Stochastic Programming Approach to Optimization under Uncertainty

In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the … Read more

On Self-Regulated Swarms, Societal Memory, Speed and Dynamics

Wasps, bees, ants and termites all make effective use of their environment and resources by displaying collective “swarm” intelligence. Termite colonies – for instance – build nests with a complexity far beyond the comprehension of the individual termite, while ant colonies dynamically allocate labor to various vital tasks such as foraging or defense without any … Read more

Societal Implicit Memory and his Speed on Tracking Extrema over Dynamic Environments using Self-Regulatory Swarms

In order to overcome difficult dynamic optimization and environment extrema tracking problems, we propose a Self-Regulated Swarm (SRS) algorithm which hybridizes the advantageous characteristics of Swarm Intelligence as the emergence of a societal environmental memory or cognitive map via collective pheromone laying in the landscape (properly balancing the exploration/exploitation nature of the search strategy), with … Read more

Optimal Information Monitoring Under a Politeness Constraint

We describe scheduling algorithms for monitoring an information source whose contents change at times modeled by a nonhomogeneous Poisson process. In a given time period of length T, we enforce a politeness constraint that we may only probe the source at most n times. This constraint, along with an optional constraint that no two probes … Read more

Preemptive scheduling with position costs

This paper is devoted to basic scheduling problems in which the scheduling cost of a job is not a function of its completion time. Instead, the cost is derived from the integration of a cost function over the time intervals on which the job is processed. This criterion is specially meaningful when job preemption is … Read more

New hybrid optimization algorithms for machine scheduling problems

Dynamic programming, branch-and-bound, and constraint programming are the standard solution principles for finding optimal solutions to machine scheduling problems. We propose a new hybrid optimization framework that integrates all three methodologies. The hybrid framework leads to powerful solution procedures. We demonstrate our approach through the optimal solution of the single-machine total weighted completion time scheduling … Read more

A New Complexity Result on Solving the Markov Decision Problem

We present a new complexity result on solving the Markov decision problem (MDP) with $n$ states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that, when the discount factor $\theta$ is strictly less than $1$, the problem can be solved in … Read more

Aggregation in Stochastic Dynamic Programming

We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more

Conditional Risk Mappings

We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings. Citation Preprint Article Download View Conditional Risk Mappings

Scheduling a sequence of tasks with general completion costs

Scheduling a sequence of tasks – in the acceptation of finding the execution times – is not a trivial problem when the optimization criterion is irregular as for instance in earliness-tardiness problems. This paper presents an efficient Dynamic Programming algorithm to solve the problem with general cost functions depending on the end time of the … Read more