Linear Programming and Mixed Integer Programming

Author(s):  
Bogdan Dumitrescu
Energies ◽  
2017 ◽  
Vol 10 (2) ◽  
pp. 241 ◽  
Author(s):  
Alberto Dolara ◽  
Francesco Grimaccia ◽  
Giulia Magistrati ◽  
Gabriele Marchegiani

1996 ◽  
Vol 26 (7) ◽  
pp. 1193-1202 ◽  
Author(s):  
Cristopher L. Brack ◽  
Peter L. Marshall

Five knowledge-based approaches (three search routines and two expert systems) to forest operations scheduling were compared with mathematical programming (linear programming and mixed integer programming) and simulation approaches for two plantation forests in New South Wales, Australia. Strategies produced using these approaches were compared on the basis of scores for timber volume flow, scenic beauty, stand health, and water quality. Timber flow scores were highest for the linear programming strategies, but some of the strategies produced by the knowledge-based approaches scored almost as high. The timber flow scores for the mixed integer programming strategies were exceeded by some of the knowledge-based strategies, because of the approximations required to achieve mixed integer programming solutions for larger problems. The knowledge-based approaches could produce higher scoring strategies for the other criteria than the mathematical programming or simulation approaches. The multiple strategies produced by two of the search procedures, and the goal hierarchy incorporated into the expert systems, allow the user to make explicit trade-offs among strategies in terms of performance for the various criteria.


Author(s):  
Fred Glover ◽  
Saïd Hanafi

Recent metaheuristics for mixed integer programming have included proposals for introducing inequalities and target objectives to guide this search. These guidance approaches are useful in intensification and diversification strategies related to fixing subsets of variables at particular values. The authors’ preceding Part I study demonstrated how to improve such approaches by new inequalities that dominate those previously proposed. In Part II, the authors review the fundamental concepts underlying weighted pseudo cuts for generating guiding inequalities, including the use of target objective strategies. Building on these foundations, this paper develops a more advanced approach for generating the target objective based on exploiting the mutually reinforcing notions of reaction and resistance. The authors demonstrate how to produce new inequalities by “mining” reference sets of elite solutions to extract characteristics these solutions exhibit in common. Additionally, a model embedded memory is integrated to provide a range of recency and frequency memory structures for achieving goals associated with short term and long term solution strategies. Finally, supplementary linear programming models that exploit the new inequalities for intensification and diversification are proposed.


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