Surrogate-Assisted Artificial Immune Systems for Expensive Optimization Problems

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Elite Accumulative Sampling Strategies for Noisy Multi-Objective Optimisation

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-15892-1_128th International Conference on Evolutionary Multi-Criterion Optimization 2015, Guimarães, Portugal, 29 March - 1 April 1 2015The codebase for this paper is available at https://github.com/fieldsend/EMO_2015_eliteWhen designing evolutionary algorithms one of the key concerns is the balance between expending function evaluations on exploration versus exploitation. When the optimisation problem experiences observational noise, there is also a trade-off with respect to accuracy refinement – as improving the estimate of a design’s performance typically is at the cost of additional function reevaluations. Empirically the most effective resampling approach developed so far is accumulative resampling of the elite set. In this approach elite members are regularly reevaluated, meaning they progressively accumulate reevaluations over time. This results in their approximated objective values having greater fidelity, meaning non-dominated solutions are more likely to be correctly identified. Here we examine four different approaches to accumulative resampling of elite members, embedded within a differential evolution algorithm. Comparing results on 40 variants of the unconstrained IEEE CEC’09 multi-objective test problems, we find that at low noise levels a low fixed resample rate is usually sufficient, however for larger noise magnitudes progressively raising the number of minimum resamples of elite members based on detecting estimated front oscillation tends to improve performance

The Markov network fitness model

Fitness modelling is an area of research which has recently received much interest among the evolutionary computing community. Fitness models can improve the efficiency of optimisation through direct sampling to generate new solutions, guiding of traditional genetic operators or as surrogates for a noisy or long-running fitness functions. In this chapter we discuss the application of Markov networks to fitness modelling of black-box functions within evolutionary computation, accompanied by discussion on the relationship betweenMarkov networks andWalsh analysis of fitness functions.We review alternative fitness modelling and approximation techniques and draw comparisons with the Markov network approach. We discuss the applicability of Markov networks as fitness surrogates which may be used for constructing guided operators or more general hybrid algorithms.We conclude with some observations and issues which arise from work conducted in this area so far

Q-Learning Induced Artificial Bee Colony for Noisy Optimization

The paper proposes a novel approach to adaptive selection of sample size for a trial solution of an evolutionary algorithm when noise of unknown distribution contaminates the objective surface. The sample size of a solution here is adapted based on the noisy fitness profile in the local surrounding of the given solution. The fitness estimate and the fitness variance of a sub-population surrounding the given solution are jointly used to signify the degree of noise contamination in its local neighborhood (LN). The adaptation of sample size based on the characteristics of the fitness landscape in the LN of a solution is realized here with the temporal difference Q-learning (TDQL). The merit of the present work lies in utilizing the reward-penalty based reinforcement learning mechanism of TDQL for sample size adaptation. This sidesteps the prerequisite setting of any specific functional form of relationship between the sample size requirement of a solution and the noisy fitness profile in its LN. Experiments undertaken reveal that the proposed algorithms, realized with artificial bee colony, significantly outperform the existing counterparts and the state-of-the-art algorithms

P.: Evolutionary optimisation of noisy multiobjective problems using confidence-based dynamic resampling

Abstract Many real-world optimisation problems approached by evolutionary algorithms are subject to noise. When noise is present, the evolutionary selection process may become unstable and the convergence of the optimisation adversely affected. In this paper, we present a new technique that efficiently deals with noise in multi-objective optimisation. This technique aims at preventing the propagation of inferior solutions in the evolutionary selection due to noisy objective values. This is done by using an iterative resampling procedure that reduces the noise until the likelihood of selecting the correct solution reaches a given confidence level. To achieve an efficient utilisation of resources, the number of samples used per solution varies based on the amount of noise in the present area of the search space. The proposed algorithm is evaluated on the ZDT benchmark problems and two complex real-world problems of manufacturing optimisation. The first realworld problem concerns the optimisation of engine component manufacturing in aviation industry, while the second real-world problem concerns the optimisation of a camshaft machining line in automotive industry. The results from the optimisations indicate that the proposed technique is successful in reducing noise, and it competes successfully with other noise handling techniques

A multi-objective evolutionary approach to simulation-based optimisation of real-world problems.

This thesis presents a novel evolutionary optimisation algorithm that can improve the quality of solutions in simulation-based optimisation. Simulation-based optimisation is the process of finding optimal parameter settings without explicitly examining each possible configuration of settings. An optimisation algorithm generates potential configurations and sends these to the simulation, which acts as an evaluation function. The evaluation results are used to refine the optimisation such that it eventually returns a high-quality solution. The algorithm described in this thesis integrates multi-objective optimisation, parallelism, surrogate usage, and noise handling in a unique way for dealing with simulation-based optimisation problems incurred by these characteristics. In order to handle multiple, conflicting optimisation objectives, the algorithm uses a Pareto approach in which the set of best trade-off solutions is searched for and presented to the user. The algorithm supports a high degree of parallelism by adopting an asynchronous master-slave parallelisation model in combination with an incremental population refinement strategy. A surrogate evaluation function is adopted in the algorithm to quickly identify promising candidate solutions and filter out poor ones. A novel technique based on inheritance is used to compensate for the uncertainties associated with the approximative surrogate evaluations. Furthermore, a novel technique for multi-objective problems that effectively reduces noise by adopting a dynamic procedure in resampling solutions is used to tackle the problem of real-world unpredictability (noise). The proposed algorithm is evaluated on benchmark problems and two complex real-world problems of manufacturing optimisation. The first real-world problem concerns the optimisation of a production cell at Volvo Aero, while the second one concerns the optimisation of a camshaft machining line at Volvo Cars Engine. The results from the optimisations show that the algorithm finds better solutions for all the problems considered than existing, similar algorithms. The new techniques for dealing with surrogate imprecision and noise used in the algorithm are identified as key reasons for the good performance.University of Skövde Knowledge Foundation Swede

Multiobjective Simulation Optimization Using Enhanced Evolutionary Algorithm Approaches

In today\u27s competitive business environment, a firm\u27s ability to make the correct, critical decisions can be translated into a great competitive advantage. Most of these critical real-world decisions involve the optimization not only of multiple objectives simultaneously, but also conflicting objectives, where improving one objective may degrade the performance of one or more of the other objectives. Traditional approaches for solving multiobjective optimization problems typically try to scalarize the multiple objectives into a single objective. This transforms the original multiple optimization problem formulation into a single objective optimization problem with a single solution. However, the drawbacks to these traditional approaches have motivated researchers and practitioners to seek alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated in stochastic environments when the objectives take on uncertain (or noisy ) values due to random influences within the system being optimized, which is the case in real-world environments. Moreover, in stochastic environments, a solution approach should be sufficiently robust and/or capable of handling the uncertainty of the objective values. This makes the development of effective solution techniques that generate Pareto optimal solutions within these problem environments even more challenging than in their deterministic counterparts. Furthermore, many real-world problems involve complicated, black-box objective functions making a large number of solution evaluations computationally- and/or financially-prohibitive. This is often the case when complex computer simulation models are used to repeatedly evaluate possible solutions in search of the best solution (or set of solutions). Therefore, multiobjective optimization approaches capable of rapidly finding a diverse set of Pareto optimal solutions would be greatly beneficial. This research proposes two new multiobjective evolutionary algorithms (MOEAs), called fast Pareto genetic algorithm (FPGA) and stochastic Pareto genetic algorithm (SPGA), for optimization problems with multiple deterministic objectives and stochastic objectives, respectively. New search operators are introduced and employed to enhance the algorithms\u27 performance in terms of converging fast to the true Pareto optimal frontier while maintaining a diverse set of nondominated solutions along the Pareto optimal front. New concepts of solution dominance are defined for better discrimination among competing solutions in stochastic environments. SPGA uses a solution ranking strategy based on these new concepts. Computational results for a suite of published test problems indicate that both FPGA and SPGA are promising approaches. The results show that both FPGA and SPGA outperform the improved nondominated sorting genetic algorithm (NSGA-II), widely-considered benchmark in the MOEA research community, in terms of fast convergence to the true Pareto optimal frontier and diversity among the solutions along the front. The results also show that FPGA and SPGA require far fewer solution evaluations than NSGA-II, which is crucial in computationally-expensive simulation modeling applications

Fitness inheritance for noisy evolutionary multi-objective optimization

This paper compares the performance of anti-noise methods, particularly probabilistic and re-sampling methods, using NSGA2. It then proposes a computationally less expensive approach to counteracting noise using re-sampling and fitness inheritance. Six problems with different difficulties are used to test the methods. The results indicate that the probabilistic approach has better convergence to the Pareto optimal front, but it looses diversity quickly. However, methods based on re-sampling are more robust against noise but they are computationally very expensive to use. The proposed fitness inheritance approach is very competitive to re-sampling methods with much lower computational cost

Fitness inheritance for noisy evolutionary multi-objective optimization

This paper compares the performance of anti-noise methods, particularly probabilistic and re-sampling methods, using NSGA2. It then proposes a computationally less expensive approach to counteracting noise using re-sampling and fitness inheritance. Six problems with different difficulties are used to test the methods. The results indicate that the probabilistic approach has better convergence to the Pareto optimal front, but it looses diversity quickly. However, methods based on re-sampling are more robust against noise but they are computationally very expensive to use. The proposed fitness inheritance approach is very competitive to re-sampling methods with much lower computational cost