Closest Substring Problem – Results from an Evolutionary Algorithm

Engineered Conditioning (EC) is a Genetic Algorithm operator that works together with the typical genetic algorithm operators: mate selection, crossover, and mutation, in order to improve convergence toward an optimal multiple fault diagnosis. When incorporated within a typical genetic algorithm, the resulting hybrid scheme produces improved reliability by exploiting the global nature of the genetic algorithm as well as “local” improvement capabilities of the Engineered Conditioning operator.

Genetic algorithms have demonstrated considerable success in providing good solutions to many NP-hard optimization problems. For such problems, exact algorithms that always find an optimal solution are only useful for small toy problems, so heuristic algorithms such as the genetic algorithm must be used in practice. In this paper, we apply the genetic algorithm to the NP-hard problem of multiple fault diagnosis (MFD). We compare a pure genetic algorithm with several variants that include local improvement operators. These operators, which are often domain-specific, are used to accelerate the genetic algorithm in converging on optimal solutions. Our empirical results indicate that by using the appropriate local improvement operator, the genetic algorithm is able to find an optimal solution in all but a tiny fraction of the cases and at a speed orders of magnitude faster than exact algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Embedding sensitivity theory in ordinal optimization for decentralized optimal power flow control

In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easy-to-apply approach designed particularly for population-based EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the so-called (N + N) EAs and we show that, on two well-known unimodal problems, leadingones and onemax , the EAs with the bitwise mutation and two commonly used selection schemes both need O(n ln n + n(2)/N) and O(n ln ln n + n ln n/N) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some population-based EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problem-specific knowledge to get the tight bounds. It is the first time a general idea for analyzing population-based EAs on unimodal problems is discussed theoretically.

Genetic algorithm for the personnel assignment problem with multiple objectives

Optimal scheduling of distributed control manufacturing systems using genetic algorithms

The Closest Substring problem (CSP), where a short string is sought that minimizes the number of mismatches between it and each of a given set of strings, is a minimization problem with polynomial time approximation schemes. In this paper, a lower bound on approximation algorithms for the CSP problem is developed. We prove that unless the Exponential Time Hypothesis (ETH Hypothesis, i.e., not all search problems in SNP are solvable in subexponential time) fails, the CSP problem has no polynomial time approximation schemes of running time f(1/Ɛ)|x|O(1/Ɛ) for any function f, where |x| is the size of input instance. This essentially excludes the possibility that the CSP problem has a practical polynomial time approximation scheme even for moderate values of the error bound Ɛ. As a consequence, it is unlikely that the study of approximation schemes for the CSP problem in the literature would lead to practical approximation algorithms for the CSP problem for small error bound Ɛ.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.

Artificial neural networks (ANN) and evolutionary algorithms are two relatively young research areas that were subject to a steadily growing interest during the past years. This paper examines the use of different evolutionary algorithms, imperialist competitive algorithm (ICA), genetic algorithm (GA), ICA-GA and recursive ICA-GA (R-ICA-GA) to train a classification problem on a multi layer perceptron (MLP) neural network. All of named evolutionary training algorithms are compared together in this paper. The first goal of the paper is to apply new evolutionary optimization algorithms ICA-GA and R-ICA-GA for training the ANN and the second goal of the paper is to compare different evolutionary algorithms. It is shown that the ICA-GA has the best performance, in number of epochs, compared to the other algorithms. For this purpose, learning algorithms are applied on six known datasets (WINE, PIMA, WDBC, IRIS, SONAR and GLASS) which are used for classification problems.

This Portfolio selection Problem (PSP) remains an intractable research problem in finance and economics and often regarded as NP-hard problem in optimization and computational intelligence. This paper solved the extended Markowitz mean- variance portfolio selection model with an efficient Metaheuristics method of Generalized Differential Evolution 3 (GDE3). The extended Markowitz mean- variance portfolio selection model consists of four constraints: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. There is no research in literature that had ever engaged the set of four constraints with GDE3 to solve PSP. This paper is the first to conduct the study in this direction. The first three sets of constraints have been presented in other researches in literatures. This paper introduced expert opinion constraint to existing portfolio selection models and solved with GDE3. The computational results obtained in this research study show improved performance when compared with other Metaheuristics methods of Genetic algorithm (GA), Simulated Annealing (SA), Tabu Search (TS) and Particle Swarm Optimization (PSO).

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.

Over the past several years, heuristic methods are often used to find optimal solution(s) of disassembly/recycle sequencing problem, for it is a NP-hard combinatorial optimization problem. In the proposed research, first, we present a method: product disassembly sequence planning problem could map onto a problem of searching the optimal tour in the disassembly feasibility information graph (DFIG). Then a genetic algorithm is proposed to search the optimal solution of disassembly/recycle problem. Optimization objective is the performance of a solution, which is mainly related with three factors: disassembling process, environment impact and disassembly & recycle line. In particular, scheduling disassembly & recycle line is also a NP-hard problem. Therefore, a heuristic genetic operator, combined with disassembly & recycle processes tree, is also presented to schedule the disassembly & recycle line

Scheduling tasks in a multiprocessor system is found to be a NP-hard problem and a considerable amount of time is used up when it is solved using conventional techniques. Therefore, evolutionary algorithms like Genetic Algorithms (GA) have been explored for scheduling tasks in a multiprocessor system. GA can be implemented in various manners. This paper investigates the performance of GA with two different selection operators. This paper also studies how introducing elitism effects the performance of GA. Extensive simulations have been carried out in order to find the better candidate among the two selection operators. The decision is made depending on stability of the GA output, the rate of convergence of output and the ability of GA to give an output which is as close as possible to the actual output.

We present a novel genetic algorithm and least square (GALS) based hybrid learning approach for the training of an artificial neural network (ANN). The approach combines evolutionary algorithms with matrix solution methods such as Gram-Schmidt, SVD, etc., to adjust weights for hidden and output layers. Our hybrid method (GALS) incorporates the evolutionary algorithm (EA) in the first layer and the least square method (LS) in the second layer of the ANN. In the proposed approach, a two-layer network is considered, the hidden layer weights are evolved using an evolutionary algorithm and the output layer weights are calculated using a linear least square method. When a certain number of generation or error goals in terms of RMS error is reached, the training is stopped. We start training with a small number of hidden neurons and then the number is increased gradually in an incremental process. The proposed algorithm was implemented and many experiments were conducted on benchmark data sets such as XOR, 10-bit odd parity, handwritten segmented characters recognition, breast cancer diagnosis and heart disease data. The experimental results showed very promising results when compared with other existing evolutionary and error back propagation (EBP) algorithms in classification rate and time complexity.

k-median and facility location problems are classical NP-hard combinatorial optimization problems. Although there are many experimental studies on them, their theoretical results are relatively few. This paper mainly contributes to investigating the approximation performance of two evolutionary algorithms for the k-median and facility location problems from a theoretical perspective. For k-median problem, we show that the evolutionary algorithms with standard bit mutation (SBM) operator can obtain approximation ratios 5 and $$3{+}2/p$$ in expected polynomial time while the evolutionary algorithm with somatic contiguous hypermutation (CHM) operator cannot obtain them. For facility location problem, we show that the evolutionary algorithms with SBM operator can obtain approximation ratio 3 in expected polynomial time while the evolutionary algorithm with CHM operator cannot obtain it. Further, we prove that on a facility location instance the evolutionary algorithm with CHM operator greatly outperforms the evolutionary algorithm with SBM operator.