Traveling salesman problem: approach to optimality

Jadczak, Radosław

doi:10.2478/eam-2014-0024

Cited by 4 publications

(2 citation statements)

References 3 publications

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“…Moreover, to confirm that the solution obtained by solving the models proposed in this study is truly optimal and unaffected by any mistake in the solver package or programming code, several optimization studies employing the brute-force search method [18][19][20][21] were used as a baseline. The brute-force search method enumerates all possible candidate solutions and then checks whether each candidate satisfies the problem statement.…”

Section: Literature Reviewmentioning

confidence: 99%

Economic Order Picker Routing Considering Travel Time and Vehicular Energy Consumption with Varying Aisle Traffic

Rojanapitoon¹,

Teeravaraprug²

2020

IJIES

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Warehousing can be expensive because order picking requires considerable vehicular movement and labor hours. Although many previous studies have focused on order picker routing, there exists a lack of research on the simultaneous increase of order picking speed and energy reduction in rectangular warehouses with varying levels of traffic in each aisle. This study accordingly developed and evaluated a mathematical model for determining optimal picker routes considering the total travel time and energy consumed. The results were validated using the brute-force search method and benchmarked with the time-staged (TS) model. The energy savings were determined by comparing a time-optimized use-case (T) with one optimized for both time and energy (TE). Both use-cases provided routes up to 44% faster than the TS and avoided more than 50% of congested paths, and TE which represents the full functionality of our model provided a possible energy savings of up to 17% over T.

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Section: Literature Reviewmentioning

confidence: 99%

Economic Order Picker Routing Considering Travel Time and Vehicular Energy Consumption with Varying Aisle Traffic

Rojanapitoon¹,

Teeravaraprug²

2020

IJIES

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“…Transporation is needed to guarantee the mobility of people and goods and as part of the economic system, transportation has an important function in national development [3]. The concept of TSP is described as follows: a salesman or a vehicle has a number of cities to visit with a distance of time between two cities and each city is visited only once (Hamiltonian cycle) and returns to the starting city then the total distance or time is minimized [4,5,6]. Distance is a key factor in transportation.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Optimization Methods for Solving Traveling Salesman Problem

Chandra

Natalia

2021

ITSSI

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The subject of this research is distance and time of several city tour problems which known as traveling salesman problem (tsp). The goal is to find out the gaps of distance and time between two types of optimization methods in traveling salesman problem: exact and approximate. Exact method yields optimal solution but spends more time when the number of cities is increasing and approximate method yields near optimal solution even optimal but spends less time than exact methods. The task in this study is to identify and formulate each algorithm for each method, then to run each algorithm with the same input and to get the research output: total distance, and the last to compare both methods: advantage and limitation. Methods used are Brute Force (BF) and Branch and Bound (B&B) algorithms which are categorized as exact methods are compared with Artificial Bee Colony (ABC), Tabu Search (TS) and Simulated Annealing (SA) algorithms which are categorized as approximate methods or known as a heuristics method. These three approximate methods are chosen because they are effective algorithms, easy to implement and provide good solutions for combinatorial optimization problems. Exact and approximate algorithms are tested in several sizes of city tour problems: 6, 9, 10, 16, 17, 25, 42, and 58 cities. 17, 42 and 58 cities are derived from tsplib: a library of sample instances for tsp; and others are taken from big cities in Java (West, Central, East) island. All of the algorithms are run by MATLAB program. The results show that exact method is better in time performance for problem size less than 25 cities and both exact and approximate methods yield optimal solution. For problem sizes that have more than 25 cities, approximate method – Artificial Bee Colony (ABC) yields better time which is approximately 37% less than exact and deviates 0.0197% for distance from exact method. The conclusion is to apply exact method for problem size that is less than 25 cities and approximate method for problem size that is more than 25 cities. The gap of time will be increasing between two methods when sample size becomes larger.

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