Visualizing Tree Structures in Genetic Programming

This paper presents methods to visualize the structure of trees that occur in genetic programming. These methods allow for the inspection of structure of entire trees even though several thousands of nodes may be involved. The methods also scale to allow for the inspection of structure for entire populations and for complete trials even though millions of nodes may be involved. Examples are given that demonstrate how this new way of “seeing” can afford a potentially rich way of understanding dynamics that underpin genetic programming. The examples indicate further studies that might be enabled by visualizing structure at these scales.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45620/1/10710_2005_Article_7621.pd

Evolutionary computation applied to combinatorial optimisation problems

This thesis addresses the issues associated with conventional genetic algorithms (GA) when applied to hard optimisation problems. In particular it examines the problem of selecting and implementing appropriate genetic operators in order to meet the validity constraints for constrained optimisation problems. The problem selected is the travelling salesman problem (TSP), a well known NP-hard problem. Following a review of conventional genetic algorithms, this thesis advocates the use of a repair technique for genetic algorithms: GeneRepair. We evaluate the effectiveness of this operator against a wide range of benchmark problems and compare these results with conventional genetic algorithm approaches. A comparison between GeneRepair and the conventional GA approaches is made in two forms: firstly a handcrafted approach compares GAs without repair against those using GeneRepair. A second automated approach is then presented. This meta-genetic algorithm examines different configurations of operators and parameters. Through the use of a cost/benefit (Quality-Time Tradeoff) function, the user can balance the computational effort against the quality of the solution and thus allow the user to specify exactly what the cost benefit point should be for the search. Results have identified the optimal configuration settings for solving selected TSP problems. These results show that GeneRepair when used consistently generates very good TSP solutions for 50, 70 and 100 city problems. GeneRepair assists in finding TSP solutions in an extremely efficient manner, in both time and number of evaluations required

Kernels of Mallows Models under the Hamming Distance for solving the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it has captured the attention of the optimization community for decades. As a result, a large number of algorithms have been proposed to tackle this problem. Among these, exact methods are only able to solve instances of size $n<40$. To overcome this limitation, many metaheuristic methods have been applied to the QAP. In this work, we follow this direction by approaching the QAP through Estimation of Distribution Algorithms (EDAs). Particularly, a non-parametric distance-based exponential probabilistic model is used. Based on the analysis of the characteristics of the QAP, and previous work in the area, we introduce Kernels of Mallows Model under the Hamming distance to the context of EDAs. Conducted experiments point out that the performance of the proposed algorithm in the QAP is superior to (i) the classical EDAs adapted to deal with the QAP, and also (ii) to the specific EDAs proposed in the literature to deal with permutation problems.Severo Ochoa SEV-2013-0323 TIN2016-78365-R PID2019-106453GAI00 SVP-2014-068574 TIN2017-82626-

Rotationally invariant techniques for handling parameter interactions in evolutionary multi-objective optimization

In traditional optimization approaches the interaction of parameters associated with a problem is not a significant issue, but in the domain of Evolutionary Multi-Objective Optimization (EMOO) traditional genetic algorithm approaches have difficulties in optimizing problems with parameter interactions. Parameter interactions can be introduced when the search space is rotated. Genetic algorithms are referred to as being not rotationally invariant because their behavior changes depending on the orientation of the search space. Many empirical studies in single and multi-objective evolutionary optimization are done with respect to test problems which do not have parameter interactions. Such studies provide a favorably biased indication of genetic algorithm performance. This motivates the first aspect of our work; the improvement of the testing of EMOO algorithms with respect to the aforementioned difficulties that genetic algorithms experience in the presence of parameter interactions. To this end, we examine how EMOO algorithms can be assessed when problems are subject to an arbitrarily uniform degree of parameter interactions. We establish a theoretical basis for parameter interactions and how they can be measured. Furthermore, we ask the question of what difficulties a multi-objective genetic algorithm experiences on optimization problems exhibiting parameter interactions. We also ask how these difficulties can be overcome in order to efficiently find the Pareto-optimal front on such problems. Existing multi-objective test problems in the literature typically introduce parameter interactions by altering the fitness landscape, which is undesirable. We propose a new suite of test problems that exhibit parameter interactions through a rotation of the decision space, without altering the fitness landscape. In addition, we compare the performance of a number of recombination operators on these test problems. The second aspect of this work is concerned with developing an efficient multi-objective optimization algorithm which works well on problems with parameter interactions. We investigate how an evolutionary algorithm can be made more efficient on multi-objective problems with parameter interactions by developing four novel rotationally invariant differential evolution approaches. We also ask whether the proposed approaches are competitive in comparison with a state-of-the-art EMOO algorithm. We propose several differential evolution approaches incorporating directional information from the multi-objective search space in order to accelerate and direct the search. Experimental results indicate that dramatic improvements in efficiency can be achieved by directing the search towards points which are more dominant and more diverse. We also address the important issue of diversity loss in rotationally invariant vector-wise differential evolution. Being able to generate diverse solutions is critically important in order to avoid stagnation. In order to address this issue, one of the directed approaches that we examine incorporates a novel sampling scheme around better individuals in the search space. This variant is able to perform exceptionally well on the test problems with much less computational cost and scales to very high decision space dimensions even in the presence of parameter interactions