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Metaheuristic algorithms are widely used for solving complex optimization problems, yet their effectiveness is often constrained by fixed structures and the need for extensive tuning. The Polymorphic Metaheuristic Framework (PMF) addresses…

Together with the NSGA-II, the SPEA2 is one of the most widely used domination-based multi-objective evolutionary algorithms. For both algorithms, the known runtime guarantees are linear in the population size; for the NSGA-II, matching…

The use of momentum in stochastic optimization algorithms has shown empirical success across a range of machine learning tasks. Recently, a new class of stochastic momentum algorithms has emerged within the Linear Minimization Oracle (LMO)…

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC)…

Learning adaptable policies is crucial for robots to operate autonomously in our complex and quickly changing world. In this work, we present a new meta-learning method that allows robots to quickly adapt to changes in dynamics. In contrast…

This paper explores the enhancement of solution diversity in evolutionary algorithms (EAs) for the maximum matching problem, concentrating on complete bipartite graphs and paths. We adopt binary string encoding for matchings and use Hamming…

Different from single-objective evolutionary algorithms, where non-elitism is an established concept, multi-objective evolutionary algorithms almost always select the next population in a greedy fashion. In the only notable exception, Bian,…

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…

A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…

We consider the ANTS problem [Feinerman et al.] in which a group of agents collaboratively search for a target in a two-dimensional plane. Because this problem is inspired by the behavior of biological species, we argue that in addition to…

In the presence of non-admissible heuristics, A* and other best-first algorithms can be converted into anytime optimal algorithms over OR graphs, by simply continuing the search after the first solution is found. The same trick, however,…

We investigate the behaviour space of meta-heuristic optimisation algorithms automatically generated by Large Language Model driven algorithm discovery methods. Using the Large Language Evolutionary Algorithm (LLaMEA) framework with a GPT…

Multi-objective alignment from human feedback (MOAHF) in large language models (LLMs) is a challenging problem as human preferences are complex, multifaceted, and often conflicting. Recent works on MOAHF considered a-priori multi-objective…

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or…

We study cubic cardinality-constrained portfolio optimization, a higher-order extension of the standard Markowitz formulation where three-way sector co-movement terms augment the quadratic risk-return objective. Classical heuristics like…

We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the…

We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $\mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies…

The compact Genetic Algorithm (cGA), parameterized by its hypothetical population size $K$, offers a low-memory alternative to evolving a large offspring population of solutions. It evolves a probability distribution, biasing it towards…

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for…

This paper presents a first mathematical runtime analysis of PAES-25, an enhanced version of the original Pareto Archived Evolution Strategy (PAES) coming from the study of telecommunication problems over two decades ago to understand the…