Dataset on a Benchmark for Equality Constrained Multi-objective Optimization.

In this Data in Brief, we provide the source code for the equality constrained multi-objective optimization benchmark problems EqDTLZ 1-4 and EqIDTLZ 1-2 proposed in the research article "A Benchmark for Equality Constrained Multi-objective Optimization" [1]. Further, we provide the codes for the multi-objective evolutionary algorithms NSGA-II, NSGA-III, aNSGA-III, GDE3, MOEA/D/D and PPS and their numerical approximations on the above mentioned test functions. All codes are provided in Matlab using the PlatEMO classes version 2.0 in order to test different algorithms.

The Set-Based Hypervolume Newton Method for Bi-Objective Optimization.

In this paper, we propagate the use of a set-based Newton method that enables computing a finite size approximation of the Pareto front (PF) of a given twice continuously differentiable bi-objective optimization problem (BOP). To this end, we first derive analytically the Hessian matrix of the hypervolume indicator, a widely used performance indicator for PF approximation sets. Based on this, we propose the hypervolume Newton method (HNM) for hypervolume maximization of a given set of candidate solutions. We first address unconstrained BOPs and focus further on first attempts for the treatment of inequality constrained problems. The resulting method may even converge quadratically to the optimal solution, however, this property is-as for all Newton methods-of local nature. We hence propose as a next step a hybrid of HNM and an evolutionary strategy in order to obtain a fast and reliable algorithm for the treatment of such problems. The strengths of both HNM and hybrid are tested on several benchmark problems and comparisons of the hybrid to state-of-the-art evolutionary algorithms for hypervolume maximization are presented.

A neural network-evolutionary computational framework for remaining useful life estimation of mechanical systems.

This paper presents a framework for estimating the remaining useful life (RUL) of mechanical systems. The framework consists of a multi-layer perceptron and an evolutionary algorithm for optimizing the data-related parameters. The framework makes use of a strided time window along with a piecewise linear model to estimate the RUL for each mechanical component. Tuning the data-related parameters in the optimization framework allows for the use of simple models, e.g. neural networks with few hidden layers and few neurons at each layer, which may be deployed in environments with limited resources such as embedded systems. The proposed method is evaluated on the publicly available C-MAPSS dataset. The accuracy of the proposed method is compared against other state-of-the art methods in the literature. The proposed method is shown to perform better than the compared methods while making use of a compact model.

Optimizing the location of ambulances in Tijuana, Mexico.

In this work we report on modeling the demand for Emergency Medical Services (EMS) in Tijuana, Baja California, Mexico, followed by the optimization of the location of the ambulances for the Red Cross of Tijuana (RCT), which is by far the largest provider of EMS services in the region. We used data from more than 10,000 emergency calls surveyed during the year 2013 to model and classify the demand for EMS in different scenarios that provide different perspectives on the demand throughout the city, considering such factors as the time of day, work and off-days. A modification of the Double Standard Model (DSM) is proposed and solved to determine a common robust solution to the ambulance location problem that simultaneously satisfies all specified constraints in all demand scenarios selecting from a set of almost 1000 possible base locations. The resulting optimization problems are solved using integer linear programming and the solutions are compared with the locations currently used by the Red Cross. Results show that demand coverage and response times can be substantially improved by relocating the current bases without the need for additional resources.

Computing gap free Pareto front approximations with stochastic search algorithms.

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation-which are entirely determined by the archiving strategy and the value of epsilon-have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a epsilon A, is "large." Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy-multi-objective continuation methods-by showing that the concept of epsilon-dominance can be integrated into this approach in a suitable way.