As automatic optimization techniques find their way into industrial applications, the behavior of many complex systems is determined by some form of planner picking the right actions to optimize a given objective function. In many cases, the mapping of plans to objective reward may change due to unforeseen events or circumstances in the real world. In those cases, the planner usually needs some additional effort to adjust to the changed situation and reach its previous level of performance. Whenever we still need to continue polling the planner even during re-planning, it oftentimes exhibits severely lacking performance. In order to improve the planner's resilience to unforeseen change, we argue that maintaining a certain level of diversity amongst the considered plans at all times should be added to the planner's objective. Effectively, we encourage the planner to keep alternative plans to its currently best solution. As an example case, we implement a diversity-aware genetic algorithm using two different metrics for diversity (differing in their generality) and show that the blow in performance due to unexpected change can be severely lessened in the average case. We also analyze the parameter settings necessary for these techniques in order to gain an intuition how they can be incorporated into larger frameworks or process models for software and systems engineering.
The author of @cite_27 describes a problem setting not unlike the one presented in this paper, i.e., the combination of maintaining diversity and searching in a changing environment. The issue of premature convergence is tackled by integrating a certain amount of random search into the genetic algorithm by performing hyper-mutation. This has since become standard procedure and is included in all genetic algorithms presented in this paper, which aims to further improve the resilience of the search process.
@cite_27
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Abstract The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability scheme is utilized to balance the global exploration and local exploitation. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and or premature convergence. Numerical experiments and comparisons on a set of well-known high dimensional benchmark functions indicate that the improved algorithm outperforms and is superior to other existing algorithms in terms of final solution quality, success rate, convergence rate, and robustness. This paper considers a new variant of the two-dimensional bin packing problem where each rectangle is assigned a due date and each bin has a fixed processing time. Hence the objective is not only to minimize the number of bins, but also to minimize the maximum lateness of the rectangles. This problem is motivated by the cutting of stock sheets and the potential increased efficiency that might be gained by drawing on a larger pool of demand pieces by mixing orders, while also aiming to ensure a certain level of customer service. We propose a genetic algorithm for searching the solution space, which uses a new placement heuristic for decoding the gene based on the best fit heuristic designed for the strip packing problems. The genetic algorithm employs an innovative crossover operator that considers several different children from each pair of parents. Further, the dual objective is optimized hierarchically with the primary objective periodically alternating between maximum lateness and number of bins. As a result, the approach produces several non-dominated solutions with different trade-offs. Two further approaches are implemented. One is based on a previous Unified Tabu Search, suitably modified to tackle this revised problem. The other is randomized descent and serves as a benchmark for comparing the results. Comprehensive computational results are presented, which show that the Unified Tabu Search still works well in minimizing the bins, but the genetic algorithm performs slightly better. When also considering maximum lateness, the genetic algorithm is considerably better. A key search mechanism in Evolutionary Algorithms is the mixing or juxtaposing of partial solutions present in the parent solutions. In this paper we look at the efficiency of mixing in genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). We compute the mixing probabilities of two partial solutions and discuss the effect of the covariance build-up in GAs and EDas. Moreover, we propose two new Evolutionary Algorithms that maximize the juxtaposing of the partial solutions present in the parents: the Recombinative Optimal Mixing Evolutionary Algorithm (ROMEA) and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). Genetic algorithms perform an adaptive search by maintaining a population of candidate solutions that are allocated dynamically to promising regions of the search space. The distributed nature of the genetic search provides a natural source of power for searching in changing environments. As long as sufficient diversity remains in the population the genetic algorithm can respond to a changing response surface by reallocating future trials. However, the tendency of genetic algorithms to converge rapidly reduces their ability to identify regions of the search space that might suddenly become more attractive as the environment changes. This paper presents a modification of the standard generational genetic algorithm that is designed to maintain the diversity required to track a changing response surface. An experimental study shows some promise for the new technique. As one of the popular evolutionary algorithms, differential evolution (DE) shows outstanding convergence rate on continuous optimization problems. But prematurity probably still occurs in classical DE when using relatively small population, which is discussed in this paper. Considering that large population may significantly raise the computational effort, we propose a modified DE using smaller population (DESP) by introducing extra disturbance to its mutation operation. In addition, an adaptive adjustment scheme is designed to control the disturbance intensity according to the improvement during the evolution. To test the performance of DESP, two groups of experiments are conducted. The results show that DESP outperforms DE in terms of convergence rate and accuracy. This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of building-block fitness or so-called collateral noise is the major source of variance, and a population-sizing equation is derived to ensure that average signal-to-collateral-noise ratios are favorable to the discrimination of the best building blocks required to solve a problem of bounded deception. The sizing relation is modified to permit the inclusion of other sources of stochasticity, such as the noise of selection, the noise of genetic operators, and the explicit noise or nondeterminism of the objective function. In a test suite of five functions, the sizing relation proves to be a conservative predictor of average correct convergence, as long as all major sources of noise are considered in the sizing calculation. These results suggest how the sizing equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior. At low population sizes the GA makes many errors of decision, and the quality of convergence is largely left to the vagaries of chance or the serial fixup of flawed results through mutation or other serial injection of diversity. At large population sizes, GAs can reliably discriminate between good and bad building blocks, and parallel processing and recombination of building blocks lead to quick solution of even difficult deceptive problems. Additionally, the paper outlines a number of extensions to this work, including the development of more refined models of the relation between generational average error and ultimate convergence quality, the development of online methods for sizing populations via the estimation of populations via the estimation of population-sizing parameters, and the investigation of populationsizing in the context of niching and other schemes designed for use in problems with high cardinality solution sets. The paper also discusses how these results may one day lead to rigorous proofs of convergence for recombinative G As operating on problems of bounded description. This paper presents a new algorithm based on integrating genetic algorithms, tabu search and simulated annealing methods to solve the unit commitment problem. The core of the proposed algorithm is based on genetic algorithms. Tabu search is used to generate new population members in the reproduction phase of the genetic algorithm. A simulated annealing method is used to accelerate the convergence of the genetic algorithm by applying the simulated annealing test for all the population members. A new implementation of the genetic algorithm is introduced. The genetic algorithm solution is coded as a mix between binary and decimal representation. The fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the proposed algorithm, a simple short-term memory procedure is used to counter the danger of entrapment at a local optimum, and the premature convergence of the genetic algorithm. A simple cooling schedule has been implemented to apply the simulated annealing test in the algorithm. Numerical results showed the superiority of the solutions obtained compared to genetic algorithms, tabu search and simulated annealing methods, and to two exact algorithms. Mutation operators such as Gaussian, Levy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests. The differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. In contrast, micro-DE (MDE) algorithms employ a very small population size, which can converge faster to a reasonable solution. However, these algorithms are vulnerable to a premature convergence as well as to high risk of stagnation. In this paper, MDE algorithm with vectorized random mutation factor (MDEVM) is proposed, which utilizes the small size population benefit while empowers the exploration ability of mutation factor through randomizing it in the decision variable level. The idea is supported by analyzing mutation factor using Monte-Carlo based simulations. To facilitate the usage of MDE algorithms with very-small population sizes, new mutation schemes for population sizes less than four are also proposed. Furthermore, comprehensive comparative simulations and analysis on performance of the MDE algorithms over various mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, and mutation factor ranges are conducted by considering population diversity analysis for stagnation and trapping in local optimum situations. The studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance and convergence speed of the proposed MDEVM algorithm. In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments. This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity. Abstract The optimal bucket order problem consists in obtaining a complete consensus ranking (ties are allowed) from a matrix of preferences (possibly obtained from a database of rankings). In this paper, we tackle this problem by using ( 1 + λ ) evolution strategies. We designed specific mutation operators which are able to modify the inner structure of the buckets, which introduces more diversity into the search process. We also study different initialization methods and strategies for the generation of the population of descendants. The proposed evolution strategies are tested using a benchmark of 52 databases and compared with the current state-of-the-art algorithm LIA G M P 2 . We carry out a standard machine learning statistical analysis procedure to identify a subset of outstanding configurations of the proposed evolution strategies. The study shows that the best evolution strategy improves upon the accuracy obtained by the standard greedy method (BPA) by 35 , and that of LIA G M P 2 by 12.5 . By synthesizing a growing body ofwork in search processes that are not driven by explicit objectives, this paper advances the hypothesis that there is a fundamental problem with the dominant paradigm of objective-based search in evolutionary computation and genetic programming: Most ambitious objectives do not illuminate a path to themselves. That is, the gradient of improvement induced by ambitious objectives tends to lead not to the objective itself but instead to deadend local optima. Indirectly supporting this hypothesis, great discoveries often are not the result of objective-driven search. For example, the major inspiration for both evolutionary computation and genetic programming, natural evolution, innovates through an open-ended process that lacks a final objective. Similarly, large-scale cultural evolutionary processes, such as the evolution of technology, mathematics, and art, lack a unified fixed goal. In addition, direct evidence for this hypothesis is presented from a recently-introduced search algorithm called novelty search. Though ignorant of the ultimate objective of search, in many instances novelty search has counter-intuitively outperformed searching directly for the objective, including a wide variety of randomly-generated problems introduced in an experiment in this chapter. Thus a new understanding is beginning to emerge that suggests that searching for a fixed objective, which is the reigning paradigm in evolutionary computation and even machine learning as a whole, may ultimately limit what can be achieved. Yet the liberating implication of this hypothesis argued in this paper is that by embracing search processes that are not driven by explicit objectives, the breadth and depth of what is reachable through evolutionary methods such as genetic programming may be greatly expanded. This paper presents algorithm for optimal reconfiguration of distribution networks using hybrid heuristic genetic algorithm. Improvements introduced in this approach make it suitable for real-life networks with realistic degree of complexity and network size. The algorithm introduces several improvements related to the generation of initial set of possible solutions as well as crossover and mutation steps in genetic algorithm. Since the genetic algorithms are often used in distribution network reconfiguration problem, its application is well known, but most of the approaches have very poor effectiveness due to high level of individuals' rejections not-fulfilling radial network constraints requirements and poor convergence rate. One part of these problems is related to ineffective creation of initial population individuals. The other part of the problem in similar approaches is related to inefficient operators implemented in crossover and mutation process over created set of population individuals. The hybrid heuristic-genetic approach presented in this paper provides significant improvements in these areas. The presented algorithm can be used to find optimal radial distribution network topology with minimum network losses or with optimally balanced network loading. The algorithm is rested on a real size network of city of Dubrovnik to identify the optimal network topology after the interpolation (connection) of a new supply point. As an important coordination and cooperation mechanism in multi-agent systems, coalition of agents exhibits some excellent characteristics and draws researchers' attention increasingly. Cooperation formation has been a very active area of research in multi-agent systems. An efficient algorithm is needed for this topic since the numbers of the possible coalitions are exponential in the number of agents. Genetic algorithm (GA) has been widely reckoned as a useful tool for obtaining high quality and optimal solutions for a broad range of combinatorial optimization problems due to its intelligent advantages of self-organization, self-adaptation and inherent parallelism. This paper proposes a GA-based algorithm for coalition structure formation which aims at achieving goals of high performance, scalability, and fast convergence rate simultaneously. A novel 2D binary chromosome encoding approach and corresponding crossover and mutation operators are presented in this paper. Two valid parental chromosomes are certain to produce a valid offspring under the operation of the crossover operator. This improves the efficiency and shortens the running time greatly. The proposed algorithm is evaluated through a robust comparison with heuristic search algorithms. We have confirmed that our new algorithm is robust, self-adaptive and very efficient by experiments. The results of the proposed algorithm are found to be satisfactory. The best achievable convergence rates of mutation-based evolutionary algorithms are known for various characteristic test problems. Most results are available for convex quadratic functions with Hessians of full rank. Here, we prove that linear convergence rates are achievable for convex quadratic functions even though the Hessians are rank-deficient. This result has immediate implications for recent convergence results for certain evolutionary algorithms for bi-objective optimization problems. Abstract This paper considers the problem of adaptively searching for an unknown target using multiple agents connected through a time-varying network topology. Agents are equipped with sensors capable of fast information processing, and we propose a decentralized collaborative algorithm for controlling their search given noisy observations. Specifically, we propose decentralized extensions of the adaptive query-based search strategy that combines elements from the 20 questions approach and social learning. Under standard assumptions on the time-varying network dynamics, we prove convergence to correct consensus on the value of the parameter as the number of iterations go to infinity. The convergence analysis takes a novel approach using martingale-based techniques combined with spectral graph theory. Our results establish that stability and consistency can be maintained even with one-way updating and randomized pairwise averaging, thus providing a scalable low complexity method with performance guarantees. We illustrate the effectiveness of our algorithm for random network topologies. This paper presents a parallel algorithm for fast word search to determine the set of biological words of an input DNA sequence. The algorithm is designed to scale well on state-of-the-art multiprocessor multicore systems for large inputs and large maximum word sizes. The pattern exhibited by many sequential solutions to this problem is a repetitive execution over a large input DNA sequence, and the generation of large amounts of output data to store and retrieve the words determined by the algorithm. As we show, this pattern does not lend itself to straightforward standard parallelization techniques. The proposed algorithm aims to achieve three major goals to overcome the drawbacks of embarrassingly parallel solution techniques: (i) to impose a high degree of cache locality on a problem that, by nature, tends to exhibit nonlocal access patterns, (ii) to be lock free or largely reduce the need for data access locking, and (iii) to enable an even distribution of the overall processing load among multiple threads. We present an implementation and performance evaluation of the proposed algorithm on DNA sequences of various sizes for different organisms on a dual processor quad-core system with a total of 8 cores. We compare the performance of the parallel word search implementation with a sequential implementation and with an embarrassingly parallel implementation. The results show that the proposed algorithm far outperforms the embarrassingly parallel strategy and achieves a speed-up's of up to 6.9 on our 8-core test system. We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems. Practical optimization problems frequently include uncertainty about the quality measure, for example due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling. In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally we show that a simple EDA called the Compact Genetic Algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property. This extended abstract summarizes our work "The Benefit of Recombination in Noisy Evolutionary Search," which appeared in Proceedings of International Symposium on Algorithms and Computation (ISAAC), 2015, pp. 140--150.