We consider global non-convex optimisation problems under uncertainty. In this setting, it is not possible to implement a desired solution exactly. Instead, any other solution within some distance to the intended solution may be implemented. The aim is to find a robust solution, i.e., one where the worst possible solution nearby still performs as well as possible.
Problems of this type exhibit another maximisation layer to find the worst case solution within the minimisation level of finding a robust solution, which makes them harder to solve than classic global optimisation problems. So far, only few methods have been provided that can be applied to black-box problems with implementation uncertainty. We improve upon existing techniques by introducing a novel particle swarm based framework which adapts elements of previous approaches, combining them with new features in order to generate more effective techniques. In computational experiments, we find that our new method outperforms state of the art comparator heuristics in almost 80% of cases.
Swarm intelligence has becoming a powerful technique in solving design and scheduling tasks. Metaheuristic algorithms are an integrated part of this paradigm, and particle swarm optimization is often viewed as an important landmark. The outstanding performance and efficiency of swarm-based algorithms inspired many new developments, though mathematical understanding of metaheuristics remains partly a mystery. In contrast to the classic deterministic algorithms, metaheuristics such as PSO always use some form of randomness, and such randomization now employs various techniques. This paper intend…
We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst possible performance over all possible perturbances. Previously, only few generic search methods have been developed for this setting. We introduce a new approach for a global search, based on placing a largest empty hypersphere. We do not assume any knowledge on the structure of the original objective function, making this approach also viable for simulation-…
Business optimization is becoming increasingly important because all business activities aim to maximize the profit and performance of products and services, under limited resources and appropriate constraints. Recent developments in support vector machine and metaheuristics show many advantages of these techniques. In particular, particle swarm optimization is now widely used in solving tough optimization problems. In this paper, we use a combination of a recently developed Accelerated PSO and a nonlinear support vector machine to form a framework for solving business optimization problems. W…
The dynamic slope scaling procedure is an approximation method successfully which solves the fixed charge network flow (FCNF) problem by iteratively linearizing the fixed cost. The parameterized dynamic slope scaling procedure adds an additional $ψ$ parameter to the procedure which can significantly improve the solution quality. Finding the optimal value of $ψ$ for a given problem is non-trivial. This paper employs multiple metaheuristic techniques, including simulated annealing, tabu search, and particle swarm optimization, to guide the search for good parameter values. In rigorous testing, w…
Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and harmony search are now becoming powerful methods for solving many tough optimization problems. In this paper, we propose a new metaheuristic method, the Bat Algorithm, based on the echolocation behaviour of bats. We also intend to combine the advantages of existing algorithms into the new bat algorithm. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing algorithms, including genetic algorithms and particle swarm optimization. Simul…
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we intend to provide an overview of convergence and efficiency studies of metaheuristics, and try to provid…
Modern optimisation algorithms are often metaheuristic, and they are very promising in solving NP-hard optimization problems. In this paper, we show how to use the recently developed Firefly Algorithm to solve nonlinear design problems. For the standard pressure vessel design optimisation, the optimal solution found by FA is far better than the best solution obtained previously in literature. In addition, we also propose a few new test functions with either singularity or stochastic components but with known global optimality, and thus they can be used to validate new optimisation algorithms. …
Nature-inspired algorithms such as Particle Swarm Optimization and Firefly Algorithm are among the most powerful algorithms for optimization. In this paper, we intend to formulate a new metaheuristic algorithm by combining Levy flights with the search strategy via the Firefly Algorithm. Numerical studies and results suggest that the proposed Levy-flight firefly algorithm is superior to existing metaheuristic algorithms. Finally implications for further research and wider applications will be discussed.
The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (ARO), a model free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of differ…
A new metaheuristic optimisation algorithm, called Cuckoo Search (CS), was developed recently by Yang and Deb (2009). This paper presents a more extensive comparison study using some standard test functions and newly designed stochastic test functions. We then apply the CS algorithm to solve engineering design optimisation problems, including the design of springs and welded beam structures. The optimal solutions obtained by CS are far better than the best solutions obtained by an efficient particle swarm optimiser. We will discuss the unique search features used in CS and the implications for…
Feedback optimisation is an emerging technique aiming at steering a system to an optimal steady state for a given objective function. We show that it is possible to employ this control strategy in a distributed manner. Moreover, we prove asymptotic convergence to the set of optimal configurations. To this scope, we show that exponential stability is needed only for the portion of the state that affects the objective function. This is showcased by driving a swarm of agents towards a target location while maintaining a target formation. Finally, we provide a sufficient condition on the topologic…
In this paper we present a metaheuristic for global optimization called General Algorithmic Search (GAS). Specifically, GAS is a stochastic, single-objective method that evolves a swarm of agents in search of a global extremum. Numerical simulations with a sample of 31 test functions show that GAS outperforms Basin Hopping, Cuckoo Search, and Differential Evolution, especially in concurrent optimization, i.e., when several runs with different initial settings are executed and the first best wins. Python codes of all algorithms and complementary information are available online.
University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）；The Alan Turing Institute（阿兰·图灵研究所）；University of Manchester（曼彻斯特大学）
ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator b…
In this paper, we propose a simple global optimisation algorithm inspired by Pareto's principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the dynamic tightening of the prominent domains while the greediness of the algorithm increases over time (iterations). Unlike traditional metaheuristics, the proposed method has no direct mutation- or crossover-like operations. It depends solely on the sequential random sampling that can be used in diversification and intensification processes while keeping the inf…
Metaheuristic algorithms for the induced P-median problem with upgrades
Universidad Rey Juan Carlos（雷乌斯·琼卡洛斯大学）；ITA-UNIFESP Graduate Program in Operations Research（ITA-UNIFESP运筹学研究生项目）；Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)（离散数学与理论计算机科学中心）
Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences (MACS), Heriot-Watt University（赫瑞-瓦特大学数学与计算机科学学院数学系麦克斯韦数学科学研究所）；University of Ferrara（费拉拉大学）
In this work we survey some recent results on the global minimization of a non-convex and possibly non-smooth high dimensional objective function by means of particle based gradient-free methods. Such problems arise in many situations of contemporary interest in machine learning and signal processing. After a brief overview of metaheuristic methods based on particle swarm optimization (PSO), we introduce a continuous formulation via second-order systems of stochastic differential equations that generalize PSO methods and provide the basis for their theoretical analysis. Subsequently, we will s…
We develop algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly the aim is to find a robust one, where the worst case in an uncertainty neighbourhood around a solution still performs well. This requires a local maximisation within a global minimisation. To investigate improved optimisation methods for robust problems, and remove the need to manually determine an effective heuristic and parameter settings, we employ an automatic generation of algorithms approach: Grammar-Guided Gen…
A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle high-dimensional global optimisation problems, and it has been successfully used to find solutions to real-life engineering problems among which the preliminary design of interplanetary spacecraft trajectories - both chemical (including multiple flybys and deep-space maneuvers) and low-thrust (limited, at the moment, to single phase trajectories), the inverse design of na…
