An Evolutionary Approach to Pickup and Delivery Problem with Time Windows

Abstract

Abstract.Recently, the quality and the diversity of transport services are more and more required. Moreover, in case of a great deal of services and selling goods, a significant part of price is transport cost. Thus, the design of models and applications which make possible efficient transport planning and scheduling becomes important. A great deal of real transport problems may be modelled by using Pickup and Delivery Problem with Time Windows (PDPTW) and capacity constraints, which is based on the realization of a set of transport requests by a fleet of vehicles with given capacities. Each request is described by pickup and delivery locations, time periods when pickup and delivery operations should be performed and needed load. Application of evolutionary approach has brought good results in case of another, simpler transport problem -the Vehicle Routing Problem with Time Windows (VRPTW). This paper is aimed at proposing a straightforward extension of VRPTW based heuristics for the PDPTW.

Solving the biobjective selective pickup and delivery problem with memetic algorithm

“…Moreover, pruning redundancy directly omits unnecessary supply: Instances with large gain values can therefore reach the lower bound of vehicle capacity. The result on n300mosA(277) with γ = 1000 clearly shows that the proposed MOMA achieves the lowest vehicle capacity, while the other nondominated solution provides an alternative 0.958697 [11,634] 0.978473 [101,4414] 0.980050 [1001,42214] n100mosB (92) [3453. 28, 92098.40] 0.956819 [11,708] 0.980140 [101,4938] 0.980820 [1001,47238] n200mosA(181) [5103.02, 184604.00] 0.954380 [11,1400] 0.985135 [101,9860] 0.987543 [1001,94460] n200mosB(184) [5349.50, 187739.00] 0.950454 [11,1371] 0.983216 [101,9291] 0.946123 [11,2131] 0.986288 [101,14821] 0.989920 [1001,141721] n300mosB(279) [6241.38, 286744.00] 0.946382 [11,2123] 0.986773 [101,14543] 0.990090 [1001,138743] n400mosA(358) [7608.35, 373033.00] 0.937040 [11,2678] 0.986653 [101,18158] 0.991664 [1001,172958] n400mosB(364) [7116.25, 372793.00] 0.936453 [13,2792] 0.985734 [101,…”

“…28, 92098.40] 0.956819 [11,708] 0.980140 [101,4938] 0.980820 [1001,47238] n200mosA(181) [5103.02, 184604.00] 0.954380 [11,1400] 0.985135 [101,9860] 0.987543 [1001,94460] n200mosB(184) [5349.50, 187739.00] 0.950454 [11,1371] 0.983216 [101,9291] 0.946123 [11,2131] 0.986288 [101,14821] 0.989920 [1001,141721] n300mosB(279) [6241.38, 286744.00] 0.946382 [11,2123] 0.986773 [101,14543] 0.990090 [1001,138743] n400mosA(358) [7608.35, 373033.00] 0.937040 [11,2678] 0.986653 [101,18158] 0.991664 [1001,172958] n400mosB(364) [7116.25, 372793.00] 0.936453 [13,2792] 0.985734 [101,19262] 0.991015 [1001,183962] n500mosA(453) [7782.54, 471843.00] 0.929813 [11,3538] 0.984752 [101,24418] 0.992336 [1001,233218] n500mosB (454) [8066. 16, 469276.00]…”

“…The substrings are determined by separating the chromosome on transitions from pickup node to delivery node and vice versa in that their respective orders will not affect feasibility and capacity required. the variation of vehicle load, where the transitions are the peaks and valleys in the load plot, e.g., 0 , (1) , (4) , (8) , and (11) . Since the subtotal of demands will keep fixed within a substring, changing its order will not influence the peak and valley values, which are critical to maintain vehicle capacity and solution feasibility.…”

“…Its applications include airlift, dial-a-ride system, discharge of larvicide, etc. Common objectives of minimizing both total travel distance and number of vehicles required are applicable to 1-1 structure [11], [12]. To reflect the needs of real-world scenarios, additional minimization objectives such as customer inconvenience, route duration, waiting time, ride time, and idle time are considered in [13], [14], [15], [16], [17].…”

Single vehicle pickup and delivery with time windows

“…Examples of approximation algorithms for the multiple vehicle case are the evolutionary approach of [2] and the grouping genetic algorithm of [14].…”