Oliver Schuetze

A new memetic strategy for the numerical treatment of multi-objective optimization problems

In this paper we propose a novel iterative search procedure for multi-objective optimization problems. The iteration process -- though derivative free -- utilizes the geometry of the directional cones of such optimization problems, and is capable both of moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. Next, we give one possible way of integrating this local search procedure into a given EMO algorithm resulting in a novel memetic strategy. Finally, we present some numerical results on some well-known benchmark problems indicating the strength of both the local search strategy as well as the new hybrid approach.

Computing finite size representations of the set of approximate solutions of an MOP with stochastic search algorithms

In this work we study the convergence of generic stochastic search algorithms toward the entire set of approximate solutions of continuous multi-objective optimization problems. Since the dimension of the set of interest is typically equal to the dimension of the parameter space, we focus on obtaining a finite and tight approximation, measured by the Hausdorff distance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results.

Evolutionary continuation methods for optimization problems

In this paper we develop evolutionary strategies for numerical continuation which we apply to scalar and multi-objective optimization problems. To be more precise, we will propose two different methods-an embedding algorithm and a multi-objectivization approach-which are designed to follow an implicitly defined curve where the aim can be to detect the endpoint of the curve (e.g., a root finding problem) or to approximate the entire curve (e.g., the Pareto set of a multi-objective optimization problem). We demonstrate that the novel approaches are very robust in finding the set of interest (point or curve) on several examples.

Handling changes of performance requirements in multi-objective problems

In this paper, the need for rapid, low-cost changes in a design, in response to changes in performance requirements (PRs), within multi-objective problems, is considered. In the current study, the rapid response is attained through a priori design of a set of satisfying solutions, such that any PR may be satisfied by at least one member of the set. The purpose is to design such a set so that once the PRs change, the changes needed in order to adapt to the existing product (one member of the set) to the new requirements are minimal, while maintaining the aspiration for optimal performances. It is assumed here that minimal changes are related to small changes in the design parameters. In order to find the optimal set, sets of candidate solutions are evolved using an evolutionary multi-objective optimisation algorithm. The algorithm enhances a search pressure towards sets with minimal distances between their members (in design space) and with optimal performances, which are assessed by utilising the hyper-volume measure. An artificial and a real life example are utilised in order to explain the approach and to show its applicability to engineering problems.

Fine Structure of Pareto Front of Multi-Objective Optimal Feedback Control Design

Recently, we have proposed the simple cell mapping method (SCM) for global solutionsof multi-objective optimization problems (MOPs). We have applied the SCM method to the multi-objective optimal time domain design of PID control gains for linear systems to simultaneously minimize the overshoot, peak time and integrated absolute tracking error of the closed-loop step response. The SCM method can efficiently obtain the Pareto set and Pareto front globally, which represent the optimal control gains and performance measures, respectively. The Pareto set and Pareto front contain a complete set of control designs with various compromises in the tracking performance, and give the system designer a much wider range of choices and flexibility. Furthermore, we have discovered a fine structure of the Pareto front of the MOP solution, which was notseen before in the literature. In this paper, we further examine the implication of the fine structure with regard to the vibration control design and expected performance of the controller, and compare our findings with the dominant method in MOP studies, i.e. the genetic algorithm.Copyright

Using gradient information for multi-objective problems in the evolutionary context

The goal of this research is to study the incorporation of gradient-based information when designing Multi-objective Evolutionary Algorithms (MOEAs). We analyze the benefits, and challenges, of using these well developed mathematical programming techniques in order to get hybrid MOEAs. Since we expect the new hybrid algorithms to search effectively and more efficiently than currently available MOEAs, a deeper study of the balance between the computational and the benefits of this coupling is highly necessary.

New challenges for memetic algorithms on continuous multi-objective problems

This work presents the main aspects to tackle when designing memetic algorithms using gradient-based local searchers.. We address the main drawbacks and advantages of this coupling, when focusing on the efficiency of the local search stage. We conclude with some guidelines and draw further research paths in these topics.

Integrated circuit optimization by means of evolutionary multi-objective optimization

The design of resource efficient integrated circuits (ICs) requires solving a minimization problem which consists of more than one objective given as measures of the available resources. This multi-objective optimization problem (MOP) can be solved on the smallest unit of the IC, the standard cells, to improve the performance of the entire circuit. In this work, transistor sizing of an IC is approached via a multi-objective approach which includes the use of multi-objective evolutionary algorithms (MOEAs). We compare the performance of two MOEAs on a four-dimensional MOP of a particular standard cell. The results indicate that evolutionary strategies are suitable for the treatment of such problems and advantageous against other rather classical methods.

Multi-Objective Optimal Control Design With the Simple Cell Mapping Method

Controls are often designed to meet different and conflicting goals. Consider the well-known LQR optimal control. The performance index contains a response measure and a control penalty, which are conflicting requirements. Proper linear or nonlinear combinations of the conflicting objective functions have led to single objective optimization problems. However, such a single objective optimization is dependent on the combination algorithm, and only provides a narrow window of all possible optimal solutions that a system may have.Multi-objective optimization provides a set of optimal solutions, known as Pareto set. There have been many studies of search algorithms for Pareto sets of multi-objective optimization problems for complex dynamical systems. Recently, the simple cell mapping (SCM) method due to C.S. Hsu has been found to be a highly effective tool to compute Pareto sets. This paper applies the SCM method to several control design problems of linear and nonlinear dynamical systems. The results of the work are very exciting to report.Copyright