Abstract
In real life, many problems are instances of combinatorial optimization. Cross-functional team selection is one of the typical issues. The decision-maker has to select solutions among ( k h ) solutions in the decision space, where k is the number of all candidates, and h is the number of members in the selected team. This paper is our continuing work since 2018; here, we introduce the completed version of the Min Distance to the Boundary model (MDSB) that allows access to both the “deep” and “wide” aspects of the selected team. The compromise programming approach enables decision-makers to ignore the parameters in the decision-making process. Instead, they point to the one scenario they expect. The aim of model construction focuses on finding the solution that matched the most to the expectation. We develop two algorithms: one is the genetic algorithm and another based on the philosophy of DC programming (DC) and its algorithm (DCA) to find the optimal solution. We also compared the introduced algorithms with the MIQP-CPLEX search algorithm to show their effectiveness.
Highlights
As mentioned in the first part of this paper, the MDSB model is a Mixed-Integer Quadratic Programming (MIQP), which can be directly solved by solvers
Genetic algorithms are useful for problems where it is extremely difficult or impossible to get an exact solution, or for difficult problems where an exact solution may not be required
CPLEX’s long processing time is understandable because it looks for a global solution whAiplepl.DScCi.A202a0n, 1d0,Gx AFOlRoPoEkERfoRrEaVIlEoWcal solution. We see that both DCA and Genetic algorithms (GA) algorithms are not committed to finding a universal optimal solution
Summary
There are many approaches to solving the (*) problem mentioned in the survey of Hwang [13] such as: (1) scalarizing: that formulating a single-objective optimization problem from the origin multi-objective optimization problem where the new objective function is the sum of the product between the separated objective and its weight parameter. (2) Visualization of the Pareto front: that allows the decision-maker to identify the preferred point at the Pareto front Most of those methods require consideration of the decision-maker to select parameters about the importance of each objective-function in the decision space. This may be difficult for the decision maker in the real life problem. Instead of using those approaches, we use the compromise programming approach
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