We consider a version of the knapsack problem in which an item size is random and revealed only when the decision maker attempts to insert it. After every successful insertion the decision maker can choose the next item dynamically based on the remaining capacity and available items, while an unsuccessful insertion terminates the process. We … Read more
In this work, we introduce multi-interdictor games, which model interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on shortest path multi-interdictor (SPMI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries attempting to traverse a common network. We first … Read more
We develop fully polynomial time $(\Sigma,\Pi)$-approximation schemes for stochastic dynamic programs with continuous state and action spaces, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls. That is, for every given additive error parameter $\Sigma>0$ and multiplicative error factor $\Pi=1+\epsilon>1$, the scheme returns a feasible solution whose value … Read more
We consider an n-player strategic game with finite action sets. The payoffs of each player are random variables. We assume that each player uses a satisficing payoff criterion defined by a chance-constraint, i.e., players face a chance- constrained game. We consider the cases where payoffs follow normal and elliptically symmetric distributions. For both cases we … Read more
This paper approximates simulation models by B-splines with a penalty on high-order finite differences of the coefficients of adjacent B-splines. The penalty prevents overfitting. The simulation output is assumed to be nonnegative. The nonnegative spline simulation metamodel is casted as a second-order cone programming model, which can be solved efficiently by modern optimization techniques. The … Read more
In this paper we address two models of non-deterministic discrete-time finite-horizon dynamic programs (DPs): implicit stochastic DPs – the information about the random events is given by value oracles to their CDFs; and sample-based DPs – the information about the random events is deduced via samples. In both models the single period cost functions are … Read more
This paper deals with the problem of finding convex bulges on the Pareto-front of a multi-objective optimization problem. The point of maximum bulge is of particular interest as this point shows good trade-off properties and it is also close to the non-attainable utopia point. Our approach is to use a population based algorithm to simultaneously … Read more
We propose an SQP type method for constrained nonlinear multiobjective optimization. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving singleobjective constrained optimization problems. Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for … Read more
We present a new algorithm for optimizing a linear function over the set of efficient solutions of a multiobjective integer program MOIP. The algorithm’s success relies on the efficiency of a new algorithm for enumerating the nondominated points of a MOIP, which is the result of employing a novel criterion space decomposition scheme which (1) … Read more
We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of … Read more