Optimisation

Optimisation is the systematic process of selecting the best configuration of decision variables to maximise or minimise a real-valued objective function under specified constraints. It spans a spectrum of problems, from continuous convex programmes—where global minima can be found efficiently—to discrete and combinatorial challenges, such as routing and scheduling, that are often NP-hard. Classical techniques include linear and nonlinear programming, relying on gradient or interior-point methods, while modern approaches harness metaheuristics—genetic algorithms, particle swarm optimisation, ant and bee colony methods—and their hybrids to explore complex, multimodal landscapes. Recent advances integrate machine learning models and surrogate‐based search to guide sampling, apply reinforcement learning to sequential decision tasks and address multi‐objective trade-offs. Optimisation underpins applications in engineering design, logistics, finance, energy systems and data science, driving innovations in robustness, scalability and real-time performance.

Research from Nature Portfolio

A novel variant of the artificial bee colony algorithm introduces Bernoulli chaotic mapping, a mutual exclusion mechanism and a neighbourhood‐search phase with a compression factor to enhance exploration and exploitation. Sustained-bee strategies further accelerate convergence, yielding improved solutions on standard engineering benchmarks and two constrained design problems. This chaotic and neighbourhood-driven ABC framework demonstrates both superior search efficiency and reliable performance in complex optimisation tasks.

A two-stage spider pheromone coordination algorithm models positioning on a cobweb followed by pheromone-guided hunting. In the first stage, multiple agents disperse to identify feasible regions; in the second, simulated pheromone release and wind effects direct collective movement towards optima. Comparative experiments on a suite of multimodal test functions reveal higher convergence accuracy and stronger global search capability than several established swarm intelligence methods, while preserving population diversity.

Research from all publishers

A 2024 survey examines convergence properties of the beetle antennae search (BAS) family, analysing adaptive step-size rules, hybridisation with gradient-informed moves and deep-learning-based parameter tuning. The review highlights accelerated convergence rates and enhanced robustness on high-dimensional benchmark functions, engineering design cases and real-time path‐planning scenarios.

Researchers have proposed a large-scale bi-level particle swarm optimisation framework to overcome stagnation and premature convergence. Two nested swarms—an upper level for coarse allocation and a lower level for detailed refinement—are coupled with an exponential acceleration factor to maintain diversity. Empirical tests show marked improvements in stability and convergence speed on benchmark suites with tens of thousands of dimensions.

An artificial bee colony algorithm based on knowledge fusion integrates multiple information sources through an adaptive learning mechanism. By sensing search status and selecting context-appropriate knowledge, this approach dynamically balances global exploration and local exploitation. It outperforms classical ABC variants and leading differential evolution schemes on a broad set of multimodal optimisation landscapes.

Optimisation publication trend

The graph below shows the total number of articles in optimisation across all publications each year (not limited to Nature Index journals).

Technical terms

Objective function: A quantitative measure to be maximised or minimised in an optimisation problem.

Metaheuristic: A high-level framework guiding subordinate heuristics to explore and exploit solution spaces without problem-specific tuning.

Exploration: The process of probing diverse regions of the search space to avoid local optima.

Exploitation: The refinement of promising solutions via focused, local search.

Convex optimisation: A class of problems with convex objective and feasible region, guaranteeing any local optimum is global.

Swarm intelligence: A family of metaheuristics inspired by collective behaviours of social organisms, using simple agents and indirect coordination.

References

1. Artificial bee colony algorithm based on knowledge fusion. Complex & Intelligent Systems (2020).
2. Research on Large-Scale Bi-Level Particle Swarm Optimization Algorithm. IEEE Access (2021).
3. A comprehensive survey of convergence analysis of beetle antennae search algorithm and its applications. Artificial Intelligence Review (2024).
4. A novel chaotic and neighborhood search-based artificial bee colony algorithm for solving optimization problems. Scientific Reports (2023).
5. An improved spider optimization algorithm coordinated by pheromones. Scientific Reports (2022).