Parameterized Runtime Analyses of Evolutionary Algorithms for the Planar Euclidean Traveling Salesperson Problem

2014 ◽  
Vol 22 (4) ◽  
pp. 595-628 ◽  
Author(s):  
Andrew M. Sutton ◽  
Frank Neumann ◽  
Samadhi Nallaperuma
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Upper Bound ◽  
Domain Knowledge ◽  
Population Based ◽  
Theoretical Understanding ◽  
Traveling Salesperson Problem ◽  
Fitness Evaluation ◽  
Expected Time ◽  
Mutation Strategy

Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound their runtime. We analyze the runtime in dependence of the number of inner points k. In the first part of the paper, we study a [Formula: see text] EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time [Formula: see text] where A is a function of the minimum angle [Formula: see text] between any three points. Based on insights provided by the analysis, we improve this upper bound by introducing a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps. This strategy improves the upper bound to [Formula: see text]. In the second part of the paper, we use the information gained in the analysis to incorporate domain knowledge to design two fixed-parameter tractable (FPT) evolutionary algorithms for the planar Euclidean TSP. We first develop a [Formula: see text] EA based on an analysis by M. Theile, 2009, ”Exact solutions to the traveling salesperson problem by a population-based evolutionary algorithm,” Lecture notes in computer science, Vol. 5482 (pp. 145–155), that solves the TSP with k inner points in [Formula: see text] generations with probability [Formula: see text]. We then design a [Formula: see text] EA that incorporates a dynamic programming step into the fitness evaluation. We prove that a variant of this evolutionary algorithm using 2-opt mutation solves the problem after [Formula: see text] steps in expectation with a cost of [Formula: see text] for each fitness evaluation.

scholarly journals Use of Energy-Based Domain Knowledge as Feedback to Evolutionary Algorithms for the Optimization of Water Distribution Networks

Water ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 3101
Author(s):  
Diego Páez ◽  
Camilo Salcedo ◽  
Alexander Garzón ◽  
María Alejandra González ◽  
Juan Saldarriaga
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Domain Knowledge ◽  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Nsga Ii ◽  
Acceptable Solution ◽  
Capital Costs ◽  
Periodic Feedback

The optimization of water distribution networks (WDN) has evolved, requiring approaches that seek to reduce capital costs and maximize the reliability of the system simultaneously. Hence, several evolutionary algorithms, such as the non-dominated sorting-based multi-objective evolutionary algorithm (NSGA-II), have been widely used despite the high computational costs required to achieve an acceptable solution. Alternatively, energy-based methods have been used to reach near-optimal solutions with reduced computational requirements. This paper presents a method to combine the domain knowledge given by energy-based methods with an evolutionary algorithm, in a way that improves the convergence rate and reduces the overall computational requirements to find near-optimal Pareto fronts (PFs). This method is divided into three steps: parameters calibration, preprocessing of the optimal power use surface (OPUS) results, and periodic feedback using OPUS in NSGA II. The method was tested in four benchmark networks with different characteristics, seeking to minimize the costs of the WDN and maximizing its reliability. Then the results were compared with a generic implementation of NSGA-II, and the performance and quality of the solutions were evaluated using two metrics: hypervolume (HV) and modified inverted generational distance (IGD+). The results showed that the feedback procedure increases the efficiency of the algorithm, particularly the first time the algorithm is retrofitted.

Estimating the Ratios of the Stationary Distribution Values for Markov Chains Modeling Evolutionary Algorithms

2009 ◽  
Vol 17 (3) ◽  
pp. 343-377 ◽  
Author(s):  
Boris Mitavskiy ◽  
Chris Cannings
Keyword(s):  
Stochastic Process ◽  
Population Genetics ◽  
Markov Chain ◽  
Evolutionary Algorithms ◽  
Markov Chains ◽  
Evolutionary Algorithm ◽  
Stationary Distribution ◽  
Genetic Load ◽  
Construction Method ◽  
Expected Time

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When the mutation rate is positive, the Markov chain modeling of an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution. Rather little is known about the stationary distribution. In fact, the only quantitative facts established so far tell us that the stationary distributions of Markov chains modeling evolutionary algorithms concentrate on uniform populations (i.e., those populations consisting of a repeated copy of the same individual). At the same time, knowing the stationary distribution may provide some information about the expected time it takes for the algorithm to reach a certain solution, assessment of the biases due to recombination and selection, and is of importance in population genetics to assess what is called a “genetic load” (see the introduction for more details). In the recent joint works of the first author, some bounds have been established on the rates at which the stationary distribution concentrates on the uniform populations. The primary tool used in these papers is the “quotient construction” method. It turns out that the quotient construction method can be exploited to derive much more informative bounds on ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the three main stages of an evolutionary algorithm: namely, selection, recombination, and mutation.

Analysis of (1+1) Evolutionary Algorithm and Randomized Local Search with Memory

2011 ◽  
Vol 19 (2) ◽  
pp. 287-323 ◽  
Author(s):  
Chi Wan Sung ◽  
Shiu Yin Yuen
Keyword(s):  
Local Search ◽  
Evolutionary Algorithm ◽  
A Priori ◽  
Hash Table ◽  
Mathematical Framework ◽  
Fitness Evaluation ◽  
Multimodal Functions ◽  
Expected Time ◽  
With Memory ◽  
New Algorithms

This paper considers the scenario of the (1+1) evolutionary algorithm (EA) and randomized local search (RLS) with memory. Previously explored solutions are stored in memory until an improvement in fitness is obtained; then the stored information is discarded. This results in two new algorithms: (1+1) EA-m (with a raw list and hash table option) and RLS-m+ (and RLS-m if the function is a priori known to be unimodal). These two algorithms can be regarded as very simple forms of tabu search. Rigorous theoretical analysis of the expected time to find the globally optimal solutions for these algorithms is conducted for both unimodal and multimodal functions. A unified mathematical framework, involving the new concept of spatially invariant neighborhood, is proposed. Under this framework, both (1+1) EA with standard uniform mutation and RLS can be considered as particular instances and in the most general cases, all functions can be considered to be unimodal. Under this framework, it is found that for unimodal functions, the improvement by memory assistance is always positive but at most by one half. For multimodal functions, the improvement is significant; for functions with gaps and another hard function, the order of growth is reduced; for at least one example function, the order can change from exponential to polynomial. Empirical results, with a reasonable fitness evaluation time assumption, verify that (1+1) EA-m and RLS-m+ are superior to their conventional counterparts. Both new algorithms are promising for use in a memetic algorithm. In particular, RLS-m+ makes the previously impractical RLS practical, and surprisingly, does not require any extra memory in actual implementation.

scholarly journals ESTIMATES FROM EVOLUTIONARY ALGORITHMS THEORY APPLIED TO DIRECTED EVOLUTION

2020 ◽  
pp. 56-76
Author(s):  
A. V. Eremeev ◽  
A. V. Spirov
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Dna Sequences ◽  
Upper Bound ◽  
Fitness Function ◽  
Optimization Methods ◽  
Target Area ◽  
Expected Time ◽  
Royal Road ◽  
Expected Hitting Time

The field of evolutionary computation emerged in the area of computer science due to transfer of ideas from biology and developed independently for several decades, enriched with techniques from probability theory, complexity theory and optimization methods. Our aim is to consider how some recent results form the theory of evolutionary computation may be transferred back into biology. It has been noted that the non-elitist evolutionary algorithms optimizing Royal Road fitness functions may be considered as models of evolutionary search for the synthetic enhancer sequences “from scratch”. This problem asks for a tight cluster of supposedly unknown motifs from the initial random (or partially random) set of DNA sequences using SELEX approaches. We apply the upper bounds on the expected hitting time of a target area of genotypic space in order to upper-bound the expected time to finding a sufficiently fit series of motifs in a SELEX procedure. On the other hand, using the theory of evolutionary computation, we propose an upper bound on the expected proportion of the DNA sequences with sufficiently high fitness at a given round of a SELEX procedure. Both approaches are evaluated in computational experiment, using a Royal Road fitness function as a model of the SELEX procedure for regulatory FIS factor binding site.

scholarly journals Evolutionary Algorithm with a Configurable Search Mechanism

2020 ◽  
Vol 10 (3) ◽  
pp. 151-171 ◽  
Author(s):  
Krystian Łapa ◽  
Krzysztof Cpałka ◽  
Łukasz Laskowski ◽  
Andrzej Cader ◽  
Zhigang Zeng
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Population Based ◽  
Exploration And Exploitation ◽  
Problem Domain ◽  
Search Mechanism ◽  
Evolutionary Operator

AbstractIn this paper, we propose a new population-based evolutionary algorithm that automatically configures the used search mechanism during its operation, which consists in choosing for each individual of the population a single evolutionary operator from the pool. The pool of operators comes from various evolutionary algorithms. With this idea, a flexible balance between exploration and exploitation of the problem domain can be achieved. The approach proposed in this paper might offer an inspirational alternative in creating evolutionary algorithms and their modifications. Moreover, different strategies for mutating those parts of individuals that encode the used search operators are also taken into account. The effectiveness of the proposed algorithm has been tested using typical benchmarks used to test evolutionary algorithms.

scholarly journals Drift Analysis and Evolutionary Algorithms Revisited

2018 ◽  
Vol 27 (4) ◽  
pp. 643-666 ◽  
Author(s):  
J. LENGLER ◽  
A. STEGER
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Random Search ◽  
Optimization Algorithms ◽  
Simple Algorithm ◽  
Linear Functions ◽  
Search Point ◽  
Drift Analysis ◽  
Fixed Constant ◽  
Greedy Optimization

One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a function f: {0,1}n → ℝ. The algorithm starts with a random search point ξ ∈ {0,1}n, and in each round it flips each bit of ξ with probability c/n independently at random, where c > 0 is a fixed constant. The thus created offspring ξ' replaces ξ if and only if f(ξ') ≥ f(ξ). The analysis of the runtime of this simple algorithm for monotone and for linear functions turned out to be highly non-trivial. In this paper we review known results and provide new and self-contained proofs of partly stronger results.

scholarly journals An automated system analysis and design tool for spacecrafts ceas space journal

2021 ◽  
Author(s):  
Manfred Ehresmann ◽  
Georg Herdrich ◽  
Stefanos Fasoulas
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Propulsion System ◽  
Optimal System ◽  
Automated System ◽  
Processing Unit ◽  
Data Set ◽  
Analysis And Design

AbstractIn this paper, a generic full-system estimation software tool is introduced and applied to a data set of actual flight missions to derive a heuristic for system composition for mass and power ratios of considered sub-systems. The capability of evolutionary algorithms to analyse and effectively design spacecraft (sub-)systems is shown. After deriving top-level estimates for each spacecraft sub-system based on heuristic heritage data, a detailed component-based system analysis follows. Various degrees of freedom exist for a hardware-based sub-system design; these are to be resolved via an evolutionary algorithm to determine an optimal system configuration. A propulsion system implementation for a small satellite test case will serve as a reference example of the implemented algorithm application. The propulsion system includes thruster, power processing unit, tank, propellant and general power supply system masses and power consumptions. Relevant performance parameters such as desired thrust, effective exhaust velocity, utilised propellant, and the propulsion type are considered as degrees of freedom. An evolutionary algorithm is applied to the propulsion system scaling model to demonstrate that such evolutionary algorithms are capable of bypassing complex multidimensional design optimisation problems. An evolutionary algorithm is an algorithm that uses a heuristic to change input parameters and a defined selection criterion (e.g., mass fraction of the system) on an optimisation function to refine solutions successively. With sufficient generations and, thereby, iterations of design points, local optima are determined. Using mitigation methods and a sufficient number of seed points, a global optimal system configurations can be found.

Co-Evolutionary Algorithm between Helicopter and Submarine

2015 ◽  
Vol 719-720 ◽  
pp. 1229-1235
Author(s):  
Ying Chun Chen ◽  
Xian Hua Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimal Strategy ◽  
Theoretical Foundation ◽  
Optimal Strategies ◽  
Evaluation Methods ◽  
Movement Model ◽  
Fitness Evaluation ◽  
Detection Model ◽  
Ocean Environment

A co-evolutionary algorithm is proposed for the play between a submarine and a helicopter equipped with dipping sonar. First, the theoretical foundation of co-evolution is elaborated. The movement model of helicopter and submarine, the detection model of dipping sonar under certain ocean environment are established. After defining the strategies of helicopter and submarine and fitness evaluation methods, the process of co-evolutionary algorithm is described. The optimal strategy of helicopter after helicopter evolution, and the optimal strategies of both helicopter and submarine after co-evolution are given

Evolutionary Algorithms In Architecture

2011 ◽  
Vol 36 (1) ◽  
pp. 16-24
Author(s):  
Peter Schwehr
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Everyday Life ◽  
Working Model ◽  
Constant Change ◽  
Buckminster Fuller ◽  
High Level

Change is a reliable constant. Constant change calls for strategies in managing everyday life and a high level of flexibility. Architecture must also rise to this challenge. The architect Richard Buckminster Fuller claimed that “A room should not be fixed, should not create a static mood, but should lend itself to change so that its occupants may play upon it as they would upon a piano (Krausse 2001).” This liberal interpretation in architecture defines the ability of a building to react to (ever-) changing requirements. The aim of the project is to investigate the flexibility of buildings using evolutionary algorithms characterized by Darwin. As a working model for development, the evolutionary algorithm consists of variation, selection and reproduction (VSR algorithm). The result of a VSR algorithm is adaptability (Buskes 2008). If this working model is applied to architecture, it is possible to examine as to what extent the adaptability of buildings – as an expression of a cultural achievement – is subject to evolutionary principles, and in which area the model seems unsuitable for the 'open buildings' criteria. (N. John Habraken). It illustrates the significance of variation, selection and replication in architecture and how evolutionary principles can be transferred to the issues of flexible buildings. What are the consequences for the building if it were to be designed and built with the help of evolutionary principles? How can we react to the growing demand for flexibilization of buildings by using evolutionary principles?

Sign in / Sign up

Export Citation Format

Share Document