Checkers Strategy Evolution with Speciated Neural Networks

The maximum cut (MAX-CUT) problem is to find a bipartition of the vertices in a given graph such that the number of edges with ends in different sets reaches the largest. Though, several experimental investigations have shown that evolutionary algorithms (EAs) are efficient for this NP-complete problem, there is little theoretical work about EAs on the problem. In this paper, we theoretically investigate the performance of EAs on the MAX-CUT problem. We find that both the (1+1) EA and the (1+1) EA*, two simple EAs, efficiently achieve approximation solutions of (m/2)+(1/4)s(G) and (m/2)+(1/2)(√{8m+1}-1), where m and s(G) are respectively the number of edges and the number of odd degree vertices in the input graph. We also reveal that for a given integer k the (1+1) EA* finds a cut of size at least k in expected runtime O(nm+1/δ(4k)) and a cut of size at least (m/2)+k in expected runtime O(n(2)m+1/δ((64/3)k(2))), where δ is a constant mutation probability and n is the number of vertices in the input graph. Finally, we show that the (1+1) EA and the (1+1) EA* are better than some local search algorithms in one instance, and we also show that these two simple EAs may not be efficient in another instance.

Popular games often have a high-quality graphic design but quite simple-minded non player characters (NPC). Recently, Computational Intelligence (CI) methods have been discovered as suitable methods to revive NPC, making games more interesting, challenging, and funny. We present a fairly large study of human players on the simple arcade game Pac-Man, controlling the ghosts behaviors by simple strategies, neural networks or evolutionary algorithms. The playerpsilas fun is of course a subjective experience, but we presume that it is related to the psychological flow concept. We deal with the question whether flow is a more reliable measure than asking human players directly for the fun experienced during the game. In order to detect flow, we introduce a measure based on the interaction time fraction between the human-controlled Pac-Man and the ghosts, and compare the outcome to the results of a fun measure suggested by Yannakakis and Hallam [1].

Population size versus runtime of a simple evolutionary algorithm

It has been widely recognized that the efficient training of neural networks (NNs) is crucial to classification performance. While a series of gradient-based approaches have been extensively developed, they are criticized for the ease of trapping into local optima and sensitivity to hyperparameters. Due to the high robustness and wide applicability, evolutionary algorithms (EAs) have been regarded as a promising alternative for training NNs in recent years. However, EAs suffer from the curse of dimensionality and are inefficient in training deep NNs (DNNs). By inheriting the advantages of both the gradient-based approaches and EAs, this article proposes a gradient-guided evolutionary approach to train DNNs. The proposed approach suggests a novel genetic operator to optimize the weights in the search space, where the search direction is determined by the gradient of weights. Moreover, the network sparsity is considered in the proposed approach, which highly reduces the network complexity and alleviates overfitting. Experimental results on single-layer NNs, deep-layer NNs, recurrent NNs, and convolutional NNs (CNNs) demonstrate the effectiveness of the proposed approach. In short, this work not only introduces a novel approach for training DNNs but also enhances the performance of EAs in solving large-scale optimization problems.

The runtime analysis of evolutionary algorithms using crossover as search operator has recently produced remarkable results indicating benefits and drawbacks of crossover and illustrating its working principles. Virtually all these results are restricted to upper bounds on the running time of the crossover-based algorithms. This work addresses this lack of lower bounds and rigorously bounds the optimization time of simple algorithms using uniform crossover on the search space $$\{0,1\}^n$$ from below via two novel techniques called decoupling and family graphs. First, a simple steady-state crossover-based evolutionary algorithm without selection pressure is analyzed and shown that after $$O(\mu \log \mu )$$ generations, bit positions are sampled almost independently with marginal probabilities corresponding to the fraction of one-bits at the corresponding position in the initial population. In the presence of weak selective pressure induced by the probabilistic application of tournament selection, it is demonstrated that the inheritance probability at an arbitrary locus quickly approaches a uniform distribution over the initial population up to additive factors that depend on the effect of selection. Afterwards, the algorithm is analyzed by a novel generalization of the family tree technique originally introduced for mutation-only EAs. Using these so-called family graphs, almost tight lower bounds on the optimization time on the OneMax benchmark function are shown.

As general purpose optimisation methods, evolutionary algorithms have been efficiently used to solve multi-objective combinatorial optimisation problems. However, few theoretical investigations have been conducted to understand the efficiency of evolutionary algorithms on such problems, and even fewer theoretical investigations have been conducted on multi-objective combinatorial optimisation problems coming from real world. In this paper, we analyse the performance of a simple multi-objective evolutionary algorithm on two simplified instances of the bi-objective minimum weight minimum label spanning tree problem, which comes from real world. Though these two instances are similar, the analysis results show that the simple multi-objective evolutionary algorithm is efficient for one instance, but it may be inefficient for the other. According to the analysis on the second instance, we think that the restart strategy may be useful in making the multi-objective evolutionary algorithm more efficient for the bi-objective problem.

Evolutionary algorithms are general-purpose randomized search heuristics. They have been successfully applied to many different kinds of search and optimization problems. They are popular in practice since they are easy to implement and easy to apply, and yet often find good solutions in reasonable time. This lead to an increased interest in gaining a thorough understanding of their strengths (and limitations). In the past decades, the theory of evolutionary algorithms has become an important and accepted field of research. This special issue Theory of Evolutionary Computation of Algorithmica contains expanded research from the theory track of the Genetic and Evolutionary Computation Conference and the International Conference on Parallel Problem Solving From Nature. All papers have been enhanced, extended, and undergone a critical journal reviewing process. The result is a collection of seven papers that all deal with theoretical aspects of evolutionary computation in a rigorous and accessible way. It contributes to the development of a better understanding of evolutionary algorithms, paving the way for a more informed application of these algorithms. Ten years after the first publication of a run-time analysis of the most simple evolutionary algorithm, the (1 + 1) evolutionary algorithm, Jens Jagerskupper reconsiders the result. By using the drift analysis method introduced by He and Yao in a sophisticated way, he obtains much more precise bounds on the expected optimization time. Drift analysis is also the topic of Pietro S. Oliveto’s and Carsten Witt’s article. They present a theorem that yields exponential lower bounds on the expected op-

Evolutionary algorithms (EA), such as the genetic algorithm (GA), have found wide popularity because of their capability of global optimum search. As an answer to the quest for faster converging evolutionary algorithms, particle swarm optimization (PSO) was introduced to the electromagnetics domain (Robinson, J. and Rahmat-Samii, Y., IEEE Trans. Antennas Propag., vol.AP-52, no.2, p.397-407, 2004). PSO is a relatively new stochastic evolutionary computation technique, based on the movement and intelligence of swarms. PSO is found to hold a superior position with respect to other evolutionary methods, such as GA. Since PSO is a very recent method, many of its capabilities are still unexplored. It benefits from the inherent simplicity of GA while it converges much faster than conventional evolutionary algorithms. The paper presents a simple and universal design procedure for planar microwave filters. To accelerate the computation phase, an equivalent circuit topology is derived from FDTD formulation. The method is fast and robust and is well suited to the fast paced engineering design environment. As a case study, a microwave band-pass filter is designed.

In this paper, an algorithm is proposed to solve the problem of optimal selected harmonic elimination (SHE) pulse-width modulation (PWM) under a fuzzy constraint that consecutive switching angles are well separated from each other. The problem is first formulated to a fuzzy constrained optimization problem and then a Quantum-inspired Evolutionary Algorithm, which is more efficient than conventional evolutionary algorithms, is applied to approximate the fuzzy solution. The proposed method can effectively reduce switching losses and the probability of switch damages in inverter bridges, and thus can improve the performance of PWM strategy and extend the life of the inverter. This work is the first report on successful application of a Quantum-inspired Evolutionary Algorithm to solve the fuzzy constrained optimization problem.

Target shape design optimization by evolving B-splines with cooperative coevolution

The Sixth International Symposium on Neural Networks (ISNN 2009)

This study presents a multiobjective energy management to optimize the renewable microgrid operation while satisfying a demand response and various operation constraints. With regard to energy cost minimization, pollutant emission reduction for better utilization of the renewable energy resources, such as wind and solar, as a competitive objective is proposed. Moreover, for maximizing the renewable microgrid operators, demand response benefits satisfying the load demand constraints amongst other operation constraints are incorporated into the operations of the renewable microgrid. The overall problem is formulated as a mixed-integer nonlinear constraint multiobjective optimization problem with different equality and inequality constraints. In this paper, an improved decomposition based multiobjective evolutionary algorithm is presented for optimal operation of the renewable microgrid with renewable energy sources and various devices such as diesel generators, micro-turbines, fuel cells, and battery energy storage. To improve the optimization process, differential evolution (DE) and the niche guided mating selection strategy are incorporated. Meanwhile, decomposition-based multiobjective evolutionary algorithm-DE is extended to tackle the constrained optimization problem. Finally, the proposed algorithm is applied in a renewable microgrid, and its superior performance is compared with the conventional evolutionary algorithms such as the multiobjective genetic algorithm and the original decomposition based multiobjective evolutionary algorithm.

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.

In this paper, we propose a hierarchical Cooperative Coevolution framework (hCC) to deal with the Very Large-scale Traveling Salesman Problem (VLSTSP). Due to the existence of the curse of dimensionality, it is difficult to find an acceptable solution for VLSTSP with conventional Evolutionary Algorithms (EAs). Cooperative Coevolution (CC) framework, which divides the problems into multiple subcomponents and optimizes them independently, offers a potential opportunity to find suitable solutions. However, conventional CC with large-scale sub-size decomposition will still be affected by the curse of dimensionality, and small-scale sub-size decomposition ignores many interactions between subcomponents. Although the initial sub-size of the proposed hCC is small-scale, the ignored interactions will be reconsidered in the higher layer of optimization. Another issue is how to decompose the VLSTSP. In the numerical experiments, we design two strategies: (1). Random decomposition. (2). Decomposition based on the greedy solution. 10 symmetric instances of VLSTSP ranging from 38,478 to 238,025 are employed to evaluate our proposal, and the basic optimizer is greedy Local Search (gLS). Experimental results show that our proposal has great potential and scalability to deal with VLSTSP, which can be easily extended to deal with various types of TSP.

In this paper, a novel cooperative coevolution (CC)-based model predictive control (MPC) is proposed to deal with formation control problem. While conventional evolutionary algorithm (EA)-based MPC approaches cannot guarantee the stability, the proposed CC-based MPC guarantees the asymptotic stability regardless of the optimality of the solution that the CC-based algorithm generates with a small number of individuals. To guarantee the stability, a terminal state constraint is found, and then a repair algorithm is applied to all candidate solutions to meet the constraint. The cooperatively coevolving particle swarm optimization (CCPSO), most recently developed algorithm among CC-based EAs, is adopted and modified to fit into the formation control problem. Experiments are performed on a group of nonholonomic mobile robots to demonstrate the effectiveness of the CC-based MPC.