Instantaneous control of interacting particle systems in the mean-field limit

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit,i.e., for an increasing number of particles.Comment: arXiv admin note: substantial text overlap with arXiv:1610.0132

SamACO: variable sampling ant colony optimization algorithm for continuous optimization

An ant colony optimization (ACO) algorithm offers algorithmic techniques for optimization by simulating the foraging behavior of a group of ants to perform incremental solution constructions and to realize a pheromone laying-and-following mechanism. Although ACO is first designed for solving discrete (combinatorial) optimization problems, the ACO procedure is also applicable to continuous optimization. This paper presents a new way of extending ACO to solving continuous optimization problems by focusing on continuous variable sampling as a key to transforming ACO from discrete optimization to continuous optimization. The proposed SamACO algorithm consists of three major steps, i.e., the generation of candidate variable values for selection, the ants’ solution construction, and the pheromone update process. The distinct characteristics of SamACO are the cooperation of a novel sampling method for discretizing the continuous search space and an efficient incremental solution construction method based on the sampled values. The performance of SamACO is tested using continuous numerical functions with unimodal and multimodal features. Compared with some state-of-the-art algorithms, including traditional ant-based algorithms and representative computational intelligence algorithms for continuous optimization, the performance of SamACO is seen competitive and promising

Differential evolution with an individual-dependent mechanism

Differential evolution (DE) is a well-known optimization algorithm that utilizes the difference of positions between individuals to perturb base vectors and thus generate new mutant individuals. However, the difference between the fitness values of individuals, which may be helpful to improve the performance of the algorithm, has not been used to tune parameters and choose mutation strategies. In this paper, we propose a novel variant of DE with an individual-dependent mechanism that includes an individual-dependent parameter (IDP) setting and an individual-dependent mutation (IDM) strategy. In the IDP setting, control parameters are set for individuals according to the differences in their fitness values. In the IDM strategy, four mutation operators with different searching characteristics are assigned to the superior and inferior individuals, respectively, at different stages of the evolution process. The performance of the proposed algorithm is then extensively evaluated on a suite of the 28 latest benchmark functions developed for the 2013 Congress on Evolutionary Computation special session. Experimental results demonstrate the algorithm's outstanding performance

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto's front which is a set of scenarios that are helpful for guiding the decision's maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization

Orthogonal learning particle swarm optimization

Particle swarm optimization (PSO) relies on its learning strategy to guide its search direction. Traditionally, each particle utilizes its historical best experience and its neighborhood’s best experience through linear summation. Such a learning strategy is easy to use, but is inefficient when searching in complex problem spaces. Hence, designing learning strategies that can utilize previous search information (experience) more efficiently has become one of the most salient and active PSO research topics. In this paper, we proposes an orthogonal learning (OL) strategy for PSO to discover more useful information that lies in the above two experiences via orthogonal experimental design. We name this PSO as orthogonal learning particle swarm optimization (OLPSO). The OL strategy can guide particles to fly in better directions by constructing a much promising and efficient exemplar. The OL strategy can be applied to PSO with any topological structure. In this paper, it is applied to both global and local versions of PSO, yielding the OLPSO-G and OLPSOL algorithms, respectively. This new learning strategy and the new algorithms are tested on a set of 16 benchmark functions, and are compared with other PSO algorithms and some state of the art evolutionary algorithms. The experimental results illustrate the effectiveness and efficiency of the proposed learning strategy and algorithms. The comparisons show that OLPSO significantly improves the performance of PSO, offering faster global convergence, higher solution quality, and stronger robustness