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This paper addresses the problem of open shop scheduling on two machines with resources constraints. In the context of our study, in order to be executed, a job requires first, for its preparation for a given period of time, a number of resources which cannot exceed a given resource capacity. Then, it goes onto its execution while the resources allocated to it become available again. We seek a schedule that minimizes the makespan. We first prove the $\mathcal{N}\mathcal{P}$ -hardness of several versions of this problem. Then, we present a well solvable case, lower bounds, and heuristic algorithms along with an experimental study. [ABSTRACT FROM AUTHOR]

This paper studies two single-machine scheduling problems with the effect of deterioration and learning. In this model, the processing times of jobs are defined as functions of their starting times and positions in a sequence. For the following two objective functions: the weighted sum of completion times and the maximum lateness, this paper proposes two heuristics according to the corresponding single machine problems without learning effect. This paper also gives the worst-case error bound for the heuristics and provides computational results to evaluate the performance of the heuristics. [ABSTRACT FROM AUTHOR]

The solution of intractable problems implies the use of heuristics. Quantum computers may find use for optimization problems, but have yet to solve any NP-hard problems. This paper demonstrates results in game theory for domain transference and the reuse of problem-solving knowledge through the application of learned heuristics. It goes on to explore the possibilities for the acquisition of heuristics for the solution of the NP-hard TSP problem. Here, it is found that simple heuristics (e.g., pairwise exchange) often work best in the context of more or less sophisticated experimental designs. Often, these problems are not amenable to exclusive logic solutions; but rather, require the application of hybrid approaches predicated on search. In general, such approaches are based on randomization and supported by parallel processing. This means that heuristic solutions emerge from attempts to randomize the search space. The paper goes on to present a constructive proof of the unbounded density of knowledge in support of the Semantic Randomization Theorem (SRT). It highlights this result and its potential impact upon the community of machine learning researchers. [ABSTRACT FROM AUTHOR]