Janusz Miroforidis

Two-Sided Pareto Front Approximations

A new approach to derive Pareto front approximations with evolutionary computations is proposed here.At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. However, accuracy of such approximations is known only if the Pareto front is known, which makes their usefulness questionable.Here we propose to exploit also elements outside feasible sets to derive pairs of such Pareto front approximations that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between elements of a pair.A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.

Multiple Criteria Decision Making and Multiobjective Optimization - A Toolbox

We present an integral approach to solving multiple criteria decision problems in sequences of intelligence, modeling, choice and review phases, often iterated, to identify the most preferred decision variant. The approach taken is human-centric, with the user taking the final decision being a sole and sovereign actor in the decision making process. To ensure generality, no assumption about the Decision Maker preferences or behavior is made. Likewise, no specific assumption about the underlying formal model is made.

Multiple Criteria Decision Making: Efficient Outcome Assessments with Evolutionary Optimization

We propose to derive assessments of outcomes to MCDM problems instead of just outcomes and carry decision making processes with the former. In contrast to earlier works in that direction, which to calculate assessments make use of subsets of the efficient set (shells), here we provide formulas for calculation of assessments based on the use of upper and lower approximations (upper and lower shells) of the efficient set, derived by evolutionary optimization. Hence, by replacing shells, which are to be in general derived by optimization, by pairs of upper and lower shells, exact optimization methods can be eliminated from MCDM.

Multiobjective optimization in the Airport Gate Assignment Problem, exact versus evolutionary multiobjective optimization

In this paper, we approach the Airport Gate Assignment Problem by Multiobjective Optimization as well as Evolutionary Multi-objective Optimization. We solve a bi-criteria formulation of this problem by the commercial mixedinteger programming solver CPLEX and a dedicated Evolutionary Multiobjective Optimization algorithm. To deal with multiple objectives, we apply a methodology that we developed earlier to capture decision-maker preferences in multi-objective environments. We present the results of numerical tests for these two approaches.

A multi-criteria approach to approximate solution of multiple-choice knapsack problem

We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the original multiple-choice knapsack problem. The method relies on solving a series of suitably defined linearly scalarized bi-objective problems. The novelty which makes the method attractive from the computational point of view is that we are able to solve explicitly those linearly scalarized bi-objective problems with the help of the closed-form formulae. The method is computationally analyzed on a set of large-scale problem instances (test problems) of two categories: uncorrelated and weakly correlated. Computational results show that after solving, in average 10 scalarized bi-objective problems, the optimal value of the original knapsack problem is approximated with the accuracy comparable to the accuracies obtained by the greedy algorithm and an exact algorithm. More importantly, the respective approximate solution to the original knapsack problem (for which the approximate optimal value is attained) can be found without resorting to the dynamic programming. In the test problems, the number of multiple-choice constraints ranges up to hundreds with hundreds variables in each constraint.

Decision Problem: Selection of a Stock Portfolio

“Yes, that’s gold, but I’m too big to go running around like that after atoms.” “No problem, we’ll give you a suitable machine!” coaxed Trurl.

Decision Problems, Continuation

Without further ado I stocked my ship with necessary provisions, took off and, after numerous adventures we need not go into here, finally spotted in a great swarm of stars one that differed from all the rest, since it was a perfect cube.

Derivation of Efficient Portfolios

Towards the end of his second audience with the King, Klapaucius inquired if perhaps Trurl were on the planet and gave a detailed description of his comrade.

Solving Decision Problems

This chapter presents the decision process scheme, its principal phases and also introduces the generic idea of decision problem solving. The idea of the scheme is to repeat the principal phases of the process in cycles, till the DM concludes that among variants identified in the decision process, one variant can be regarded, in his/her opinion, as the most preferred variant.

Derivation of Efficient Variants

The subject of this chapter are methods for derivation of efficient variants in problems, in which variants are explicitly given as a list of variants.