The influence of mutation on population dynamics in multiobjective genetic programming

Using multiobjective genetic programming with a complexity objective to overcome tree bloat is usually very successful but can sometimes lead to undesirable collapse of the population to all single-node trees. In this paper we report a detailed examination of why and when collapse occurs. We have used different types of crossover and mutation operators (depth-fair and sub-tree), different evolutionary approaches (generational and steady-state), and different datasets (6-parity Boolean and a range of benchmark machine learning problems) to strengthen our conclusion. We conclude that mutation has a vital role in preventing population collapse by counterbalancing parsimony pressure and preserving population diversity. Also, mutation controls the size of the generated individuals which tends to dominate the time needed for fitness evaluation and therefore the whole evolutionary process. Further, the average size of the individuals in a GP population depends on the evolutionary approach employed. We also demonstrate that mutation has a wider role than merely culling single-node individuals from the population; even within a diversity-preserving algorithm such as SPEA2 mutation has a role in preserving diversity

Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

Recombination and Self-Adaptation in Multi-objective Genetic Algorithms

This paper investigates the influence of recombination and self-adaptation in real-encoded Multi-Objective Genetic Algorithms (MOGAs). NSGA-II and SPEA2 are used as example to characterize the efficiency of MOGAs in relation to various recombination operators. The blend crossover, the simulated binary crossover and the breeder genetic crossover are compared for both MOGAs on multi-objective problems of the literature. Finally, a self-adaptive recombination scheme is proposed to improve the robustness of MOGAs

Mutual benefits of two multicriteria analysis methodologies: A case study for batch plant design

This paper presents a MultiObjective Genetic Algorithm (MOGA) optimization framework for batch plant design. For this purpose, two approaches are implemented and compared with respect to three criteria, i.e., investment cost, equipment number and a flexibility indicator based on work in process (the so-called WIP) computed by use of a discrete-event simulation model. The first approach involves a genetic algorithm in order to generate acceptable solutions, from which the best ones are chosen by using a Pareto Sort algorithm. The second approach combines the previous Genetic Algorithm with a multicriteria analysis methodology, i.e., the Electre method in order to find the best solutions. The performances of the two procedures are studied for a large-size problem and a comparison between the procedures is then made

ETEA: A euclidean minimum spanning tree-Based evolutionary algorithm for multiobjective optimization

© the Massachusetts Institute of TechnologyAbstract The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in the space, where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based Evolutionary Algorithm (ETEA) to solve multiobjective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically in ETEA, four strategies are introduced: 1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; 2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; 3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; 4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/K001310/1, and the National Natural Science Foundation of China under Grant 61070088

Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

MaaSim: A Liveability Simulation for Improving the Quality of Life in Cities

Urbanism is no longer planned on paper thanks to powerful models and 3D simulation platforms. However, current work is not open to the public and lacks an optimisation agent that could help in decision making. This paper describes the creation of an open-source simulation based on an existing Dutch liveability score with a built-in AI module. Features are selected using feature engineering and Random Forests. Then, a modified scoring function is built based on the former liveability classes. The score is predicted using Random Forest for regression and achieved a recall of 0.83 with 10-fold cross-validation. Afterwards, Exploratory Factor Analysis is applied to select the actions present in the model. The resulting indicators are divided into 5 groups, and 12 actions are generated. The performance of four optimisation algorithms is compared, namely NSGA-II, PAES, SPEA2 and eps-MOEA, on three established criteria of quality: cardinality, the spread of the solutions, spacing, and the resulting score and number of turns. Although all four algorithms show different strengths, eps-MOEA is selected to be the most suitable for this problem. Ultimately, the simulation incorporates the model and the selected AI module in a GUI written in the Kivy framework for Python. Tests performed on users show positive responses and encourage further initiatives towards joining technology and public applications.Comment: 16 page