A dual-ascent-based branch-and-bound framework for the prize-collecting Steiner tree and related problems

Categories Combinatorial Optimization, Integer Programming, Network Optimization Tags , , , ,

In this work we present a branch-and-bound (B&B) framework for the asymmetric prize-collecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS) and the node-weighted Steiner tree problem (NWSTP). The main component of … Read more

Guaranteed Bounds for General Non-discrete Multistage Risk-Averse Stochastic Optimization Programs

Categories Stochastic Programming Tags , , , , ,

In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such ”infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite … Read more

DESSLib – Benchmark Instances for Optimization of Decentralized Energy Supply Systems

Categories Applications - Science and Engineering Tags , , , , , ,

DESSLib (http://www.math2.rwth-aachen.de/DESSLib) provides benchmark instances obtained by real world data for synthesis problems of decentralized energy supply systems (DESS). In this paper, the considered optimization problem is described in detail. For a description of the functions and parameters used to describe the system and equipment, see the documentation found on DESSLib website http://www.math2.rwth-aachen.de/DESSLib. ArticleDownload View … Read more

An Adaptive Discretization MINLP Algorithm for Optimal Synthesis of Decentralized Energy Supply Systems

Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , , ,

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and … Read more

Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more

Convergence Analysis of ISTA and FISTA for “Strongly + Semi” Convex Programming

Categories Convex Optimization Tags , , , , ,

The iterative shrinkage/thresholding algorithm (ISTA) and its faster version FISTA have been widely used in the literature. In this paper, we consider general versions of the ISTA and FISTA in the more general “strongly + semi” convex setting, i.e., minimizing the sum of a strongly convex function and a semiconvex function; and conduct convergence analysis … Read more

On cone based decompositions of proper Pareto optimality

Categories Global Optimization, Multi-Criteria Optimization Tags , , ,

In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeo ffs. Imposing a strict tradeo ff bound allows specifying how many units … Read more

An exact hybrid method for the vehicle routing problem with time windows and multiple deliverymen

Categories Combinatorial Optimization, Transportation

The vehicle routing problem with time windows and multiple deliverymen (VRPTWMD) is a variant of the vehicle routing problem with time windows in which service times at customers depend on the number of deliverymen assigned to the route that serves them. Hence, in addition to the usual routing and scheduling decisions, the crew size for … Read more

Inexact Newton-Type Optimization with Iterated Sensitivities

Categories Systems governed by Differential Equations Optimization Tags , , ,

This paper presents and analyzes an Inexact Newton-type optimization method based on Iterated Sensitivities (INIS). A particular class of Nonlinear Programming (NLP) problems is considered, where a subset of the variables is defined by nonlinear equality constraints. The proposed algorithm considers an arbitrary approximation for the Jacobian of these constraints. Unlike other inexact Newton methods, … Read more

The proximal point method for locally Lipschitz functions in multiobjective optimization

Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the … Read more