Iki amaçlı karışık tamsayılı programlama problemlerinin nondominated noktaları

The nondominated frontier in the objective space of biobjective mixed-integer linear/nonlinear programming problems consists of points that cannot be improved in value of one of the objectives without degrading the other objective value. This frontier is usually very involved consisting of many isolated points and open, closed, or half-open/half-closed line segments or curves. Some researchers considered specific classes of these problems to reduce the complexities in nondominated frontier. Some algorithms have been also proposed to find a subset of nondominated set. Several mathematical models for nonlinear process network problems have been developed and solved using epsilon-constraint, weighted sum, and minimum distance. This thesis outlines some possible complexities in nondominated frontier of BOMILPs and drawbacks of existing algorithms, and proposes an effective algorithm, EnpoBomip, to find the exact nondominated frontier of general BOMILPs, as well as all possible values of integer variables associated with each nondominated point. We also investigate biobjective mixed-integer nonlinear problems that are formulated using generalized disjunctive programming for nonlinear network synthesis problems and propose an effective algorithm, epsilon-OA, based on augmented epsilon-constraint and logic-based outer approximation (OA). We provide theoretical characterization of the proposed algorithm and show that the solutions generated are efficient. An experimental study is conducted to present a comparative analysis between EnpoBomip and the existing algorithms on three well-known problems, and show that our novel algorithm significantly outperforms others with respect to solution quality and computational performance. We also illustrate the effectiveness of epsilon-OA compared to the augmented epsilon-constraint with/without OA, and the traditional epsilon-constraint. Based on the results, epsilon-OA is very effective in solving the biobjective generalized disjunctive programming problems in the synthesis of nonlinear process networks.