Alberto Moraglio

University of Exeter | UoE · College of Engineering, Mathematics and Physical Sciences

Quadratic unconstrained binary optimisation (QUBO) problems is a general class of combinatorial optimisation problems and a basis for recent advances in quantum(-inspired) computing. Many well-known optimisation problems are constrained and can be converted to QUBO via penalty methods. But it is challenging to find valid penalty weights, which guar...

Paper presented at NASO 2022 workshop (https://sites.google.com/view/naso-2022)

Quadratic unconstrained binary optimisation (QUBO) problems is a general class of combinatorial optimisation problems, which regained popularity after recent advances in quantum computing. Quantum-inspired hardware like Fujitsu's Digital Annealer (DA), based on simulated annealing, can solve QUBO problems much faster than traditional computers. Pen...

Evolutionary Algorithms (EAs) with no mutation can be generalized across representations as Convex Evolutionary Search algorithms (CSs). However, the crossover operator used by CSs does not faithfully generalize the standard two-parents crossover: it samples a convex hull instead of a segment. Segmentwise Evolutionary Search algorithms (SESs) are d...

The Convex Search Algorithm (CSA) is a generalization across representations of Evolutionary Algorithms (EAs) with crossover and no mutation. The Standard Evolutionary Search Algorithm (SESA) is a more accurate generalization of EAs with crossover and no mutation, using a standard two-parents crossover. This work extends the runtime analysis of the...

I present the paper "A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search"

Program Trace Optimisation (PTO), a highly general optimisation framework, is applied to a range of combinatorial optimisation (COP) problems. It effectively combines “smart” problem-specific constructive heuristics and problem-agnostic metaheuristic search, automatically and implicitly designing problem-appropriate search operators. A weakness is...

Previous work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem's landscape belongs to certain abstract convex landscape classes, where certain recombination-based EAs (wit...

Previous work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem's landscape belongs to certain abstract convex landscape classes, where certain recombination-based EAs (wit...

We introduce Program Trace Optimization (PTO), a system for ‘universal heuristic optimization made easy’. This is achieved by strictly separating the problem from the search algorithm. New problem definitions and new generic search algorithms can be added to PTO easily and independently, and any algorithm can be used on any problem. PTO automatical...

Based on a geometric theory of evolutionary algorithms, it was shown that all evolutionary algorithms equipped with a geometric crossover and no mutation operator do the same kind of convex search across representations, and that they are well-matched with generalised forms of concave fitness landscapes for which they provably find the optimum in p...

PPSN 2018 conference poster

Based on a geometric theory of evolutionary algorithms, it was shown that all evolutionary algorithms equipped with a geometric crossover and no mutation operator do the same kind of convex search across representations, and that they are well-matched with generalised forms of concave fitness landscapes for which they provably find the optimum in p...

Geometric Semantic Genetic Programming (GSGP) is a novel form of Genetic Programming (GP), based on a geometric theory of evolutionary algorithms, which directly searches the semantic space of programs. In this chapter, we extend this framework to Grammatical Evolution (GE) and refer to the new method as Geometric Semantic Grammatical Evolution (GS...

Since its introduction, Geometric Semantic Genetic Programming (GSGP) has been the inspiration to ideas on how to reach optimal solutions efficiently. Among these, in 2016 Pawlak has shown how to analytically construct optimal programs by means of a linear combination of a set of random programs. Given the simplicity and excellent results of this m...

Geometric Semantic Genetic Programming (GSGP) induces a unimodal fitness landscape for any problem that consists in finding a function fitting given input/output examples. Most of the work around GSGP to date has focused on real-world applications and on improving the originally proposed search operators, rather than on broadening its theoretical f...

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optim...

Geometric crossover is a formal class of crossovers which includes many well-known recombination operators across representations. In previous work, it was shown that all evolutionary algorithms with geometric crossover (but with no mutation) do the same form of convex search regardless of the underlying representation, the specific selection mecha...

An underlying problem in genetic programming (GP) is how to ensure sufficient useful diversity in the population during search. Having a wide range of diverse (sub)component structures available for recombination and/or mutation is important in preventing premature converge. We propose two new fitness disaggregation approaches that make explicit us...

Semantic genetic programming is a recent, rapidly growing trend in Genetic Programming (GP) that aims at opening the 'black box' of the evaluation function and make explicit use of more information on program behavior in the search. In the most common scenario of evaluating a GP program on a set of input-output examples (fitness cases), the semanti...

Surrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with soluti...

Metaheuristics, and evolutionary algorithms in particular, are known to provide efficient, adaptable solutions for many real-world problems, but the often informal way in which they are defined and applied has led to misconceptions, and even successful applications are sometimes the outcome of trial and error. Ideally, theoretical studies should ex...

Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP) that searches the semantic space of functions/programs. The fitness landscape seen by GSGP is always -- for any domain and for any problem -- unimodal with a linear slope by construction. This makes the search for the optimum much easier than for...

Geometric Semantic Genetic Programming (GSGP) is a recently introduced framework to design domain-specific search operators for Genetic Programming (GP) to search directly the semantic space of functions. The fitness landscape seen by GSGP is always - for any domain and for any problem - unimodal with a constant slope by construction. This makes th...

Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP), rooted in a geometric theory of representations, that searches directly the semantic space of functions/programs, rather than the space of their syntactic representations (e.g., trees) as in traditional GP. Remarkably, the fitness landscape seen...

This book constitutes the refereed proceedings of the 16th European Conference on Genetic Programming, EuroGP 2013, held in Vienna, Austria, in April 2013 co-located with the Evo* 2013 events, EvoMUSART, EvoCOP, EvoBIO, and EvoApplications. The 18 revised full papers presented together with 5 poster papers were carefully reviewed and selected from...

Geometric differential evolution (GDE) is a very recently introduced formal generalization of tradi-tional differential evolution (DE) that can be used to derive specific GDE for both continuous and combinatorial spaces retaining the same geometric interpretation of the dynamics of the DE search across representations. In this article, we first rev...

Traditional Genetic Programming (GP) searches the space of functions/programs by using search operators that manipulate their syntactic representation (e.g., parse trees), regardless of their semantic. Recently, semantically aware search operators have been shown to outperform purely syntactic operators. In this work, using a formal geometric view...

Geometric crossover formalises the notion of crossover operator across representations. In previous work, it was shown that all evolutionary algorithms with geometric crossover (but with no mutation) do a generalised form of convex search. Furthermore, it was suggested that these search algorithms could perform well on concave and approximately con...

Genetic programming has proven capable of evolving solutions to a wide variety of problems. However, the successes have largely been with programs without iteration or recursion; evolving recursive programs has turned out to be particularly challenging. The main obstacle to evolving recursive programs seems to be that they are particularly fragile...

We present a new crossover operator for real-coded genetic algorithms employing a novel methodology to remove the inherent bias of pre-existing crossover operators. This is done by transforming the topology of the hyper-rectangular real space by gluing opposite boundaries and designing a boundary extension method for making the fitness function smo...

The aim of the tutorial is to introduce a formal, unified point of view on evolutionary algorithms across representations based on geometric ideas, and to present the benefits for both theory and practice brought by this novel perspective. The key idea behind the geometric framework is that search operators are not defined directly on solution repr...

The Nelder-Mead Algorithm (NMA) is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). In recent work, PSO, DE and NMA have been generalized using a formal geometric framework that treats solution representations in a uniform way. These formal algorithms can be used as templates to derive rigorously specific PSO,...

In continuous optimisation, surrogate models (SMs) are used when tackling real-world problems whose candidate solutions are expensive to evaluate. In previous work, we showed that a type of SMs - radial basis function networks (RBFNs) - can be rigorously generalised to encompass combinatorial spaces based in principle on any arbitrarily complex und...

In continuous optimisation, Surrogate Models (SMs) are often indispensable components of optimisation algorithms aimed at tackling real-world problems whose candidate solutions are very expensive to evaluate. Because of the inherent spatial intuition behind these models, they are naturally suited to continuous problems but they do not seem applicab...

We extend a geometric framework for the interpretation of search operators to encompass the genotype-phenotype mapping derived from an equivalence relation defined by an isometry group. We show that this mapping can be naturally interpreted using the concept of quotient space, in which the original space corresponds to the genotype space and the qu...

Geometric crossover is a formal class of crossovers which includes many well-known recombination operators across representations. In this paper, we present a general result showing that all evolutionary algorithms using geometric crossover with no mutation perform the same form of convex search regardless of the underlying representation, the spec...

Geometric crossovers are a class of representation-independent search operators for evolutionary algorithms that are well-defined once a notion of distance over a solution space is defined. In this paper we explore the specialisation of geometric crossovers to the permutation representation analysing the consequences of the availability of more tha...

This paper presents a framework for heuristic portfolio optimisation applied to a hedge fund investment strategy. The first contribution of the paper is to present a framework for implementing portfolio optimisation of a market neutral hedge fund strategy. The paper also illustrates the application of the recently developed Geometric Nelder-Mead Al...

Uniform crossover for binary strings has a natural geometric interpretation that allows us to generalize it rigorously to any search space endowed with a notion of distance and any representation [6]. In this paper, we present an analogous characterization for one-point crossover and explicitly derive formally specific one-point crossovers for a nu...

Ant Colony Optimization (ACO) differs substantially from other meta-heuristics such as Evolutionary Algorithms (EA). Two of its distinctive features are: (i) it is constructive rather than based on iterative improvements, and (ii) it employs problem knowledge in the construction process via the heuristic function, which is essential for its success...

The Nelder-Mead Algorithm (NMA) is an almost half-century old method for numerical optimization, and it is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). In recent work, PSO, DE and NMA have been generalized using a formal geometric framework that treats solution representations in a uniform way. These formal...

The Nelder-Mead Algorithm (NMA) is an almost half-century old method for numerical optimization, and it is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). Geometric Particle Swarm Optimization (GPSO) and Geometric Differential Evolution (GDE) are recently introduced formal generalization of traditional PSO and...

Geometric Differential Evolution (GDE) is a very recently introduced formal generalization of traditional Differential Evolution (DE) that can be used to derive specific GDE for both continuous and combinatorial spaces retaining the same geometric interpretation of the dynamics of the DE search across representations. In this paper, we derive form...

Motif discovery is a general and important problem in bioinformat-ics, as motifs often are used to infer biologically important sites in bio-molecular sequences. Many problems in bioinformatics are naturally cast in terms of sequences, and distance measures for se-quences derived from edit distance is fundamental in bioinformat-ics. Geometric Cross...

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, t...

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually search...

Geometric Particle Swarm Optimization (GPSO) is a recently introduced formal generalization of traditional Particle Swarm Optimization (PSO) that applies naturally to both continuous and combinatorial spaces. Differential Evolution (DE) is similar to PSO but it uses different equations governing the motion of the particles. This paper generalizes t...

Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of a simplified form of traditional particle swarm optimization (PSO) without the inertia term that applies naturally to both continuous and combinatorial spaces. In this paper, we propose an extension of GPSO, the inertial GPSO (IGPSO), that generalizes the...

The smoothness of a fitness landscape, to date still an elusive notion, is considered to be a fundamental empirical requirement to obtain good performance for many existing meta-heuristics. In this paper, we suggest that a theory of smooth fitness landscapes is central to bridge the gap between theory and practice in EC. As a first step towards thi...

This book constitutes the refereed proceedings of the 11th European Conference on Genetic Programming, EuroGP 2009, held in Tübingen, Germany, in April 2009 colocated with the Evo* 2009 events. The 21 revised plenary papers and 9 revised poster papers were carefully reviewed and selected from a total of 57 submissions. A great variety of topics are...

Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of traditional particle swarm optimization (PSO) that applies naturally to both continuous and combinatorial spaces. In this paper we apply GPSO to the space of genetic programs represented as expression trees, uniting the paradigms of genetic programming an...

Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric PSO (GPSO) applies...

In most forms of selection, when multiple individuals are needed for an operation, these are drawn independently from the population. So, for example, in the case of crossover, the probability of a particular pair of parents being selected is given by the product of the selection probabilities of each parent. In this paper we investigate a form of...

Geometric particle swarm optimization (GPSO) is a recently introduced generalization of traditional particle swarm op- timization (PSO) that applies to all combinatorial spaces. The aim of this paper is to demonstrate the applicability of GPSO to non-trivial combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic idea...

Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of traditional particle swarm optimization (PSO) that applies naturally to both continuous and combinatorial spaces. In previous work we have developed the theory behind it. The aim of this paper is to demonstrate the applicability of GPSO in practice. We de...

Geometric crossover is a representation-independent gener- alization of the class of traditional mask-based crossover for binary strings. It is based on the distance of the search space seen as a metric space. Although real-code represen- tation allows for a very familiar notion of distance, namely the Euclidean distance, there are also other dista...

Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimization (PSO) and evolutionary algorithms. This connection enables us to generalize PSO to virtually any solution representation in a natural and straightforward way. We demonstrate this for the cases of...

Geometric crossover is a representation-independent defini-tion of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombi-nation operators for the most frequently used representa-tions. Using a distance tailored to the problem at hand...

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as a basis for geometric crossover, one can design new crossovers for any representation. Using a distance tailored to the...

Geometric crossover is a representation-independent general- ization of traditional crossover for binary strings. It is defined in a simple geometric way by using the distance associated with the search space. Many interesting recombination operators for the most frequently used representations are geometric crossovers under some suitable distance....

We propose a new crossover that generalizes cycle crossover to permutations with repetitions and naturally suits parti- tion problems. We tested it on graph partitioning problems obtaining excellent results. Categories and Subject Descriptors: G.2.3 (Mathemat-

Geometric crossover is a representation-independent gener- alization of the traditional crossover dened using the dis- tance of the solution space. Using a distance tailored to the problem at hand, the formal denition of geometric crossover allows to design new problem-specic crossovers that embed problem-knowledge in the search. The standard encod...

This paper extends a geometric framework for interpreting crossover and mutation (4) to the case of sequences. This representation is important because it is the link between artificial evolution and bio- logical evolution. We define and theoretically study geometric crossover for sequences under edit distance and show its intimate connection with...

This paper extends a geometric framework for interpreting crossover and mutation (5) to the case of sets and related representations. We show that a deep geometric duality exists between the set represen- tation and the vector representation. This duality reveals the equivalence of geometric crossovers for these representations. (10) within his for...

Geometric crossover is a representation-independent defini- tion of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand,...

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most used representations. Using a distance tailored to the problem at hand, the abstract...

The relationship between search space, distances and genetic operators for syntactic trees is little understood. Geometric crossover and geometric mutation are representation-independent operators that are well-defined once a notion of distance over the solution space is defined. In this paper we apply this geometric framework to the syntactic tree...

Topological crossovers are a class of representation-independent operators that are well-defined once a notion of distance over the solution space is defined. In this paper we explore how the topological framework applies to the permutation representation and in particular analyze the consequences of having more than one notion of distance availabl...

Abstract crossover and abstract mutation are representation-independent operators that are well-defined once a notion of distance over the solution space is defined. They were obtained as generalization of genetic operators for binary strings and real vectors. In this paper we explore how the abstract geometric framework applies to the permutation...

The Job Shop Scheduling Problem is a strongly NP-hard problem of combinatorial optimisation and one of the best-known machine scheduling problem. Taboo Search is an effective local search algorithm for the job shop scheduling problem, but the quality of the best solution found depends on the initial solution. To overcome this problem we present a n...

Topological crossovers are a class of representation-independent operators that are well-defined once a notion of distance over the solution space is defined. In this paper we explore how the topological framework applies to the permutation representation and in particular analyse the consequences of having more than one notion of distance availabl...

In this paper we give a representation-independent topological definition of crossover that links it tightly to the notion of fitness landscape. Building around this definition, a geometric/topological framework for evolutionary algorithms is introduced that clarifies the connection between representation, genetic operators, neighbourhood structure...

The Human Based Genetic Algorithm is an extension of the field of Interactive Evolutionary Computation where, in addition to fitness and selection, the user performs all the other genetic operators. The definition of operators is left intentionally loose to stimulate the user's creativity in the evolutionary process.

Geometric crossover is a representation-independent gen-eralization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as basis for geometric crossover, one can design new crossovers for any representation. In previous work we have applied...

Geometric crossover is a representation-independent gener- alisation of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as basis for geometric crossover, one can design new crossovers for any representation. In previous work, we have applie...

Evolutionary algorithms are only superficially dierent and can be unified within an axiomatic geometric framework by abstraction of the solution representation. This framework describes the evolutionary search in a representation-independent way, purely in geometric terms, paving the road to a general theory of evolutionary algorithms. It also lead...