Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are present...Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.展开更多
In order to optimize the knapsack problem further, this paper proposes an innovative model based on dynamic expectation efficiency, and establishes a new optimization algorithm of 0-1 knapsack problem after analysis a...In order to optimize the knapsack problem further, this paper proposes an innovative model based on dynamic expectation efficiency, and establishes a new optimization algorithm of 0-1 knapsack problem after analysis and research. Through analyzing the study of 30 groups of 0-1 knapsack problem from discrete coefficient of the data, we can find that dynamic expectation model can solve the following two types of knapsack problem. Compared to artificial glowworm swam algorithm, the convergence speed of this algorithm is ten times as fast as that of artificial glowworm swam algorithm, and the storage space of this algorithm is one quarter that of artificial glowworm swam algorithm. To sum up, it can be widely used in practical problems.展开更多
Obnoxious facilities are those crucial to human living, yet antagonistic to the public or environment. However, the interactions between obnoxious facilities and their clients have been less frequently investigated. A...Obnoxious facilities are those crucial to human living, yet antagonistic to the public or environment. However, the interactions between obnoxious facilities and their clients have been less frequently investigated. A state-of-the-art model for this problem involves numerous 0 - 1 variables, rendering it difficult to solve. This study aims at removing most of these 0 - 1 variables to enhanced model efficiency. A compact model is presented in this study, with the equivalence between the new and original models proved. Additionally, numerical tests were conducted to show that the proposed compact model is more efficient than the original one.展开更多
文摘Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.
文摘In order to optimize the knapsack problem further, this paper proposes an innovative model based on dynamic expectation efficiency, and establishes a new optimization algorithm of 0-1 knapsack problem after analysis and research. Through analyzing the study of 30 groups of 0-1 knapsack problem from discrete coefficient of the data, we can find that dynamic expectation model can solve the following two types of knapsack problem. Compared to artificial glowworm swam algorithm, the convergence speed of this algorithm is ten times as fast as that of artificial glowworm swam algorithm, and the storage space of this algorithm is one quarter that of artificial glowworm swam algorithm. To sum up, it can be widely used in practical problems.
文摘Obnoxious facilities are those crucial to human living, yet antagonistic to the public or environment. However, the interactions between obnoxious facilities and their clients have been less frequently investigated. A state-of-the-art model for this problem involves numerous 0 - 1 variables, rendering it difficult to solve. This study aims at removing most of these 0 - 1 variables to enhanced model efficiency. A compact model is presented in this study, with the equivalence between the new and original models proved. Additionally, numerical tests were conducted to show that the proposed compact model is more efficient than the original one.
