.

Method consistency warning: Maeneo ya matumizi ya Haversine, pedestrian-network na driving-network distances hayajatenganishwa kikamilifu. Kuna tofauti kati ya definitions za mutation na crossover. Simulated annealing na lower-level solver settings hazijakamilika.

Statistical interpretation limit: Mann–Whitney U tests zimetolewa kwa time metrics; lakini separate test results zinazoonyesha kwamba final objective values za initialization methods ni statistically equal hazijatolewa.

Maudhui haya ya Kiswahili yameandaliwa kwa kutegemea mathematical model, tables, maps, quantum circuit diagrams, simulation conditions, time measurements na statistical results za utafiti uliopakiwa pekee. Hakuna municipal implementation, real passenger satisfaction, operating cost, quantum advantage au performance claim maalumu kwa Türkiye ambayo haipo katika utafiti iliyoongezwa.