95 research outputs found
A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs
This work deals with a class of problems under interval data uncertainty,
namely interval robust-hard problems, composed of interval data min-max regret
generalizations of classical NP-hard combinatorial problems modeled as 0-1
integer linear programming problems. These problems are more challenging than
other interval data min-max regret problems, as solely computing the cost of
any feasible solution requires solving an instance of an NP-hard problem. The
state-of-the-art exact algorithms in the literature are based on the generation
of a possibly exponential number of cuts. As each cut separation involves the
resolution of an NP-hard classical optimization problem, the size of the
instances that can be solved efficiently is relatively small. To smooth this
issue, we present a modeling technique for interval robust-hard problems in the
context of a heuristic framework. The heuristic obtains feasible solutions by
exploring dual information of a linearly relaxed model associated with the
classical optimization problem counterpart. Computational experiments for
interval data min-max regret versions of the restricted shortest path problem
and the set covering problem show that our heuristic is able to find optimal or
near-optimal solutions and also improves the primal bounds obtained by a
state-of-the-art exact algorithm and a 2-approximation procedure for interval
data min-max regret problems
Minmax regret combinatorial optimization problems: an Algorithmic Perspective
Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty
Ph.DDOCTOR OF PHILOSOPH
Generalizing the Min-Max Regret Criterion using Ordered Weighted Averaging
In decision making under uncertainty, several criteria have been studied to
aggregate the performance of a solution over multiple possible scenarios,
including the ordered weighted averaging (OWA) criterion and min-max regret.
This paper introduces a novel generalization of min-max regret, leveraging the
modeling power of OWA to enable a more nuanced expression of preferences in
handling regret values. This new OWA regret approach is studied both
theoretically and numerically. We derive several properties, including
polynomially solvable and hard cases, and introduce an approximation algorithm.
Through computational experiments using artificial and real-world data, we
demonstrate the advantages of our OWAR method over the conventional min-max
regret approach, alongside the effectiveness of the proposed clustering
heuristics
The robust single machine scheduling problem with uncertain release and processing times
In this work, we study the single machine scheduling problem with uncertain
release times and processing times of jobs. We adopt a robust scheduling
approach, in which the measure of robustness to be minimized for a given
sequence of jobs is the worst-case objective function value from the set of all
possible realizations of release and processing times. The objective function
value is the total flow time of all jobs. We discuss some important properties
of robust schedules for zero and non-zero release times, and illustrate the
added complexity in robust scheduling given non-zero release times. We propose
heuristics based on variable neighborhood search and iterated local search to
solve the problem and generate robust schedules. The algorithms are tested and
their solution performance is compared with optimal solutions or lower bounds
through numerical experiments based on synthetic data
A fast ILP-based Heuristic for the robust design of Body Wireless Sensor Networks
We consider the problem of optimally designing a body wireless sensor
network, while taking into account the uncertainty of data generation of
biosensors. Since the related min-max robustness Integer Linear Programming
(ILP) problem can be difficult to solve even for state-of-the-art commercial
optimization solvers, we propose an original heuristic for its solution. The
heuristic combines deterministic and probabilistic variable fixing strategies,
guided by the information coming from strengthened linear relaxations of the
ILP robust model, and includes a very large neighborhood search for reparation
and improvement of generated solutions, formulated as an ILP problem solved
exactly. Computational tests on realistic instances show that our heuristic
finds solutions of much higher quality than a state-of-the-art solver and than
an effective benchmark heuristic.Comment: This is the authors' final version of the paper published in G.
Squillero and K. Sim (Eds.): EvoApplications 2017, Part I, LNCS 10199, pp.
1-17, 2017. DOI: 10.1007/978-3-319-55849-3\_16. The final publication is
available at Springer via http://dx.doi.org/10.1007/978-3-319-55849-3_1
Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability
The purpose of this thesis is twofold. The first and major part is devoted to
sensitivity analysis of various discrete optimization problems while the second
part addresses methods applied for calculating measures of solution stability
and solving multicriteria discrete optimization problems.
Despite numerous approaches to stability analysis of discrete optimization
problems two major directions can be single out: quantitative and qualitative.
Qualitative sensitivity analysis is conducted for multicriteria discrete optimization
problems with minisum, minimax and minimin partial criteria. The main
results obtained here are necessary and sufficient conditions for different stability
types of optimal solutions (or a set of optimal solutions) of the considered
problems.
Within the framework of quantitative direction various measures of solution
stability are investigated. A formula for a quantitative characteristic called
stability radius is obtained for the generalized equilibrium situation invariant
to changes of game parameters in the case of the H¨older metric. Quality of the
problem solution can also be described in terms of robustness analysis. In this
work the concepts of accuracy and robustness tolerances are presented for a
strategic game with a finite number of players where initial coefficients (costs)
of linear payoff functions are subject to perturbations.
Investigation of stability radius also aims to devise methods for its calculation.
A new metaheuristic approach is derived for calculation of stability
radius of an optimal solution to the shortest path problem. The main advantage
of the developed method is that it can be potentially applicable for
calculating stability radii of NP-hard problems.
The last chapter of the thesis focuses on deriving innovative methods based
on interactive optimization approach for solving multicriteria combinatorial
optimization problems. The key idea of the proposed approach is to utilize
a parameterized achievement scalarizing function for solution calculation and
to direct interactive procedure by changing weighting coefficients of this function.
In order to illustrate the introduced ideas a decision making process is
simulated for three objective median location problem.
The concepts, models, and ideas collected and analyzed in this thesis create
a good and relevant grounds for developing more complicated and integrated
models of postoptimal analysis and solving the most computationally challenging
problems related to it.Siirretty Doriast
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