A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

Evidence of coevolution in multi-objective evolutionary algorithms

This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking allow for a form of coevolutionary dynamics that is observed when 1) changes are made in what solutions are able to interact during the ranking process and 2) evolution takes place in a multi-objective environment. This research contributes to the study of simulated evolution in a at least two ways. First, it establishes a broader relationship between coevolution and multi-objective optimization than has been previously considered in the literature. Second, it demonstrates that the preconditions for coevolutionary behavior are weaker than previously thought. In particular, our model indicates that direct cooperation or competition between species is not required for coevolution to take place. Moreover, our experiments provide evidence that environmental perturbations can drive coevolutionary processes; a conclusion that mirrors arguments put forth in dual phase evolution theory. In the discussion, we briefly consider how our results may shed light onto this and other recent theories of evolution

Prospects for computational steering of evolutionary computation

Currently, evolutionary computation (EC) typically takes place in batch mode: algorithms are run autonomously, with the user providing little or no intervention or guidance. Although it is rarely possible to specify in advance, on the basis of EC theory, the optimal evolutionary algorithm for a particular problem, it seems likely that experienced EC practitioners possess considerable tacit knowledge of how evolutionary algorithms work. In situations such as this, computational steering (ongoing, informed user intervention in the execution of an otherwise autonomous computational process) has been profitably exploited to improve performance and generate insights into computational processes. In this short paper, prospects for the computational steering of evolutionary computation are assessed, and a prototype example of computational steering applied to a coevolutionary algorithm is presented

Nash Equilibria, collusion in games and the coevolutionary particle swarm algorithm

In recent work, we presented a deterministic algorithm to investigate collusion between players in a game where the players’ payoff functions are subject to a variational inequality describing the equilibrium of a transportation system. In investigating the potential for collusion between players, the diagonalization algorithm returned a local optimum. In this paper, we apply a coevolutionary particle swarm optimization (PSO) algorithm developed in earlier research in an attempt to return the global maximum. A numerical experiment is used to verify the performance of the algorithm in overcoming local optimum

Spatial Evolutionary Generative Adversarial Networks

Generative adversary networks (GANs) suffer from training pathologies such as instability and mode collapse. These pathologies mainly arise from a lack of diversity in their adversarial interactions. Evolutionary generative adversarial networks apply the principles of evolutionary computation to mitigate these problems. We hybridize two of these approaches that promote training diversity. One, E-GAN, at each batch, injects mutation diversity by training the (replicated) generator with three independent objective functions then selecting the resulting best performing generator for the next batch. The other, Lipizzaner, injects population diversity by training a two-dimensional grid of GANs with a distributed evolutionary algorithm that includes neighbor exchanges of additional training adversaries, performance based selection and population-based hyper-parameter tuning. We propose to combine mutation and population approaches to diversity improvement. We contribute a superior evolutionary GANs training method, Mustangs, that eliminates the single loss function used across Lipizzaner's grid. Instead, each training round, a loss function is selected with equal probability, from among the three E-GAN uses. Experimental analyses on standard benchmarks, MNIST and CelebA, demonstrate that Mustangs provides a statistically faster training method resulting in more accurate networks

Resource allocation and scheduling of multiple composite web services in cloud computing using cooperative coevolution genetic algorithm

In cloud computing, resource allocation and scheduling of multiple composite web services is an important and challenging problem. This is especially so in a hybrid cloud where there may be some low-cost resources available from private clouds and some high-cost resources from public clouds. Meeting this challenge involves two classical computational problems: one is assigning resources to each of the tasks in the composite web services; the other is scheduling the allocated resources when each resource may be used by multiple tasks at different points of time. In addition, Quality-of-Service (QoS) issues, such as execution time and running costs, must be considered in the resource allocation and scheduling problem. Here we present a Cooperative Coevolutionary Genetic Algorithm (CCGA) to solve the deadline-constrained resource allocation and scheduling problem for multiple composite web services. Experimental results show that our CCGA is both efficient and scalable

A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to solve the emerging large-scale problems both effectively and efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA that can not only produce high-quality solution by solving sub-problems separately, but also highly utilizes the power of parallel computing by solving the sub-problems simultaneously. Existing DC-based EAs that were deemed to enjoy the same advantages of the proposed algorithm, are shown to be practically incompatible with the parallel computing scheme, unless some trade-offs are made by compromising the solution quality.Comment: 12 pages, 0 figure