We propose a dynamic traveling salesman problem (TSP) with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which a decision’s cost is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate the problem as a dynamic program (DP) and compare it to static counterparts to … Read more
In multi-objective optimization the objective is to reach a point which is Pareto ecient. However we usually encounter many such points and choosing a point amongst them possesses another problem. In many applications we are required to choose a point having a good spread over all objective functions which is a direct consequence of the … Read more
In the execution cost problem, an investor wants to minimize the total expected cost and risk in the execution of a portfolio of risky assets to achieve desired positions. A major source of the execution cost comes from price impacts of both the investor’s own trades and other concurrent institutional trades. Indeed price impact of … Read more
With every law invariant coherent risk measure is associated its conditional analogue. In this paper we discuss lower and upper bounds for the corresponding nested (composite) formulations of law invariant coherent risk measures. In particular, we consider the Average Value-at-Risk and comonotonic risk measures. ArticleDownload View PDF
We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of {\it all } Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions {\it corresponding to one} Pareto efficient/Henig proper … Read more
Operations Research (OR) is the discipline of applying advanced analytical methods to help make better decisions (Horner (2003)). OR is characterized by its broad applicability and its interdisciplinary nature. Currently, in addition to mathematics, many other undergraduate programs such as management sciences, business, economics, electrical engineering, civil engineering, chemical engineering, and related fields, have incorporated … Read more
In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more
In this paper we are interested in the convergence analysis of the Stochastic Dual Dynamic Algorithm (SDDP) algorithm in a general framework, and regardless of whether the underlying probability space is discrete or not. We consider a convex stochastic control program not necessarily linear and the resulting dynamic programming equation. We prove under mild assumptions … Read more
This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more
Optimization in dynamic environments is a challenging but important task since many real-world optimization problems are changing over time. Evolutionary computation and swarm intelligence are good tools to address optimization problems in dynamic environments due to their inspiration from natural self-organized systems and biological evolution, which have always been subject to changing environments. Evolutionary optimization … Read more