https://repub.eur.nl/pub/86676/REPUB_86676_OA.pdf

Auction optimization using regression trees and linear models as integer programs

Several engineering problems involve simultaneously several objective functions where at least one of them is expensive to evaluate. This fact has yielded to a new class of Multi-Objective Problems (MOPs) called expensive MOPs. Several attempts have been conducted in the literature with the goal to minimize the number of expensive evaluations by using surrogate models stemming from the machine learning field. Usually, researchers substitute the expensive objective function evaluation by an estimation drawn from the used surrogate. In this paper, we propose a new way to tackle expensive MOPs. The main idea is to use Neural Networks (NNs) within the Indicator-Based Evolutionary Algorithm (IBEA) in order to estimate the contribution of each generated offspring in terms of hypervolume. After that, only fit individuals with respect to the estimations are exactly evaluated. Our proposed algorithm called NN-SS-IBEA (Neural Networks assisted Steady State IBEA) have been demonstrated to provide good performance with a low number of function evaluations when compared against the original IBEA and MOEA/D-RBF on a set of benchmark problems in addition to the airfoil design problem.

Steady state IBEA assisted by MLP neural networks for expensive multi-objective optimization problems

A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate-based algorithms are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate-based algorithm that uses a linear combination of rectified linear units, defined in such a way that (local) optima satisfy the integer constraints. This method outperforms the state of the art on several synthetic benchmarks with up to 238 continuous and integer variables, and achieves competitive performance on two real-life benchmarks: XGBoost hyperparameter tuning and Electrostatic Precipitator optimisation.

/pdf/black-box-mixed-variable-optimisation-using-a-surrogate-26tdjpotkn.pdf

Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints

In many practical optimization problems, evaluation of objectives and constraints often involve computationally expensive procedures. To handle such problems, a metamodel-assisted approach is usually used to complete an optimization run in a reasonable amount of time. A metamodel is an approximate mathematical model of an objective or a constrained function which is constructed with a handful of solutions evaluated exactly. However, when comes to solving multi-objective optimization problems involving numerous constraints, it may be too much to metamodel each and every objective and constrained function independently. The cumulative effect of errors from each metamodel may turn out to be detrimental for the accuracy of the overall optimization procedure. In this paper, we propose a taxonomy of various metamodeling methodologies for multi-objective optimization and provide a comparative study by discussing advantages and disadvantages of each method. The first results presented in this paper are obtained using the well-known Kriging metamodeling approach. Based on our proposed taxonomy and an extensive literature search, we also highlight new and promising methods for multi-objective metamodeling algorithms.

Classifying Metamodeling Methods for Evolutionary Multi-objective Optimization: First Results

markdownIn this thesis we focus on two different aspects of auctions and we employ techniques and methods from both operations research and computer science. 
_First,_ we study the allocation of tasks to agents at the end of an auction. Usually, tasks are allocated in such a way that minimizes the total cost for the auctioneer. This allocation is optimal in a one-shot auction, but if the auction is repeated, this can have negative consequences for the results in the long run. Therefore, we consider a fair allocation, which costs slightly more in a one-shot auction, but has positive effects on the participation level of agents and the total cost for the auctioneer in repeated auctions. 
_Second,_ we consider the auction design. How an auction is set up, like which tasks should be auctioned first, or what the starting price should be, impacts the result. Usually there are experts who know what has occurred in previous auctions and how a future auction should be designed in order to obtain the best results. However, historical auctions can obtain so much information that experts overlook things. We use a combination of machine learning and optimization models to extract information from historical auctions and use this information to help design future auctions for better results.

/pdf/multi-objective-optimization-methods-for-allocation-and-10wtgeg0qe.pdf

Multi-objective Optimization Methods for Allocation and Prediction

Incremental learning is useful for processing streaming data, where data elements are produced at a high rate and cannot be stored. An incremental learner typically updates its model with each new instance that arrives. To avoid skipped instances, the model update must finish before the next element arrives, so it should be fast. However, there can be a trade-off between the efficiency of the update and how many updates are needed to get a good model. We investigate this trade-off in the context of model trees. We compare FIMT, a state-of-the-art incremental model tree learner developed for streaming data, with two alternative methods that use a more expensive update method. We find that for data with relatively low (but still realistic) dimensionality, the most expensive method often yields the best learning curve: the system converges faster to a smaller and more accurate model tree.

Slower Can Be Faster: The iRetis Incremental Model Tree Learner

Mobile workers employed by a utility company, for instance, electricians or plumbers, are becoming increasingly autonomous. Instead of signing in at the company everyday to receive their assignments, they are now often on the road for several days, receiving their instructions on a mobile device equipped with 3G technology. Much more than regular users of cellular networks, mobile workers require a reliable connection while traveling between locations. Unfortunately, 3G technology is not very reliable. Signal strength can fluctuate widely between locations. Furthermore, commercial claims of network quality, and existing theoretical coverage maps are often inconsistent with reality. We aim to compute a practical connectivity strength map for Flanders that can be used to predict network connectivity for mobile workers. To our knowledge such a map does not currently exist. Based on this map and a predicted future location, a modem would be able to automatically choose the optimal 3G technology and bandwidth in order to maintain a stable network connection while traveling. Additionally, the map provides users with a visualization of the network connectivity in an area. The computation of the coverage map is based on anonymous real-time measurements collected from mobile workers. Each measurement consists of a unique network cell identifier, GPS coordinates, a received signal strength indication (RSSI), and download rate. We distinguish two phases in the computation. First, we apply a constraint programming approach to match cell identifiers with their physical location. The constraints are based on knowledge about the practical limitations of cellular network technology, such as he maximum broadcasting angle of an antenna. Second, we predict the network strength at a given location by using the geostatistical interpolation technique Kriging, also known as Gaussian Process regression [Ras06]. In the future, we plan to adapt Kriging so that the coverage map is updated incrementally with real-time measurements.

https://lirias.kuleuven.be/bitstream/123456789/414541/1/OptimalMobileConnectivity.pdf

Optimal mobile connectivity using a practical coverage map

https://lirias.kuleuven.be/bitstream/123456789/447724/1/benelearn14VerbeeckBlockeel.pdf

Sensitivity analysis of search-space dimensionality on recent multi-objective evolutionary algorithms

https://lirias.kuleuven.be/bitstream/123456789/463078/1/DS2014_LBP_Verbeeck.pdf

iMauve: A fast incremental model tree learner

Multi-objective optimization problems are usually solved with evolutionary algorithms when the objective functions are cheap to compute, or with surrogate-based optimizers otherwise. In the latter case, the objective functions are modeled with powerful non-linear model learners such as Gaussian Processes or Support Vector Machines, for which the training time can be prohibitively large when dealing with optimization problems with moderately expensive objective functions. In this paper, we investigate the use of model trees as an alternative kind of model, providing a good compromise between high expressiveness and low training time. We propose a fast surrogate-based optimizer exploiting the structure of model trees for candidate selection. The empirical results show the promise of the approach for problems on which classical surrogate-based optimizers are painfully slow.

Multi-objective optimization with surrogate trees

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