In this paper, we consider a large-scale global optimization problem, which takes place in distribution of large number of products into individual orders. In general, the amount of each product is limited and the pac...
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ISBN:
(纸本)9781538694688
In this paper, we consider a large-scale global optimization problem, which takes place in distribution of large number of products into individual orders. In general, the amount of each product is limited and the packaging is constrained, which means that the initial problems can be reduced to constrained nonlinear optimization problem. The high dimensionality and complexity of this problem leads to developing of the specific problem-oriented optimization tool. Two different approaches of solving this problem were considered. The first one is based on the reduction of the initial problem to the discrete optimization problem with dimension is equal to the product of orders number and number of products. The second approach is based on the decomposition of the initial problem into two related problems: combinatorial problem of ranking orders and combinatorial/discrete optimization problem of optimal distributing. As the main extremum seeking approaches, the evolution based and nature-inspired algorithms were used and modified for efficiently solving the considered problem. We also propose the set of particular problems: different combinations of orders and products, which were used for the algorithms' parameters tuning. In addition, the proposed reduction approaches and related algorithms were compared in its performance on these particular problems.
We consider a new variant of the knapsackproblem with dependencies between items. In this variant, the set of items is partitioned into subsets with dependencies among them, and an item can be selected from a subset ...
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We consider a new variant of the knapsackproblem with dependencies between items. In this variant, the set of items is partitioned into subsets with dependencies among them, and an item can be selected from a subset only if at least one item is selected from each of its dependent subsets. We develop pseudo-polynomial algorithms to solve this new constrained version in the cases where the dependencies (between the subsets of items rather than items) are represented by out-trees, in-trees, and directed acyclic graphs. We consider both cases, when the weight and profit of each item are similar, which is the classical Subset Sum problem, and the case when they take arbitrary non-negative values. The proposed algorithms run in O(nW) times and spaces for out-trees, while for in-trees and acyclic digraphs it runs in O(nW +m(W )) and O(nW + max{m(W ),m(nW)}), 2 2 respectively, where n is the number of items, W is the knapsack capacity, and m is the number of nodes. Experiments on randomly generated knapsack instances with different graphs of dependency are carried out to assess algorithm efficiency, and show the running dependency on different instance parameters.
In this paper, we consider a large-scale global optimization problem, which takes place in distribution of large number of products into individual orders. In general, the amount of each product is limited and the pac...
详细信息
ISBN:
(数字)9781538694688
ISBN:
(纸本)9781538694695
In this paper, we consider a large-scale global optimization problem, which takes place in distribution of large number of products into individual orders. In general, the amount of each product is limited and the packaging is constrained, which means that the initial problems can be reduced to constrained nonlinear optimization problem. The high dimensionality and complexity of this problem leads to developing of the specific problem-oriented optimization tool. Two different approaches of solving this problem were considered. The first one is based on the reduction of the initial problem to the discrete optimization problem with dimension is equal to the product of orders number and number of products. The second approach is based on the decomposition of the initial problem into two related problems: combinatorial problem of ranking orders and combinatorial/discrete optimization problem of optimal distributing. As the main extremum seeking approaches, the evolution based and nature-inspired algorithms were used and modified for efficiently solving the considered problem. We also propose the set of particular problems: different combinations of orders and products, which were used for the algorithms' parameters tuning. In addition, the proposed reduction approaches and related algorithms were compared in its performance on these particular problems.
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