Exposing market mechanism design trade-offs via multi-objective evolutionary search

Market mechanisms are a means by which resources in contention can be allocated between contending parties, both in human economies and those populated by software agents. Designing such mechanisms has traditionally been carried out by hand, and more recently by automation. Assessing these mechanisms typically involves them being evaluated with respect to multiple conflicting objectives, which can often be nonlinear, noisy, and expensive to compute. For typical performance objectives, it is known that designed mechanisms often fall short on being optimal across all objectives simultaneously. However, in all previous automated approaches, either only a single objective is considered, or else the multiple performance objectives are combined into a single objective. In this paper we do not aggregate objectives, instead considering a direct, novel application of multi-objective evolutionary algorithms (MOEAs) to the problem of automated mechanism design. This allows the automatic discovery of trade-offs that such objectives impose on mechanisms. We pose the problem of mechanism design, specifically for the class of linear redistribution mechanisms, as a naturally existing multi-objective optimisation problem. We apply a modified version of NSGA-II in order to design mechanisms within this class, given economically relevant objectives such as welfare and fairness. This application of NSGA-II exposes tradeoffs between objectives, revealing relationships between them that were otherwise unknown for this mechanism class. The understanding of the trade-off gained from the application of MOEAs can thus help practitioners with an insightful application of discovered mechanisms in their respective real/artificial markets.

Fitness and novelty in evolutionary art

In this paper the effects of introducing novelty search in evolutionary art are explored. Our algorithm combines fitness and novelty metrics to frame image evolution as a multi-objective optimisation problem, promoting the creation of images that are both suitable and diverse. The method is illustrated by using two evolutionary art engines for the evolution of figurative objects and context free design grammars. The results demonstrate the ability of the algorithm to obtain a larger set of fit images compared to traditional fitness-based evolution, regardless of the engine used.

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary Algorithm

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. It is shown that random partnering strategies perform best by providing better sampling and more diversity.

'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. 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 conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

A Pyramidal Evolutionary Algorithm with Different Inter-Agent Partnering Strategies for Scheduling Problems

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the agents on solution quality are examined for two multiple-choice optimisation problems. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements.

'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. 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 conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary Algorithm

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. It is shown that random partnering strategies perform best by providing better sampling and more diversity.

A Pyramidal Evolutionary Algorithm with Different Inter-Agent Partnering Strategies for Scheduling Problems

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the agents on solution quality are examined for two multiple-choice optimisation problems. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements.