The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

GIS routing and modelling of residential waste collection for operational management and cost optimization

In this paper, optimum routing was developed based on the travel salesman method and integrated in ArcInfo GIS using linear programming. The results of the optimized travel distances and times for residential waste collection and routing to disposal site were used to calculate the number and type of required track collection, labour requirement, costing of waste collection and to determine the overall solid waste management efficiency through waste management operation research methods. The objective of the study was to optimize residential collection and hauling to disposal site through operation cost minimization for Petaling Jaya Municipality in the state of Selangor, Malaysia. The study determined that with optimized routes and recycling possibilities, the total cost of waste collections could be reduced from RM90,372 to RM20,967, with a reduction of 76.8%. It was also revealed that optimum routes might not necessarily be the shortest distance from point A to point B as travel time maybe high on short distances due to traffic congestion and the presence of many traffic lights. Techniques and methods developed using general GIS have proven effective in route optimization and allowed management of data to suit local conditions and limitations of waste management for the studied area. Thus, scenarios of travel distances, time and waste quantity value generated from the GIS enabled appropriate determination of the number of waste trucks and labour requirements for the operation and the overall calculation of costs of waste management based on the operation research methods used in the study

Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be one of the major challenges nowadays. Detailed atomistic mathematical models play an important role towards this aim. In this work it is shown how one can exploit the Equation Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic simulation with coarse-grained, systems-level, analysis. The methodology provides a systematic approach for analyzing the parametric behavior of complex/ multi-scale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based epidemic model deploying on a random regular connected graph. Using the individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level under a pairwise representation perspective

OPTIMIZATION OF SINGLY REINFORCED BEAM DESIGN USING SIMULATED ANNEALING

This paper investigated the optimization of a singly reinforced concrete beam using the simulated annealing. The enhancement of minimum cost of structures and the adoption of the algorithm method of simulated annealing were projected in resolving the complications of constraints associated with optimization problems. The variables are the width, depth, compression steel, tension steel, and cost. The constraints are steel ratios, ultimate moment of resistance, maximum and minimum area of reinforcements while materials costs are considered as the objective function. It is demonstrated that using the concrete compressive strength of 25MPa, simulated annealing can be used to optimize the design of concrete beams effectively. The results also indicate that the complications connected to the actual and genuine evaluation of costs of structures and the connectivity with the compulsory restraints can be adequately resolved using this method

Mobile robotics in agricultural operations: A narrative review on planning aspects

The advent of mobile robots in agriculture has signaled a digital transformation with new automation technologies optimize a range of labor-intensive, resources-demanding, and time-consuming agri-field operations. To that end a generally accepted technical lexicon for mobile robots is lacking as pertinent terms are often used interchangeably. This creates confusion among research and practice stakeholders. In addition, a consistent definition of planning attributes in automated agricultural operations is still missing as relevant research is sparse. In this regard, a “narrative” review was adopted (1) to provide the basic terminology over technical aspects of mobile robots used in autonomous operations and (2) assess fundamental planning aspects of mobile robots in agricultural environments. Based on the synthesized evidence from extant studies, seven planning attributes have been included: (i) high-level control-specific attributes, which include reasoning architecture, the world model, and planning level, (ii) operation-specific attributes, which include locomotion–task connection and capacity constraints, and (iii) physical robot-specific attributes, which include vehicle configuration and vehicle kinematics.</jats:p

A Hybrid MCDM Approach to Transshipment Port Selection

Port selection is an intrinsic supply-chain problem that has substantial impact on development of local economies. Shipping business environment developed into complex system where decision making is derived from uncertain and incomplete data. In this study we present a conceptual integrated Multi-Criteria Decision solution to transshipment port selection problem based on Best-Worst MCDM and Artificial Bee Colony Algorithm. Through literature review and expert analysis, 50 relevant criteria have been identified as relevant to the transshipment port selection problem. Decision makers within liner shipping companies evaluate transshipment port selection criteria and establish ranking that is used to determine crisp solution with lowest consistency ratio. ABC based algorithm is used to reduce computational complexity and deliver a single optimal solution by solving both objective and constraint violation functions