Ant colony optimization with direct communication for the traveling salesman problem

This article is posted here with permission from IEEE - Copyright @ 2010 IEEEAnts in conventional ant colony optimization (ACO) algorithms use pheromone to communicate. Usually, this indirect communication leads the algorithm to a stagnation behaviour, where the ants follow the same path from early stages. This occurs because high levels of pheromone are developed, which force the ants to follow the same corresponding trails. As a result, the population gets trapped into a local optimum solution which is difficult to escape from it. In this paper, a direct communication (DC) scheme is proposed where ants are able to exchange cities with other ants that belong to their communication range. Experiments show that the DC scheme delays convergence and improves the solution quality of conventional ACO algorithms regarding the traveling salesman problem, since it guides the population towards the global optimum solution. The ACO algorithm with the proposed DC scheme has better performance, especially on large problem instances, even though it increases the computational time in comparison with a conventional ACO algorithm

Exact Markov Chain-based Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax

Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain "easy" reference problems in a black-box setting, namely the sorting problem and the problem OneMAX. In our analysis we use a Markov-model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov-model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration

A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization

This thesis introduces the novel hybrid algorithm DisCOptER for globally optimal flight planning. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) com- bines discrete and continuous optimization in a two-stage approach to find optimal trajectories up to arbitrary precision in finite time. In the discrete phase, a directed auxiliary graph is created in order to define a set of candidate paths that densely covers the relevant part of the trajectory space. Then, Yen’s algorithm is employed to identify a set of promising candidate paths. These are used as starting points for the subsequent stage in which they are refined with a locally convergent optimal control method. The correctness, accuracy, and complexity of DisCOptER are intricately linked to the choice of the switch-over point, defined by the discretization coarseness. Only a sufficiently dense graph enables the algorithm to find a path within the convex domain surrounding the global minimizer. Initialized with such a path, the second stage rapidly converges to the optimum. Conversely, an excessively dense graph poses the risk of overly costly and redundant computations. The determination of the optimal switch-over point necessitates a profound understanding of the local behavior of the problem, the approximation properties of the graph, and the convergence characteristics of the employed optimal control method. These topics are explored extensively in this thesis. Crucially, the density of the auxiliary graph is solely dependent on the en- vironmental conditions, yet independent of the desired solution accuracy. As a consequence, the algorithm inherits the superior asymptotic convergence properties of the optimal control stage. The practical implications of this computational efficiency are demonstrated in realistic environments, where the DisCOptER algorithm consistently delivers highly accurate globally optimal trajectories with exceptional computational efficiency. This notable improvement upon existing approaches underscores the algorithm’s significance. Beyond its technical prowess, the DisCOptER algorithm stands as a valuable tool contributing to the reduction of costs and the overall enhancement of flight operations efficiency.In dieser Dissertation wird der neuartige hybride Algorithmus DisCOptER für global optimale Flugplanung vorgestellt. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) verbindet diskrete und kontinuierliche Optimierung in einem zweistufigen Ansatz um optimale Trajektorien unter strengen Genauigkeitsanforderungen in endlicher Zeit zu finden. Im ersten Schritt wird ein gerichteter Graph erzeugt und damit implizit eine Menge potentieller Pfade definiert, die den relevanten Teil des Trajektorienraumes gleichmäßig abdeckt. Vielversprechende Kandidaten werden mithilfe von Yen’s Algorithmus identifiziert. Diese dienen als Startpunkte für die zweite Stufe, in welcher lokal konvergente Methoden der Optimalsteuerung eingesetzt werden um kontinuierliche Lösungen zu generieren. Die Korrektheit, Genauigkeit und Komplexität der DisCOptER Methode sind untrennbar verknüpft mit der Wahl des Umschaltpunktes, definiert durch die Dichte des Graphen. Nur auf einem ausreichend dichten Graphen kann ein Pfad gefunden werden, der innerhalb des Konvergenzbereichs um ein globales Optimum liegt. Ausgehend von einem solchen Pfad konvergiert die zweite Stufe schnell zum Optimum. Demgegenüber birgt ein übermäßig dichter Graph das Risiko für aufwändige und redundante Berechnungen. Die Identifikation dieses Umschaltpunktes verlangt nach einem tiefgehenden Verständnis des lokalen Problemverhaltens, der Approximationseigenschaften des benutzten Graphen, sowie der Konvergenzeigenschaften der eingesetzten kontinuier- lichen Optimierungsmethode. Diese Aspekte werden in der vorliegenden Arbeit ausführlich untersucht. Eine zentrale Stärke des vorgestellten diskret-kontinuierlichen Ansatzes ist, dass die nötige Graphendichte ausschließlich von den Umgebungsbedingungen, jedoch nicht von der geforderten Lösungsgüte, abhängt. Dies hat zur Folge, dass asymptotisch die vorteilhaften Konvergenzeigenschaften der kontinuierlichen Op- timierung beibehalten werden. Die Effizienz der vorgestellten Methode wird unter realistischen Bedingungen praktisch nachgewiesen. Es wird demonstriert, dass der DisCOptER Algorithmus mit minimalem Aufwand konsistent hochpräzise global optimale Lösungen erzielt und so einen doppelten Vorteil im Vergleich zu bestehenden Methoden bietet. Einerseits wird eine gesteigerte algorithmische Effizienz erreicht. Andererseits trägt die verbesserte Qualität der Trajektorien wesentlich dazu bei, den Luftfahrtsektor effizienter und umweltfreundlicher zu gestalten

A comparative study of metaheuristic algorithms for the fertilizer optimization problem

Hard combinatorial optimization (CO) problems pose challenges to traditional algorithmic solutions. The search space usually contains a large number of local optimal points and the computational cost to reach a global optimum may be too high for practical use. In this work, we conduct a comparative study of several state-of-the-art metaheuristic algorithms for hard CO problems solving. Our study is motivated by an industrial application called the Fertilizer Blends Optimization. We focus our study on a number of local search metaheuristics and analyze their performance in terms of both runtime efficiency and solution quality. We show that local search granularity (move step size) and the downhill move probability are two major factors that affect algorithm performance, and we demonstrate how experimental tuning work can be applied to obtain good performance of the algorithms. Our empirical result suggests that the well-known Simulated Annealing (SA) algorithm showed the best performance on the fertilizer problem. The simple Iterated Improvement Algorithm (IIA) also performed surprisingly well by combining strict uphill move and random neighborhood selection. A novel approach, called Delivery Network Model (DNM) algorithm, was also shown to be competitive, but it has the disadvantage of being very sensitive to local search granularity. The constructive local search method (GRASP), which combines heuristic space sampling and local search, outperformed IIA without a construction phase; however, the improvement in performance is limited and generally speaking, local search performance is not sensitive to initial search positions in our studied fertilizer problem

Determination of optimal tool path in drilling operation using Modified Shuffled Frog Leaping Algorithm

Applications like boilerplates, food-industry processing separator, printed circuit boards, drum and trammel screens, etc. consists of a matrix of a large number of holes. The primary issue involved in hole-making operations is a tool travel time. It is often necessary to find the optimal sequence of operations so that the total processing cost of hole-making operations can be minimized. In this work, therefore an attempt is made to reduce the total tool travel of hole-making operations by applying a relatively new optimization algorithm known as modified shuffled frog leaping for determining the optimal sequence of operations. Modification is made in the existing shuffled frog-leaping algorithm by introducing three parameters with their positive values to widen the search capability of existing algorithms. A case study of the printed circuit board is considered in this work to demonstrate the proposed approach. Obtained results of optimization using modified shuffled frog leaping algorithm are compared with those obtained using particle swarm optimization, firefly algorithm and shortest path search algorithm

The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms

Evolutionary algorithms (EAs), a large class of general purpose optimization algorithms inspired from the natural phenomena, are widely used in various industrial optimizations and often show excellent performance. This paper presents an attempt towards revealing their general power from a statistical view of EAs. By summarizing a large range of EAs into the sampling-and-learning framework, we show that the framework directly admits a general analysis on the probable-absolute-approximate (PAA) query complexity. We particularly focus on the framework with the learning subroutine being restricted as a binary classification, which results in the sampling-and-classification (SAC) algorithms. With the help of the learning theory, we obtain a general upper bound on the PAA query complexity of SAC algorithms. We further compare SAC algorithms with the uniform search in different situations. Under the error-target independence condition, we show that SAC algorithms can achieve polynomial speedup to the uniform search, but not super-polynomial speedup. Under the one-side-error condition, we show that super-polynomial speedup can be achieved. This work only touches the surface of the framework. Its power under other conditions is still open

Adjustability of a discrete particle swarm optimization for the dynamic TSP

This paper presents a detailed study of the discrete particle swarm optimization algorithm (DPSO) applied to solve the dynamic traveling salesman problem which has many practical applications in planning, logistics and chip manufacturing. The dynamic version is especially important in practical applications in which new circumstances, e.g., a traffic jam or a machine failure, could force changes to the problem specification. The DPSO algorithm was enriched with a pheromone memory which is used to guide the search process similarly to the ant colony optimization algorithm. The paper extends our previous work on the DPSO algorithm in various ways. Firstly, the performance of the algorithm is thoroughly tested on a set of newly generated DTSP instances which differ in the number and the size of the changes. Secondly, the impact of the pheromone memory on the convergence of the DPSO is investigated and compared with the version without a pheromone memory. Moreover, the results are compared with two ant colony optimization algorithms, namely the (Formula presented.)–(Formula presented.) ant system (MMAS) and the population-based ant colony optimization (PACO). The results show that the DPSO is able to find high-quality solutions to the DTSP and its performance is competitive with the performance of the MMAS and the PACO algorithms. Moreover, the pheromone memory has a positive impact on the convergence of the algorithm, especially in the face of dynamic changes to the problem’s definition

Data-Driven Predictive Modeling to Enhance Search Efficiency of Glowworm-Inspired Robotic Swarms in Multiple Emission Source Localization Tasks

In time-sensitive search and rescue applications, a team of multiple mobile robots broadens the scope of operational capabilities. Scaling multi-robot systems (\u3c 10 agents) to larger robot teams (10 – 100 agents) using centralized coordination schemes becomes computationally intractable during runtime. One solution to this problem is inspired by swarm intelligence principles found in nature, offering the benefits of decentralized control, fault tolerance to individual failures, and self-organizing adaptability. Glowworm swarm optimization (GSO) is unique among swarm-based algorithms as it simultaneously focuses on searching for multiple targets. This thesis presents GPR-GSO—a modification to the GSO algorithm that incorporates Gaussian Process Regression (GPR) based data-driven predictive modeling—to improve the search efficiency of robotic swarms in multiple emission source localization tasks. The problem formulation and methods are presented, followed by numerical simulations to illustrate the working of the algorithm. Results from a comparative analysis show that the GPR-GSO algorithm exceeds the performance of the benchmark GSO algorithm on evaluation metrics of swarm size, search completion time, and travel distance