Using convex preference cones in multiple criteria decision making and related fields

This paper reviews our own and colleagues’ research on using convex preference cones in multiple criteria decision making and related fields. The original paper by Korhonen, Wallenius, and Zionts was published in Management Science in 1984. We first present the underlying theory, concepts, and method. Then we discuss applications of the theory, particularly for finding the most preferred alternative, finding a partial and total rank ordering of alternatives, as well as developing algorithms for solving multi-objective integer and other optimization problems

Numerical tools to validate stationary points of SO(8)-gauged N=8 D=4 supergravity

Until recently, the preferred strategy to identify stationary points in the scalar potential of SO(8)-gauged N=8 supergravity in D=4 has been to consider truncations of the potential to sub-manifolds of E_{7(+7)}/SU(8) that are invariant under some postulated residual gauge group G of SO(8). As powerful alternative strategies have been shown to exist that allow one to go far beyond what this method can achieve -- and in particular have produced numerous solutions that break the SO(8) gauge group to no continuous residual symmetry -- independent verification of results becomes a problem due to both the complexity of the scalar potential and the large number of new solutions. This article introduces a conceptually simple self-contained piece of computer code that allows independent numerical validation of claims on the locations of newly discovered stationary points.Comment: 9 pages, program code can be obtained by downloading paper's source from arxiv; new version contains code cleanup and extensions (scalar mass matrix code

Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker’s most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker’s preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems

Exact And Representative Algorithms For Multi Objective Optimization

In most real-life problems, the decision alternatives are evaluated with multiple conflicting criteria. The entire set of non-dominated solutions for practical problems is impossible to obtain with reasonable computational effort. Decision maker generally needs only a representative set of solutions from the actual Pareto front. First algorithm we present is for efficiently generating a well dispersed non-dominated solution set representative of the Pareto front which can be used for general multi objective optimization problem. The algorithm first partitions the criteria space into grids to generate reference points and then searches for non-dominated solutions in each grid. This grid-based search utilizes achievement scalarization function and guarantees Pareto optimality. The results of our experimental results demonstrate that the proposed method is very competitive with other algorithms in literature when representativeness quality is considered; and advantageous from the computational efficiency point of view. Although generating the whole Pareto front does not seem very practical for many real life cases, sometimes it is required for verification purposes or where DM wants to run his decision making structures on the full set of Pareto solutions. For this purpose we present another novel algorithm. This algorithm attempts to adapt the standard branch and bound approach to the multi objective context by proposing to branch on solution points on objective space. This algorithm is proposed for multi objective integer optimization type of problems. Various properties of branch and bound concept has been investigated and explained within the multi objective optimization context such as fathoming, node selection, heuristics, as well as some multi objective optimization specific concepts like filtering, non-domination probability, running in parallel. Potential of this approach for being used both as a full Pareto generation or an approximation approach has been shown with experimental studies

Some algorithms to solve a bi-objectives problem for team selection

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 (kh) 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

Optimization of a dynamic supply portfolio considering risks and discount’s constraints

Purpose: Nowadays finding reliable suppliers in the global supply chains has become so important for success, because reliable suppliers would lead to a reliable supply and besides that orders of customer are met effectively . Yet, there is little empirical evidence to support this view, hence the purpose of this paper is to fill this need by considering risk in order to find the optimum supply portfolio. Design/methodology/approach: This paper proposes a multi objective model for the supplier selection portfolio problem that uses conditional value at risk (CVaR) criteria to control the risks of delayed, disrupted and defected supplies via scenario analysis. Also we consider discount’s constraints which are common assumptions in supplier selection problems. The proposed approach is capable of determining the optimal supply portfolio by calculating value-at-risk and minimizing conditional value-at-risk. In this study the Reservation Level driven Tchebycheff Procedure (RLTP) which is one of the reference point methods, is used to solve small size of our model through coding in GAMS. As our model is NP-hard; a meta-heuristic approach, Non-dominated Sorting Genetic Algorithm (NSGA) which is one of the most efficient methods for optimizing multi objective models, is applied to solve large scales of our model. Findings and Originality/value: In order to find a dynamic supply portfolio, we developed a Mixed Integer Linear Programming (MILP) model which contains two objectives. One objective minimizes the cost and the other minimizes the risks of delayed, disrupted and defected supplies. CVaR is used as the risk controlling method which emphases on low-probability, high-consequence events. Discount option as a common offer from suppliers is also implanted in the proposed model. Our findings show that the proposed model can help in optimization of a dynamic supplier selection portfolio with controlling the corresponding risks for large scales of real word problems. Practical implications: To approve the capability of our model various numerical examples are made and non-dominated solutions are generated. Sensitive analysis is made for determination of the most important factors. The results shows that how a dynamic supply portfolio would disperse the allocation of orders among the suppliers combined with the allocation of orders among the planning periods, in order to hedge against the risks of delayed, disrupted and defected supplies. Originality/value: This paper provides a novel multi objective model for supplier selection portfolio problem that is capable of controlling delayed, disrupted and defected supplies via scenario analysis. Also discounts, as an option offered from suppliers, are embedded in the model. Due to the large size of the real problems in the field of supplier selection portfolio a meta-heuristic method, NSGA II, is presented for solving the multi objective model. The chromosome represented for the proposed solving methodology is unique and is another contribution of this paper which showed to be adaptive with the essence of supplier selection portfolio problemPeer Reviewe