Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of thesemulti-objective optimization problemsare characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties,stochasticandrobust optimizationtechniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

The reliability of today's electronic products suffers from a growing variability of failure and ageing effects. In this paper, we investigate a technique for the efficient derivation of uncertainty distributions of system reliability. We assume that a system is composed of unreliable components whose reliabilities are modeled as probability distributions. Existing Monte Carlo (MC) simulation-based techniques, which iteratively select a sample from the probability distributions of the components, often suffer from high execution time and/or poor coverage of the sample space. To avoid the costly re-evaluation of a system reliability during MC simulation, we propose to employ the Taylor expansion of the system reliability function. Moreover, we propose a stratified sampling technique which is based on the fact that the contribution (or importance) of the components on the uncertainty of their system may not be equivalent. This technique finely/coarsely stratifies the probability distribution of the components with high/low contribution. The experimental results show that the proposed technique is more efficient and provides more accurate results compared to previously proposed techniques.

Real-world problems often require the simultaneous optimization of multiple, often conflicting, criteria called objectives. Additionally, many of these problems carry on top a wide range of uncertainties in their fitness functions and decision variables, rendering the optimization task even more complex. Several robust optimization techniques do exist to address uncertainty in different aspects of such problems. However, they typically fail to investigate the actual uncertainty distributions while comparing candidate solutions. This paper presents a novel histogram-based approach that enables to compare candidate solutions with arbitrarily distributed uncertain objectives. The proposed comparison operator receives the uncertainty distribution of each objective of two candidate solutions to be compared, and accurately calculates the probability that one objective is greater than the other. Thereby, it enables to determine whether one solution dominates the other. We employ this comparison operator in an existing multi-objective optimization algorithm to allow for finding robust solutions to problems with uncertain objectives. We also extend a well-known multi-objective benchmark suite with various uncertainties, and integrate it together with the proposed comparison operator into an existing framework that incorporates several multi-objective optimization problems and algorithms. Our experiments show that the proposed comparison operator enables achieving better optimization quality and higher robustness compared to the state-of-the-art.

Common cause failures (CCFs) are simultaneous failures of multiple components in a system and must be considered for accurate and realistic reliability analysis. Traditional CCF analysis techniques typically assume deterministic failures of the affected components. However, CCFs are usually probabilistic, i.e., when a common cause occurs, the affected components fail with different probabilities. Existing techniques that consider probabilistic CCFs (PCCFs) introduce significant execution time and memory overheads to the underlying reliability analysis—limiting their application to small systems only. This paper proposes a fast and automatic PCCF analysis that is based on i) deriving the mutually exclusive success paths of the system using binary decision diagrams (BDDs), and ii) analyzing each path considering PCCFs using explicit and implicit methods. Moreover, an alternative stochastic logic-based technique is presented that compromises analysis accuracy for execution time, and can be used when BDD-based techniques are prohibitive due to their memory overheads. Experimental results show that compared to the state of the art, our methods calculate the system's reliability between 1.1$\times$and 43.4$\times$faster while requiring up to 99.94 % less memory.

In recent years, reliability has become a major issue and objective during the design of embedded systems. Here, different techniques to increase reliability like hardware-/software-based redundancy or component hardening are applied systematically during Design Space Exploration (DSE), aiming at achieving highest reliability at lowest possible cost. Existing approaches typically solely provide reliability measures, e.g. failure rate or Mean-Time-To-Failure (MTTF), to the optimization engine, poorly guiding the search which parts of the implementation to change. As a remedy, this work proposes an efficient approach that (a) determines the importance of resources with respect to the system's reliability and (b) employs this knowledge as part of a local search to guide the optimization engine which components/design decisions to investigate. First, we propose a novel approach to derive Importance Measures (IMs) using a structural evaluation of Success Trees (STs). Since ST-based reliability analysis is already used for MTTF calculation, our approach comes at almost no overhead. Second, we enrich the global DSE with a local search. Here, we propose strategies guided by the IMs that directly change and enhance the implementation. In our experimental setup, the available measures to enhance reliability are the selection of hardening levels during resource allocation and software-based redundancy during task binding; exemplarily, the proposed local search considers the selected hardening levels. The results show that the proposed method outperforms a state-of-the-art approach regarding optimization quality, particularly in the search for highly-reliable yet affordable implementations -- at negligible runtime overhead.

This paper proposes an efficient concurrent error detection method using control flow checking for embedded processors. The proposed method is based on the co-operation of two hardware modules: 1) an on-chip hardware component to detect branch instructions and generate signatures for the running program, and 2) an external watchdog processor to compare runtime signatures and branch addresses with the information extracted offline. The proposed method is implemented on an embedded processor core and is evaluated by a simulation based statistical fault injection approach where faults are injected into cache and main memory. Experimental results show that the proposed method detects more than 96.7% of all errors with only 2.6% overhead in area and less than 1% increase in power consumption. Furthermore, this technique imposes almost no performance degradation.