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Machine learning systems appear stochastic but are deterministically random, as seeded pseudorandom number generators produce identical realisations across repeated executions. Standard evaluation practice typically treats runs across…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We study an impact of a random environment on lifetimes of coherent systems with dependent components. There are two combined sources of this dependence. One results from the dependence of the components of the coherent system operating in…
Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes…
This manuscript studies the preventive replacement policy for a series or parallel system consisting of n independent or dependent heterogeneous components. Firstly, for the age replacement policy, Some sufficient conditions for the…
We consider the non-stationary stochastic lot sizing problem with backorder costs and make a cost comparison among different lot-sizing strategies. We initially provide an overview of the strategies and some corresponding solution…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector…
Neural network models for dynamic systems can be trained either in parallel or in series-parallel configurations. Influenced by early arguments, several papers justify the choice of series-parallel rather than parallel configuration…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have $n$ arbitrary length jobs to be scheduled on $m$ identical machines, $f$ of which are prone…
The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…