For many real-world decision-making problems subject to uncertainty, it may be essential to deal with multiple and often conflicting objectives while taking the decision-makers' risk preferences into account. Conditional value-at-risk (CVaR) is a widely applied risk measure to address risk-averseness of the decision-makers. In this paper, we use the subset-based polyhedral representation of the CVaR to reformulate the bi-objective two-stage stochastic facility location problem presented in Nazemi et al. (2021). We propose an approximate cutting-plane method to deal with this more computationally challenging subset-based formulation. Then, the cutting plane method is embedded into the epsilon-constraint method, the balanced-box method, and a recently developed matheuristic method to address the bi-objective nature of the problem. Our computational results show the effectiveness of the proposed method. Finally, we discuss how incorporating an approximation of the subset-based polyhedral formulation affects the obtained solutions.

For stochastic multi-objective combinatorial optimization (SMOCO) problems, the adaptive Pareto sampling (APS) framework has been proposed, which is based on sampling and on the solution of deterministic multi-objective subproblems. We show that when plugging in the well-known simple evolutionary multi-objective optimizer (SEMO) as a subprocedure into APS, ε-dominance has to be used to achieve fast convergence to the Pareto front. Two general theorems are presented indicating how runtime complexity results for APS can be derived from corresponding results for SEMO. This may be a starting point for the runtime analysis of evolutionary SMOCO algorithms.

Many applications such as project scheduling, workflow modeling, or business process re-engineering incorporate the common idea that a product, task, or service consisting of interdependent time-related activities should be produced or performed within given time limits. In real-life applications, certain measures like the use of additional manpower, the assignment of highly-skilled personnel to specific jobs, or the substitution of equipment are often considered as means of increasing the probability of meeting a due date and thus avoiding penalty costs. This paper investigates the problem of selecting, from a set of possible measures of this kind, the combination of measures that is the most cost-efficient. Assuming stochastic activity durations, the computation of the optimal combination of measures may be very expensive in terms of runtime. In this article, we introduce a powerful stochastic optimization approach to determine a set of efficient measures that crash selected activities in a stochastic activity network. Our approach modifies the conventional Stochastic Branch-and-Bound, using a heuristic—instead of exact methods—to solve the deterministic subproblem. This modification spares computational time and by doing so provides an appropriate method for solving various related applications of combinatorial stochastic optimization. A comparative computational study shows that our approach not only outperforms standard techniques but also definitely improves conventional Stochastic Branch-and-Bound.

This paper compares partition testing and random testing on the assumption that program failure rates are not known with certainty before testing and are, therefore, modeled by random variables. It is shown that under uncertainty, partition testing compares more favorably to random testing than suggested by prior investigations concerning the deterministic case: the restriction to failure rates that are known with certainty systematically favors random testing. In particular, we generalize a result by Weyuker and Jeng (1991) stating equal fault detection probabilities for partition testing and random testing in the case where the failure rates in the subdomains defined by the partition are equal. It turns out that for independent random failure rates with equal expectation, the case above is a boundary case (the worst case for partition testing), and the fault detection probability of partition testing can be up to k times higher than that of random testing, where k is the number of subdomains. Also in a related model for dependent failure rates, partition testing turns out to be consistently better than random testing. The dominance can also be verified for the expected (weighted) number of detected faults as an alternative comparison criterion.

Several authors have addressed the problem of reliability optimization of modular software with redundancy. At present, these approaches seem to be limited by the fact that they use statistical independence assumptions for different program versions. In view of strong empirical evidence of positive failure correlations between program versions, it is desirable to generalize these reliability optimization techniques by taking such correlations explicitly into consideration. In the presented paper, this is done based on a multiversion software failure correlation model tracing back to D.E Eckhardt and L.D. Lee (1985). We show how taking failure correlation into account extends the corresponding optimization problems, and how they can be treated computationally. In particular, in the (practically relevant) case of components with relatively high reliability, the optimization problems reduce to knapsack type problems which can, for relevant problem sizes, be solved with rather low computational effort. Also for the general case, solution techniques are outlined.

We generalize the input domain based software reliability measures by E.C. Nelson (1973) and by S.N. Weiss and E.J. Weyuker (1988), introducing expected failure costs under the operational distribution as a measure for software unreliability. This approach incorporates in the reliability concept a distinction between different degrees of failure severity. It is shown how to estimate the proposed quantity by means of random testing, using the Importance Sampling technique from Rare Event Simulation. A test input distribution that yields an unbiased estimator with minimum variance is determined. The practical application of the presented method is outlined, and a detailed numerical example is given.>