【正文】 he development of optimal route layouts and frequency determination. Other studies, additionally, consid ered fares (Kocur and Hendrickson 1982。 Yu and Yang 2020) and bus types (Delle Site and Filippi 2020). 6 Network Structure Some early studies focused on the design of systems in simplified radial (Byrne 1975。 Kocur and Hendrickson 1982). Van Nes et al. (1988) applied a simultaneous distributionmodal split model based on transit deterrence for es timating demand for public transportation. In a series of studies, Chang and Schonfeld (1991, 1993a,b) and Spacovic et al. (1994) estimated demand as a direct function of travel times and fares with respect to their elasticities, while Chien and 7 Spacovic (2020), followed the same approach assuming that demand is ad ditionally affected by headways, route spacing and fares. Finally, studies by Leblanc (1988), Imam (1998), Cipriani et al. (2020), Lee and Vuchic (2020)。 Pucher et al. 2020）。它包括對(duì)路線輔設(shè)的設(shè)計(jì)和諸如頻率、車(chē)輛種 類(lèi)等相關(guān)特點(diǎn)的決定。循環(huán)性是在運(yùn)輸頻率需求限制（最小和最大允許頻率分別決定安全和可忍受的等待時(shí)間）、所期望的運(yùn)載因素、車(chē)隊(duì)規(guī)模和可用性下，基于對(duì)沿線的乘客量預(yù)估（通過(guò)觀察法或是運(yùn)用流動(dòng)分布計(jì)算方法）而決定的。Chua(1984)對(duì)現(xiàn)存的公交網(wǎng)絡(luò)設(shè)計(jì)的各項(xiàng) 工作進(jìn)行了大量回顧，他發(fā)表了五種公交系統(tǒng)設(shè)計(jì)模式：一，手工的；二，市場(chǎng)分析；三，系統(tǒng)分析；四，帶有交互式圖表的系統(tǒng)分析；五，數(shù)學(xué)最優(yōu)化方法。最后，在一系列近期的研究中， Fan 和 Machemehl（ 2020， 2020a,b）把 TRNDP方法分為實(shí)踐法、理想條件下的最優(yōu)分析模型、為解決實(shí)際問(wèn)題的啟發(fā)性步驟。 TRNDP：目標(biāo) 公共交通試圖用最低的執(zhí)行成本去扮演一個(gè)非常重要的社會(huì)角色。因?yàn)閳?zhí)行成本的降低通常會(huì)帶來(lái)服務(wù)質(zhì)量的下降，這些目標(biāo)之間往往是相沖突的。 如乘客舒適、中轉(zhuǎn)次數(shù)、利潤(rùn)和運(yùn)輸力最大化、旅行時(shí)間最短化、能耗最小化就是這樣的目標(biāo)。解決 TRNDP的多目標(biāo)模型是基于對(duì)代表不同目標(biāo)的指標(biāo)的計(jì)算，分別從用戶和執(zhí)行者的角度，如對(duì)于用戶的旅行和等待時(shí)間，對(duì)于執(zhí)行者的運(yùn)載能力和執(zhí)行成本。 決定變量 TRNDP 最常見(jiàn)的決定變量是路線和運(yùn)輸頻率（見(jiàn)表 1）。 Chang和 Schonfeld 1983。但是，自十九世紀(jì)八十年代早期起，研究開(kāi)始在為 TRNDP 建模中包括了彈性需求。在一系列的研究中， Chang和 Schonfeld等人把需求估計(jì)為就它們的彈性而言的、旅行時(shí)間和票價(jià)的一個(gè)直接的功能，而 Chien和 Spacovic 則使用同一種方法，假設(shè)需求是被間隔距離、路線分步和票價(jià)影響的。 Spacovic 和 Schonfeld 1994）和公車(chē)種類(lèi)（ Delle Site 和 Filippi 2020）。 Byrne 和Vuchic 1972。相反，Bielli（ 2020）、 Chakroborty（ 2020）、 Dwivedi（ 2020）等人把各指標(biāo)歸納為一個(gè)總體的數(shù)值，作為決定最優(yōu)公交網(wǎng)絡(luò)的依據(jù)。 Baaj 和 Mahmassani 1991。根據(jù) Ceder 和 Wilson(1986)的觀點(diǎn)，總成本或是時(shí)間的最小化，或是消費(fèi)者剩余的最大化，是在建立公交網(wǎng)絡(luò)設(shè)計(jì)模型中最常被選擇的目標(biāo)。理論提倡，在設(shè)計(jì)這樣一個(gè)系統(tǒng)時(shí)，所有研究同時(shí)著眼于服務(wù)和經(jīng)濟(jì)效益。在這一描述上，我們建議 一種為構(gòu)成 TRNDP方法的三層結(jié)構(gòu)（目標(biāo)、標(biāo)準(zhǔn)、方法）。 Ceder 和 Wilson（ 1986）報(bào)告了之前對(duì)于 TRNDP 的研究，并區(qū)分了專注于理想的公交網(wǎng)絡(luò)的研究和專注于實(shí)際路線的研究，同時(shí)提出 TRNDP的主要特點(diǎn)包括了需求特性、目標(biāo)和限制、解決辦法。 Black(1995)和 Vuchic（ 2020）的兩本手冊(cè)描述了供設(shè)計(jì)者在設(shè)計(jì)公交路線網(wǎng)絡(luò)時(shí)遵循的框架，包括：一，為該網(wǎng)絡(luò)設(shè)計(jì)目標(biāo)；二，定義執(zhí)行環(huán)境（馬路結(jié)構(gòu)，需求模式，特點(diǎn)）；三，發(fā)展；四，評(píng)估可選的公交路線網(wǎng)絡(luò)。路線輔設(shè)的設(shè)計(jì)是由客流來(lái)引導(dǎo)的；路線是為產(chǎn)生流動(dòng)需求的地點(diǎn)和 9 地區(qū)間（如住宅和活動(dòng)中心）提供直接和間接的聯(lián)系而建立的（ Levinson 1992）。 Vuchic 2020)。本文系統(tǒng)地呈現(xiàn)和回顧了基于 TRNDP構(gòu)造中三個(gè)不同方面的研究：設(shè)計(jì)目標(biāo)，執(zhí)行環(huán)境因素和解決辦法。 Vaughan 1986), or rectangular grid road works (Hurdle 1973。 Chang and Schonfeld 1991。 Baaj and Mahmassani 1991。 and (6) mod els for simultaneously determining routes and frequencies. Spa covic et al. (1994) and Spacovic and Schonfeld (1994) proposed a matrix organization and classified each study according to design parameters examined, objectives anticipated, work geometry, and demand characteristics. Ceder and Israeli (1997) suggested broad categorizations for TRNDP models into passenger flow simulation and mathematical programming models. Russo (1998) adopted the same categorization and noted that mathematical pro gramming models guarantee optimal transit work design but sacrifice the level of detail in passenger representation and design parameters, while simulation models address passenger behavior but use heuristic procedures obtaining a TRNDP solution. Ceder (2020) enhanced his earlier categorization by classifying TRNDP models into simulation, ideal work, and mathematical pro gramming models. Finally, in a recent series of studies, Fan and Machemehl (2020, 2020a,b) divided TRNDP approaches into practical approaches, analytical optimization models for idealized conditions, and metaheuristic procedures for practical problems. The TRNDP is an optimization problem where objectives are defined, its constraints are determined, and a methodology is se lected and validated for obtaining an optimal solution. The TRNDP is described by the objectives of the public transportation work service to be achieved, the operational characteristics and environment under which the work will operate, and the meth odological approach for obtaining the optimal work design. Based on this description of the TRNDP, we propose a threelayer structure for organizing TRNDP approaches (Objectives, Param eters, and Methodology). Each layer includes one or more items that characterize each study. The “Objectives” layer incorporates the goals set when design ing a public transportation system such as the minimization of the costs of the system or the maximization of the quality of 4 services provided. The “Parameters” layer describes the operating environ ment and includes both the design variables expected to be de rived for the transit work (route layouts, frequencies) as well as environmental and operational parameters affecting and con straining that work (for example, allowable frequencies, de sired load factors, fleet availability, demand characteristics and patterns, and so on). Finally, the “Methodology” layer covers the logical–mathematical framework and algorithmic tools necessary to formulate and solve the T