Kostas Florios

An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

Generation (or a posteriori) methods in Multi-Objective Mathematical Programming (MOMP) is the most computationally demanding category among the MOMP approaches. Due to the dramatic increase in computational speed and the improvement of Mathematical Programming algorithms the generation methods become all the more attractive among todays decision makers. In the current paper we present the generation method AUGMECON2 which is an improvement of our development, AUGMECON. Although AUGMECON2 is a general purpose method, we will demonstrate that AUGMECON2 is especially suitable for Multi-Objective Integer Programming (MOIP) problems. Specifically, AUGMECON2 is capable of producing the exact Pareto set in MOIP problems by appropriately tuning its running parameters. In this context, we compare the previous and the new version in a series of new and old benchmarks found in the literature. We also compare AUGMECON2s performance in the generation of the exact Pareto sets with established methods and algorithms based on specific MOIP problems (knapsack, set packing) and on published results. Except from other Mathematical Programming methods, AUGMECON2 is found to be competitive also with Multi-Objective Meta-Heuristics (MOMH) in producing adequate approximations of the Pareto set in Multi-Objective Combinatorial Optimization (MOCO) problems.

Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature, with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive [epsilon]-constraint method [Laumanns, M., Thiele, L., Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169, 932-942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive [epsilon] -constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance).

Generation of the exact Pareto set in Multi-Objective Traveling Salesman and Set Covering Problems

Abstract The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering Problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems.

Energy planning in buildings under uncertainty in fuel costs: The case of a hospital in Greece

Abstract Hospitals are among the largest energy consumers in the tertiary sector where energy planning may greatly facilitate investment decisions for efficienty meeting energy demand. In this case study the energy rehabilitation of a hospital is examined and due to the recent conditions some new energy alternatives are investigated: a CHP unit for providing power and heat, an absorption unit or/and a compression unit for providing cooling load. The basic innovation of the above mentioned energy model is that it is designed to handle uncertainty in the most uncertain parameters of the objective function, namely, the fuel costs and the interest rate used for the investment discouting of new units. These uncertain parameters are modeled as Triangular Fuzzy Numbers (TFN) and the MILP model is appropriately transformed into a multiobjective MILP model. The solution of the multiobjective model provides the pareto set which means the candidate designs under the existent uncertainty.

Exact Computation of Censored Least Absolute Deviations Estimators

We show that exact computation of Powells (1984) censored least absolute deviations (CLAD) estimator may be achieved by formulating the estimator as a solvable linear Mixed Integer Programming (MIP) problem with disjunctive constraints. We apply our approach to two previously used censored datasets and find that standard heuristic/approximate approaches to computation of the estimator can lead to substantial errors and misleading economic conclusions. Additionally, we present a small Monte Carlo study which illustrates that MIP computation using widely available solvers is practical and efficient for data sets of sizes typically encountered in econometric applications.

Application of the Maximum Score/Maximum Profit Bi-Objective Estimator to Stocks of the Banking Sector in the Athens Stock Exchange

We are familiar with the maximum score estimator of (Manski, C.F., 1975, Journal of Econometrics 3, 205-228). A generalization of the maximum score estimator is the maximum profit estimator of (Skouras, S., 2003, Computational Statistics and Data Analysis 42, 349-361). The general case is the maximum weighted score estimator (K. Florios, S. Skouras, 2008, Journal of Econometrics, 146, 86-91). First, we define the bi-objective estimator maximum score/maximum profit (MS-MP). In this paper, we study mainly the computational characteristics of MS-MP in a study of four stocks of the Banking Sector from the Athens Stock Exchange (ASE). The estimation techniques that are used are Non Dominated Sorting Genetic Algorithm II (NSGA-II) and the e-Constraint method of mathematical programming. The comparison of the two estimation techniques results in a tie and the choice of technique depends on the familiarity of the user with available methods and the availability of software. Further comparison to more sophisticated mathematical programming techniques can be organized.