Multi-performance based computational model for the cuboid open traveling salesman problem in a smart floating city

Abstract

The term ?smart city? has been emerged as a novel solution to uphold the useless urban areas and the term has taken the advantage of sustainable and environmental resources. On the other hand the term ?floating city? has been studied for just only a few years as alternative living spaces for humanity across the world since land scarcity has already begun. Therefore in this research we propose multi-objective optimization algorithms to obtain the Pareto front solutions for the cuboid open traveling salesman problem (COTSP) in a ?smart floating city? context. Given n nodes and the distances between each pair of nodes the COTSP in this paper aims to find the shortest possible tour with a traveling distance that starts from the depot (i.e. node 1) and visits each node exactly once without needing to return to the depot. As known a cuboid has height length and depth and the COTSP defines its x y z coordinates as a cuboid corresponding to height length and depth. In addition to the traveling distance the platform (building breakwaters) cost is measured by the z coordinates (depths) of the nodes/platforms that represent both the platforms below the sea level. Note that unlike the traditional TSP it has a variable seed number and a variable number of nodes/platforms in each solution. The paper aims to find the Pareto front solutions by minimizing the traveling distance and platform cost of the infrastructures below the sea level simultaneously. We develop a multi-objective self-adaptive differential evolution (MOJDE) algorithm a nondominated sorting genetic algorithm (NSGAII) and a harmony search (MOHS) algorithm to solve the problem in such a way that we minimize the traveling distance while minimizing the platform cost simultaneously. All algorithms are compared to each other. The computational results show that the MOJDE and NSGAII algorithms outperform the MOHS algorithm in terms of commonly used performance measures from the literature.