An interacting replica approach applied to the traveling salesman problem

We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with multiple extrema. Our method involves (i) coupling otherwise independent simulations of a system ("replicas") via geometrical distances as well as (ii) probabilistic inference applied to the solutions found by individual replicas. The {\it ensemble} of replicas evolves as to maximize the inter-replica correlation while simultaneously minimize the local intra-replica cost function (e.g., the total path length in the Traveling Salesman Problem within each replica). We demonstrate how our method improves the performance of rudimentary local optimization schemes long applied to the NP hard Traveling Salesman Problem. In particular, we apply our method to the well-known "$k$-opt" algorithm and examine two particular cases- $k=2$ and $k=3$. With the aid of geometrical coupling alone, we are able to determine for the optimum tour length on systems up to $280$ cities (an order of magnitude larger than the largest systems typically solved by the bare $k=3$ opt). The probabilistic replica-based inference approach improves $k-opt$ even further and determines the optimal solution of a problem with $318$ cities and find tours whose total length is close to that of the optimal solutions for other systems with a larger number of cities.Comment: To appear in SAI 2016 conference proceedings 12 pages,17 figure

Finding the best tour for travelling salesman problem using artificial ecosystem optimization

This paper presents a new method based on the artificial ecosystem optimization (AEO) algorithm for finding the shortest tour of the travelling salesman problem (TSP). Wherein, AEO is a newly developed algorithm based on the idea of the energy flow of living organisms in the ecosystem consisting of production, consumption and decomposition mechanisms. In order to improve the efficiency of the AEO for the TSP problem, the 2-opt movement technique is equipped to enhance the quality of the solutions created by the AEO. The effectiveness of AEO for the TSP problem has been verified on four TSP instances consisting of the 14, 30, 48 and 52 cities. Based on the calculated results and the compared results with the previous methods, the proposed AEO method is one of the effective approaches for solving the TSP problem

A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs

Discrete Flower Pollination Algorithm for solving the symmetric Traveling Salesman Problem

A dissertation submitted in fulfilment of the requirements for the degree of Masters of Science in Engineering (Electrical) to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, 2017The Travelling Salesman Problem (TSP) is an important NP-hard combinatorial optimisation problem that forms the foundation of many modern-day, practical problems such as logistics or network route planning. It is often used to benchmark discrete optimisation algorithms since it is a fundamental problem that has been widely researched. The Flower Pollination Algorithm (FPA) is a continuous optimisation algorithm that demonstrates promising results in comparison to other well-known algorithms. This research proposes the design, implementation and testing of two new algorithms based on the FPA for solving discrete optimisation problems, more specifically the TSP, namely the Discrete Flower Pollination Algorithm (DFPA) and the iterative Discrete Flower Pollination Algorithm (iDFPA). The iDFPA uses two proposed update methods, namely the Best Tour Update (BTU) and the Rejection Update (RU), to perform the iterative update process. The two algorithms are compared to the Ant Colony Optimisation’s (ACO) MAX−MIN Ant System (MMAS) as well as the Genetic Algorithm (GA) since they are well studied and developed. The DFPA and iDFPA results are significantly better than the GA and the iDFPA is able to outperform the ACO in all tested instances. The iDFPA with 300 iterations was able to achieve the optimal solution in the Berlin52 benchmark TSP problem as well as have improvements of up to 4.56% and 41.87% compared to the ACO and GA respectively. An analysis of how the RU and the annealing schedule used in the RU impacts on the overall results of the iDFPA is given. The RU analysis demonstrates how the annealing schedule can be manipulated to achieve certain results from the iDFPA such as faster convergence or better overall results. A parameter analysis is performed on both the DFPA and iDFPA for different TSP problem sizes and the suggested initial parameters for these algorithms are outlined.XL201

Distributed Swarm Formation Using Mobile Agents

This chapter presents decentralized control algorithms for composing formations of swarm robots. The robots are connected by communication networks. They initially do not have control program to compose formations. Control programs that implement our algorithm are introduced later from outside as mobile software agents. Our controlling algorithm is based on the pheromone communication of social insects such as ants. We have implemented the ant and the pheromone as mobile software agents. Ant agents control the robots. Each ant agent has partial information about the formation it is supposed to compose. The partial information consists of relative locations with neighbor robots that are cooperatively composing the formation. Once the ant agent detects an idle robot, it occupies that robot and generates the pheromone agent to attract other ant agents to the location for neighbor robots. Then the pheromone agent repeatedly migrates to other robots to diffuse attracting information. Once the pheromone agent reaches the robot with an ant agent, the ant agent migrates to the robot closest to the location pointed by the pheromone agent and then drives the robot to the location. We have implemented simulators based on our algorithm and conducted experiments to demonstrate the feasibility of our approach

Ant Colony Optimization With Local Search for Dynamic Traveling Salesman Problems

For a dynamic traveling salesman problem (DTSP), the weights (or traveling times) between two cities (or nodes) may be subject to changes. Ant colony optimization (ACO) algorithms have proved to be powerful methods to tackle such problems due to their adaptation capabilities. It has been shown that the integration of local search operators can significantly improve the performance of ACO. In this paper, a memetic ACO algorithm, where a local search operator (called unstring and string) is integrated into ACO, is proposed to address DTSPs. The best solution from ACO is passed to the local search operator, which removes and inserts cities in such a way that improves the solution quality. The proposed memetic ACO algorithm is designed to address both symmetric and asymmetric DTSPs. The experimental results show the efficiency of the proposed memetic algorithm for addressing DTSPs in comparison with other state-of-the-art algorithms

Particle swarm optimization for cooperative multi-robot task allocation: a multi-objective approach

This paper presents a new Multi-Objective Particle Swarm Optimization (MOPSO) approach to a Cooperative Multi Robot Task Allocation (CMRTA) problem, where the robots have to minimize the total team cost and, additionally, balance their workloads. We formulate the CMRTA problem as a more complex variant of multiple Travelling Salesman Problems (mTSP) and, in particular, address how to minimize the total travel distance of the entire robot team, as well as how to minimize the highest travel distance of an individual robot. The proposed approach extends the standard single-objective Particle Swarm Optimization (PSO) to cope with the multiple objectives, and its novel feature lies in a Pareto front refinement strategy and a probability-based leader selection strategy. To validate the proposed approach, we first use three benchmark functions to evaluate the performance of finding the true Pareto fronts in comparison with four existing well-known algorithms in continuous spaces. Afterwards, we use six datasets to investigate the task allocation mechanisms in dealing with the CMRTA problem in discrete spaces.benchmark functions to evaluate the performance of findingthe true Pareto fronts in comparison with four existing wellknownalgorithms in continuous spaces. Afterwards, we use sixdatasets to investigate the task allocation mechanisms in dealingwith the CMRTA problem in discrete spaces

The Application of Ant Colony Optimization

The application of advanced analytics in science and technology is rapidly expanding, and developing optimization technics is critical to this expansion. Instead of relying on dated procedures, researchers can reap greater rewards by utilizing cutting-edge optimization techniques like population-based metaheuristic models, which can quickly generate a solution with acceptable quality. Ant Colony Optimization (ACO) is one the most critical and widely used models among heuristics and meta-heuristics. This book discusses ACO applications in Hybrid Electric Vehicles (HEVs), multi-robot systems, wireless multi-hop networks, and preventive, predictive maintenance

Flexible protein folding by ant colony optimization

Protein structure prediction is one of the most challenging topics in bioinformatics. As the protein structure is found to be closely related to its functions, predicting the folding structure of a protein to judge its functions is meaningful to the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice model. Different from the previous ant algorithms for PFPs, the pheromones in the proposed algorithm are placed on the arcs connecting adjacent squares in the lattice. Such pheromone placement model is similar to the one used in the traveling salesmen problems (TSPs), where pheromones are released on the arcs connecting the cities. Moreover, the collaboration of effective heuristic and pheromone strategies greatly enhances the performance of the algorithm so that the algorithm can achieve good results without local search methods. By testing some benchmark two-dimensional hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed algorithm is quite competitive compared with some other well-known methods for solving the same protein folding problems

OPERATIONAL PLANNING AND OPTIMIZATION OF SMALL DOMAIN SWARM DEFENSE STRATEGIES

This thesis considers the case of a drone defending a high-value target from a number of inbound attacking drones. The defending drone is equipped with short-range weapons and must destroy each of the attacking drones in the most efficient manner. This problem sits at the intersection of several open problems in applied mathematics, such as optimal motion planning in the presence of attrition, as well as solving a “traveling salesman problem” (TSP) with moving targets. The purpose of our research was to analyze this problem by decomposing it into the component problems and then presenting proof-of-concept solutions of each component. The primary results of this thesis include a modeling framework where optimization can be performed without requiring constraints; comparing the strengths of using different types of cost functions for optimization (e.g., minimizing the chance of high-value unit destruction versus a metric based on the path of the defender relative to attackers); and solving moving-target TSP in certain limits by mapping it onto standard TSP or using machine learning.Cruiser/ONRMajor, United States Marine CorpsApproved for public release. Distribution is unlimited