In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. Th...In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.展开更多
A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of...A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.展开更多
This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The m...This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.展开更多
文摘In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.
文摘A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.
文摘This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.
