Elitist archiving for multi-objective evolutionary algorithms: To adapt or not to adapt

Objective-space discretization is a popular method to control the elitist archive size for evolutionary multi-objective optimization and avoid problems with convergence. By setting the level of discretization, the proximity and diversity of the Pareto approximation set can be controlled. This paper proposes an adaptive archiving strategy which is developed from a rigid-grid discretization mechanism. The main advantage of this strategy is that the practitioner just decides the desirable target size for the elitist archive while all the maintenance details are automatically handled. We compare the adaptive and rigid archiving strategies on the basis of a performance indicator that measures front quality, success rate, and running time. Experimental results confirm the competitiveness of the adaptive method while showing its advantages in terms of transparency and ease of use

The Port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors.

International audienceThis paper proposes a thermodynamical pseudo Hamiltonian formulation of Continuous Stirred Tank Reactor model in which takes place some chemical reaction. This is done both in the isothermal and non isothermal cases. It is shown that the Gibbs free energy and the opposite of entropy can be chosen as Hamiltonian function respectively. For the non isothermal case, the so called Interconnection and Damping Assignment Passivity Based Control method is applied to stabilize the system at a desired state. For this general reaction scheme, the control problem is shown to be easy to solve as soon as the closed loop Hamiltonian function is chosen to be proportional to the so called thermodynamic availability function. Simulation results based on a simple first order reaction and operating conditions leading to multiple steady states of the CSTR are given to validate the proposed control design procedure

Exploiting linkage information and problem-specific knowledge in evolutionary distribution network expansion planning

This article tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introd uced to satisfy the future power demands. Because of many real-world details involved, the structure of the problem is not exploited easily using mathematical programming techniques, for which reason we consider solving this problem with evolutionary algorithms (EAs). We compare three types of EAs for optimizing expansion plans : the classic genetic algorithm (GA), the estimation-of-distribution algorith m (EDA), and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). Not fully k nowing the structure of the problem, we study the effect of linkage learning through the use of three linkage models: univariate, marginal product, and linkage tree. We furthermore experiment with the impact of incorporating different levels of proble m-specific knowledge in the variation operators. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions. In all EAs, the marginal product model and its linkage learning pro cedure have difficulty in capturing and exploiting the DNEP problem structure. GOMEA, especially when combined with the linkage tree structure, is found to have the most robust performance by far

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the interleaved multi-start scheme

The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA

Multi-objective gene-pool optimal mixing evolutionary algorithms

In this paper, by constructing the Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA), we pinpoint key features for scalable multi objective optimizers. First, an elitist archive is beneficial for keeping track of non-dominated solutions. Second, clustering can be crucial if different parts of the Pareto-optimal front need to be handled separately. Next, an efficient linkage learning procedure with a lean linkage model is required to capture the underlying dependencies among decision variables. It is also important that the optimizers can effectively exploit the learned linkage relations to generate new offspring solutions, steering the search toward promising regions in the search space

Multi-objective gene-pool optimal mixing evolutionary algorithms

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), with a lean, but sufficient, linkage model and an efficient variation operator, has been shown to be a robust and efficient methodology for solving single objective (SO) optimization problems with superior performance compared to classic genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). In this paper, we bring the strengths of GOMEAs to the multi-objective (MO) optimization realm. To this end, we modify the linkage learning procedure and the variation operator of GOMEAs to better suit the need of finding the whole Pareto-optimal front rather than a single best solution. Based on state-of-the-art studies on MOEAs, we further pinpoint and incorporate two other essential components for a scalable MO optimizer. First, the use of an elitist archive is beneficial for keeping track of non-dominated solutions when the main population size is limited. Second, clustering can be crucial if different parts of the Pareto-optimal front need to be handled differently. By combining these elements, we construct a multi-objective GOMEA (MO-GOMEA). Experimental results on various MO optimization problems confirm the capability and scalability of our MO-GOMEA that compare favorably with those of the well-known GA NSGA-II and the more recently introduced EDA mohBOA

Exploiting Linkage Information and Problem-Specific Knowledge in Evolutionary Distribution Network Expansion Planning

This paper tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introduced to satisfy the future power demands. We compare two evolutionary algorithms (EAs) for optimizing expansion plans: the classic genetic algorithm (GA) with uniform crossover and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) that learns and exploits linkage information between problem variables. We study the impact of incorporating different levels of problem-specific knowledge in the variation operators as well as two constraint-handling techniques: constraint domination and repair mechanisms. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions to the DNEP problem. GOMEA is found to have far more robust performance even when an out-of-box variant is used that doesn't exploit problem-specific knowledge. Based on experiments, we suggest that when selecting optimization algorithms for real-world applications like DNEP, EAs that have the ability to model and exploit problem structures, such as GOMEAs and estimation-of-distribution algorithms, should be given priority, especially when problem-specific knowledge is not straightforward to exploit, e.g. in the case of black-box optimization

Passivity-based nonlinear control of CSTR via asymptotic observers.

International audienceThis work makes use of a passivity-based approach (PBA) and tools from Lyapunov theory to design a nonlinear controller for the asymptotic stabilization of a class of non isothermal Continuous Stirred Tank Reactors (CSTR) around any desired stationary point. The convergence and stability proofs are derived in the port Hamiltonian framework. Asymptotic observers that do not require knowledge of reaction kinetics are also proposed for a system with incomplete state measurement. Numerical simulations are given to illustrate the application of the theoretical results to a CSTR with multiple steady states

Medium-Voltage Distribution Network Expansion Planning with Gene-pool Optimal Mixing Evolutionary Algorithms

Medium-voltage distribution network expansion planning involves finding the most economical adjustments of both the capacity and the topology of the network such that no operational constraints are violated and the expected loads, that the expansion is planned for, can be supplied. This paper tackles this important real-world problem using realistic yet computationally feasible models and, for the first time, using two instances of the recently proposed class of Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) that have previously been shown to be a highly efficient integration of local search and genetic recombination, but only on standard benchmark problems. One GOMEA instance that we use employs linkage learning and one instance assumes no dependencies among problem variables. We also conduct experiments with a widely used traditional Genetic Algorithm (GA). Our results show that the favorable performance of GOMEA instances over traditional GAs extends to the real-world problem at hand. Moreover, the use of linkage learning is shown to further increase the algorithm's effectiveness in converging toward optimal solutions

Efficiency enhancements for evolutionary capacity planning in distribution grids

In this paper, we tackle the distribution network expansion planning (DNEP) problem by employing two evolutionary algorithms (EAs): the classical Genetic Algorithm (GA) and a linkage-learning EA, specifically a Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). We furthermore develop two efficiency-enhancement techniques for these two EAs for solving the DNEP problem: a restricted initialization mechanism to reduce the size of the explorable search space and a means to filter linkages (for GOMEA) to disregard linkage groups during genetic variation that are likely not useful. Experimental results on a benchmark network show that if we may assume that the optimal network will be very similar to the starting network, restricted initialization is generally useful for solving DNEP and moreover it becomes more beneficial to use the simple GA. However, in the more general setting where we cannot make the closeness assumption and the explorable search space becomes much larger, GOMEA outperforms the classical GA