Genetic algorithm based distance spectrum technique for performance union bound of space-time trellis coded OFDM

This paper derives the performance union bound of space-time trellis codes in orthogonal frequency division multiplexing system (STTC-OFDM) over quasi-static frequency selective fading channels based on the distance spectrum technique. The distance spectrum is the enumeration of the codeword difference measures and their multiplicities by exhausted searching through all the possible error event paths. Exhaustive search approach can be used for low memory order STTC with small frame size. However with moderate memory order STTC and moderate frame size the computational cost of exhaustive search increases exponentially, and may become impractical for high memory order STTCs. This requires advanced computational techniques such as Genetic Algorithms (GAS). In this paper, a GA with sharing function method is used to locate the multiple solutions of the distance spectrum for high memory order STTCs. Simulation evaluates the performance union bound and the complexity comparison of non-GA aided and GA aided distance spectrum techniques. It shows that the union bound give a close performance measure at high signal-to-noise ratio (SNR). It also shows that GA sharing function method based distance spectrum technique requires much less computational time as compared with exhaustive search approach but with satisfactory accuracy.

The dynamics of a genetic algorithm for a simple learning problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using method s from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

A hybrid genetic algorithm for the multi-depot vehicle routing problem

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assumption that there is only one depot. In cases, for instance, where a logistics company has more than one depot, the VRP is not suitable. To resolve this limitation, this paper focuses on the VRP with multiple depots, or multi-depot VRP (MDVRP). The MDVRP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To deal with the problem efficiently, two hybrid genetic algorithms (HGAs) are developed in this paper. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method and the nearest neighbor heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different problem sizes. It is proved that the performance of HGA2 is superior to that of HGA1 in terms of the total delivery time.

Using non-parametric search algorithms to forecast daily excess stock returns

Are the learning procedures of genetic algorithms (GAs) able to generate optimal architectures for artificial neural networks (ANNs) in high frequency data? In this experimental study,GAs are used to identify the best architecture for ANNs. Additional learning is undertaken by the ANNs to forecast daily excess stock returns. No ANN architectures were able to outperform a random walk,despite the finding of non-linearity in the excess returns. This failure is attributed to the absence of suitable ANN structures and further implies that researchers need to be cautious when making inferences from ANN results that use high frequency data.

Genetic Algorithm for Finding the Key’s Length and Cryptanalysis of the Permutation Cipher

In this article we discuss a possibility to use genetic algorithms in cryptanalysis. We developed and described the genetic algorithm for finding the secret key of a block permutation cipher. In this case key is a permutation of some first natural numbers. Our algorithm finds the exact key’s length and the key with controlled accuracy. Evaluation of conducted experiment’s results shows that the almost automatic cryptanalysis is possible.

Genetic Algorithm Approach for Solving the Task Assignment Problem

This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.

Distributed Genetic Algorithm Implementation by Means of Remote Methods Invocation Technique – Java RMI

The aim of this work is distributed genetic algorithm implementation (so called island algorithm) to accelerate the optimum searching process in space of solutions. Distributed genetic algorithm has also smaller chances to fall in local optimum. This conception depends on mutual cooperation of the clients which realize separate working of genetic algorithms on local machines. As a tool for implementation of distributed genetic algorithm, created to produce net's applications Java technology was chosen. In Java technology, there is a technique of remote methods invocation - Java RMI. By means of invoking remote methods it can send objects between clients and server RMI.

An Adaptive Genetic Algorithm with Dynamic Population Size for Optimizing Join Queries

The problem of finding the optimal join ordering executing a query to a relational database management system is a combinatorial optimization problem, which makes deterministic exhaustive solution search unacceptable for queries with a great number of joined relations. In this work an adaptive genetic algorithm with dynamic population size is proposed for optimizing large join queries. The performance of the algorithm is compared with that of several classical non-deterministic optimization algorithms. Experiments have been performed optimizing several random queries against a randomly generated data dictionary. The proposed adaptive genetic algorithm with probabilistic selection operator outperforms in a number of test runs the canonical genetic algorithm with Elitist selection as well as two common random search strategies and proves to be a viable alternative to existing non-deterministic optimization approaches.

'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus learning can amount to 'counting' in the case of multinomial distributions. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

'Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem'

There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem.

Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem

There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem.

'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus learning can amount to 'counting' in the case of multinomial distributions. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

An Indirect Genetic Algorithm for a Nurse Scheduling Problem

This paper describes a Genetic Algorithms approach to a manpower-scheduling problem arising at a major UK hospital. Although Genetic Algorithms have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical Genetic Algorithms paradigm in handling the conflict between objectives and constraints. The approach taken here is to use an indirect coding based on permutations of the nurses, and a heuristic decoder that builds schedules from these permutations. Computational experiments based on 52 weeks of live data are used to evaluate three different decoders with varying levels of intelligence, and four well-known crossover operators. Results are further enhanced by introducing a hybrid crossover operator and by making use of simple bounds to reduce the size of the solution space. The results reveal that the proposed algorithm is able to find high quality solutions and is both faster and more flexible than a recently published Tabu Search approach.

'Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem'

There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem.