Automated Heuristic Design (AHD) using Large Language Models (LLMs) has achieved notable success in the past two years. Despite the effectiveness of existing approaches, they only design a single heuristic to serve all problem instances, often inducing poor generalization across different distributions or sizes. To address this issue, we propose Automated Heuristic Set Design (AHSD), a new methodology for LLM-driven AHD. The aim of AHSD is to automatically design a small-sized complementary heuristic set to serve diverse problem instances, such that each problem instance could be optimized by at least one heuristic in this set. We propose Evolution of Heuristic Set (EoH-S), which realizes AHSD using an evolutionary search framework. It incorporates a complementary population management and a memetic search to design a set of heuristics. Extensive experiments on online bin packing, traveling salesman problem, and capacitated vehicle routing problem show that EoH-S consistently outperforms existing AHD methods. The resulting heuristics exhibit complementary performance across instances of varying sizes and distributions.

Disagreement optimization is an emerging research issue in social networks. Although leaders are often selected to shape the opinions of followers, little effort has been made to investigate how to optimize the disagreement between them. This paper aims to address this issue by proposing and solving the following subset selection problem called leader-follower disagreement minimization (LFDMP): given a social network with n vertices and m edges, how to select k (kn) vertices as leaders such that the disagreement between leaders and followers is minimized. We show that the objective function of LFDMP is monotone and supermodular, and the state-of-the-art algorithm called Pareto optimization for subset selection (POSS) can solve this problem with (1-1/e) approximation in O(k2n4) expected time. To address the computational challenge faced by POSS while maintaining its theoretical advantage, we further develop a fast algorithm called Pareto optimization for leader selection (POLS) within its framework. We demonstrate that POLS can solve LFDMP with -related approximation in O(k2mn) expected time, where is an error parameter. Extensive experiments on various real-world social networks illustrate both the effectiveness and efficiency of POLS.

Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., $>100$) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.

Maximizing the influence of opinions is an emerging research topic in social networks. Although the community is a key structure of social networks, little effort has been made to investigate how to maximize the influence of opinions on all communities. This article proposes a systematic approach to address this issue. First, we construct a multifaceted opinion evolution (MFOE) model with three critical influence factors, namely, individuals, neighbors, and communities, to describe the opinion evolution process in social networks. The convergence analysis confirms its ability to reveal the influence of opinions. Then, we define the overall community opinion to measure the influence of opinions on all communities and employ it as the objective function to formulate an optimization problem called community opinion maximization (COM). We show that the COM problem is NP-hard. To optimize this problem, a memetic algorithm with three problem-specific schemes is developed and termed MACOM. Extensive experimental studies on real-world social networks demonstrate the plausibility of the MFOE model and the effectiveness of MACOM.

Integrating non-elitist evolution strategies into MOEA/D is challenging because the former usually requires many samples for updates, which is costly for MOEAID. In contrast, we suggest using (1+ 1)-ES for three reasons: fewer samples needed for updates, lower computational overhead, and better flexibility for subproblem collaboration. To verify this, we introduce (1+1)-MOEA/D-CMA, where each subproblem is solved by a different (1+1)-ES solver, and the solvers collaborate through a novel solution injection scheme. Comprehensive experiments show that the proposed algorithm performs better than several widely used algorithms. More importantly, owing to the lightweight nature of (1+1)-CMA-ES, the algorithm is shown to run faster and scale better to large population sizes, than other MOEA/D variants based on (µ/µw, λ)-CMA-ES.