RESUMEN

Multiobjective evolutionary algorithms are successfully applied in many real-world multiobjective optimization problems. As for many other AI methods, the theoretical understanding of these algorithms is lagging far behind their success in practice. In particular, previous theory work considers mostly easy problems that are composed of unimodal objectives. As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OneJumpZeroJump problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark. We prove that the simple evolutionary multiobjective optimizer (SEMO) with probability one does not compute the full Pareto front, regardless of the runtime. In contrast, for all problem sizes n and all jump sizes k∈[4..n2-1], the global SEMO (GSEMO) covers the Pareto front in an expected number of Θ((n-2k)nk) iterations. For k=o(n), we also show the tighter bound 32enk+1±o(nk+1), which might be the first runtime bound for an MOEA that is tight apart from lower-order terms. We also combine the GSEMO with two approaches that showed advantages in single-objective multimodal problems. When using the GSEMO with a heavy-tailed mutation operator, the expected runtime improves by a factor of at least kΩ(k). When adapting the recent stagnation-detection strategy of Rajabi and Witt (2022) to the GSEMO, the expected runtime also improves by a factor of at least kΩ(k) and surpasses the heavy-tailed GSEMO by a small polynomial factor in k. Via an experimental analysis, we show that these asymptotic differences are visible already for small problem sizes: A factor-5 speed-up from heavy-tailed mutation and a factor-10 speed-up from stagnation detection can be observed already for jump size 4 and problem sizes between 10 and 50. Overall, our results show that the ideas recently developed to aid single-objective evolutionary algorithms to cope with local optima can be effectively employed also in multiobjective optimization.

Asunto(s)

Algoritmos , Evolución Biológica , Benchmarking , Mutación , Factor X

RESUMEN

Most state-of-the-art Multiobjective Evolutionary Algorithms (moeas) promote the preservation of diversity of objective function space but neglect the diversity of decision variable space. The aim of this article is to show that explicitly managing the amount of diversity maintained in the decision variable space is useful to increase the quality of moeas when taking into account metrics of the objective space. Our novel Variable Space Diversity-based MOEA (vsd-moea) explicitly considers the diversity of both decision variable and objective function space. This information is used with the aim of properly adapting the balance between exploration and intensification during the optimization process. Particularly, at the initial stages, decisions made by the approach are more biased by the information on the diversity of the variable space, whereas it gradually grants more importance to the diversity of objective function space as the evolution progresses. The latter is achieved through a novel density estimator. The new method is compared with state-of-art moeas using several benchmarks with two and three objectives. This novel proposal yields much better results than state-of-the-art schemes when considering metrics applied on objective function space, exhibiting a more stable and robust behavior.

Asunto(s)

Algoritmos

RESUMEN

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multiobjective EA, that is, GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties and its explicit formulation is not needed. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this article studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., g-c) with a size constraint, where g is a so-called non-negative monotone approximately submodular function and c is a so-called non-negative modular function, resulting in the objective function (g-c) being non-monotone non-submodular in general. Different from previous analyses, we prove that by optimizing the original objective function (g-c) and the size simultaneously, the GSEMO fails to achieve a good polynomial-time approximation guarantee. However, we also prove that by optimizing a distorted objective function and the size simultaneously, the GSEMO can still achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.

Asunto(s)

Algoritmos , Evolución Biológica , Teorema de Bayes , Investigación Empírica , Modelos Teóricos

RESUMEN

Diversity of cellular metabolism can be harnessed to produce a large space of molecules. However, development of optimal strains with high product titers, rates, and yields required for industrial production is laborious and expensive. To accelerate the strain engineering process, we have recently introduced a modular cell design concept that enables rapid generation of optimal production strains by systematically assembling a modular cell with an exchangeable production module(s) to produce target molecules efficiently. In this study, we formulated the modular cell design concept as a general multiobjective optimization problem with flexible design objectives derived from mass balance. We developed algorithms and an associated software package, named ModCell2, to implement the design. We demonstrated that ModCell2 can systematically identify genetic modifications to design modular cells that can couple with a variety of production modules and exhibit a minimal tradeoff among modularity, performance, and robustness. Analysis of the modular cell designs revealed both intuitive and complex metabolic architectures enabling modular production of these molecules. We envision ModCell2 provides a powerful tool to guide modular cell engineering and sheds light on modular design principles of biological systems.

Asunto(s)

Algoritmos , Ingeniería Celular , Anaerobiosis , Evolución Molecular Dirigida , Escherichia coli/genética , Escherichia coli/metabolismo , Ingeniería Metabólica/métodos , Reproducibilidad de los Resultados , Programas Informáticos

RESUMEN

In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.