Denis Pallez

Mixed-integer optimization (MIO) involves solving a problem defined by both discrete and continuous decision variables. Although common in real-world applications, MIO is difficult to solve because traditional metaheuristics are primarily designed for a single variable type. This paper compares six different strategies identified in a recent survey, categorizing them as either global strategies (GS), which treat the decision vector as a unified type, or decomposition-based strategies (DS), which split the problem into continuous and discrete subproblems. We benchmark these strategies based on a genetic algorithm across the 24 functions of the COCO BBOB-mixint test suite. The results show that GS are more efficient at performing simple functions and are more robust in multi-modal landscapes. As expected, however, DS are vulnerable to variable interdependencies. A resolution limit has been identified for high conditioning functions, whereby all strategies reach a performance ceiling. This is partly because the landscape features are smaller than the minimum integer step size of 1, causing the algorithm to exceed the optimal level. These results suggest that future research should explore hybrid metaheuristics to overcome the inherent constraints of the integer grid.

Multiobjective sequential optimization problems consist of building a solution as a sequence of decisions, while searching for optimal trade-offs among multiple, often conflicting, objectives. In this context, the Pareto-Nested Rollout Policy Adaptation (P-NRPA) algorithm has recently been proposed as a competitive Monte Carlo approach, notably on the multiobjective Traveling Salesman Problem. However, P-NRPA was designed for discrete environments, which limits its applicability to many real-world continuous problems. In this paper, we propose an extension of P-NRPA to the continuous domain, called Continuous P-NRPA (C-PNRPA), that integrates a progressive widening mechanism from the Monte Carlo Tree Search (MCTS) family. This mechanism forces the algorithm to consider a growing set of candidate decisions, rather than immediately facing an infinite space of possible decisions. C-PNRPA is then compared against a continuous multiobjective variant of MCTS, NSGA-II and MOEA/D on sequential continuous optimization benchmarks. Results show that C-PNRPA operates reliably in the continuous domain, consistently outperforming the MCTS baseline, matching NSGA-II on one benchmark, and falling short of both NSGA-II and MOEA/D on the other.

The identification of condition-specific gene sets from transcriptomic experiments is important to reveal regulatory and signaling mechanisms associated with a given cellular response. Statistical methods of differential expression analysis, designed to assess individual gene variations, have trouble highlighting modules of small varying genes whose interaction is essential to characterize phenotypic changes. To identify these highly informative gene modules, several methods have been proposed in recent years, but they have many limitations that make them of little use to biologists. Here, we propose an efficient method for identifying these active modules that operates on a data embedding combining gene expressions and interaction data. Applications carried out on real datasets show that our method can identify new groups of genes of high interest corresponding to functions not revealed by traditional approaches. Software is available athttps://github.com/claudepasquier/amine.

The identification of condition-specific gene sets from transcriptomic experiments is important to reveal regulatory and signaling mechanisms associated with a given cellular response. Statistical approaches using only expression data allow the identification of genes whose expression is most altered between different conditions. However, a phenotype is rarely a direct consequence of the activity of a single gene, but rather reflects the interplay of several genes to carry out certain molecular processes. Many methods have been proposed to analyze the activity of genes in light of our knowledge of their molecular interactions. However, existing methods have many limitations that make them of limited use to biologists: they detect modules that are too large, too small, or they require the users to specify a priori the size of the modules they are looking for.We propose AMINE (Active Module Identification through Network Embedding), an efficient method for the identification of active modules. Experiments carried out on artificial data sets show that the results obtained are more reliable than many available methods. Moreover, the size of the modules to be identified is not a fixed parameter of the method and does not need to be specified; rather, it adjusts according to the size of the modules to be found. The applications carried out on real datasets show that the method enables to find important genes already highlighted by approaches solely based on gene variations, but also to identify new groups of genes of high interest. In addition, AMINE method can be used as a web service on your own data (http://amine.i3s.unice.fr).