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Heuristics for the General Multiple non-linear Knapsack Problem

Electronic Notes in Discrete Mathematics 2016年 55卷 69-72页

作者： Mencarelli, Luca Di Zio, Angelo Martello, Silvano CNRS UMR 7161 LIX École Polytechnique Palaiseau France Ferrari S.p.A. Maranello Italy DEI “Guglielmo Marconi” Bologna Italy

We propose heuristic algorithms for the multiple non-linear knapsack problem with separable non-convex profit and weight functions. First, we design a fast constructive algorithm that provides good initial solutions. Secondly, we improve the quality of these solutions through local search procedures. We compare the proposed methods with exact and heuristic algorithms for mixed integer non-linear programming problems, proving that our approach provides good-quality solutions in smaller CPU time. © 2016 Elsevier B.V.

关键词： Heuristic algorithm Local search mixed-integer non-linear programming Multiple non-linear knapsack problem

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Unbounded convex sets for non-convex mixed-integer quadratic programming

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MATHEMATICAL programming 2014年第1-2期143卷 231-256页

作者： Burer, Samuel Letchford, Adam N. Univ Iowa Dept Management Sci Tippie Coll Business Iowa City IA 52242 USA Univ Lancaster Dept Management Sci Lancaster England

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a face of a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some other well-studied convex sets. Several classes of valid and facet-inducing inequalities are also derived.

关键词： mixed-integer non-linear programming Global optimisation Polyhedral combinatorics Convex analysis

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An Iterated Local Search Algorithm for Multi-Period Water Distribution Network Design Optimization

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WATER 2016年第8期8卷 359-359页

作者： De Corte, Annelies Sorensen, Kenneth Univ Antwerp ANT OR Operat Res Grp Prinsstr 13 B-2000 Antwerp Belgium

Water distribution networks consist of different components, such as reservoirs and pipes, and exist to provide users (households, agriculture, industry) with high-quality water at adequate pressure and flow. Water distribution network design optimization aims to find optimal diameters for every pipe, chosen from a limited set of commercially available diameters. This combinatorial optimization problem has received a lot of attention over the past forty years. In this paper, the well-studied single-period problem is extended to a multi-period setting in which time varying demand patterns occur. Moreover, an additional constraint-which sets a maximum water velocity-is imposed. A metaheuristic technique called iterated local search is applied to tackle this challenging optimization problem. A full-factorial experiment is conducted to validate the added value of the algorithm components and to configure optimal parameter settings. The algorithm is tested on a broad range of 150 different (freely available) test networks.

关键词： water distribution network design iterated local search metaheuristic mixed-integer non-linear programming pipe sizing

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Designing group layout of unequal-area facilities in a dynamic cellular manufacturing system with variability in number and shape of cells

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2015年第11期53卷 3390-3418页

作者： Kia, R. Shirazi, H. Javadian, N. Tavakkoli-Moghaddam, R. Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Islamic Azad Univ Qom Branch Dept Ind Management Qom Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Univ Tehran Sch Ind Engn Coll Engn Tehran Iran

This paper presents a new mixed-integer non-linear programming model for designing the group layout (GL) of unequal-area facilities in a cellular manufacturing system (CMS) under a dynamic environment. There are some features that make the presented model different from the previous studies. These include: (1) manufacturing cells with variable numbers and shapes, (2) machine depot keeping idle machines, (3) machines of unequal-areas, (4) manufacturing cells with rectangle regular shapes established on the continuous shop floor and (5) integration of cell formation and GL as interrelated decisions involved in the design of a CMS in a dynamic environment. The objective function is to minimises the total costs of intra- and inter-cell material handling, machine overhead, machine relocation, machine processing, purchasing machines and forming cells. Since the problem is NP-hard, an efficient simulated annealing (SA) algorithm is developed to solve the presented model. The performance of this model is illustrated by two numerical examples. It is then tested using several test problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison to the classical genetic algorithm (GA). The obtained results show that the quality of the solutions obtained by SA is better than GA.

关键词： group layout simulated annealing unequal-area facilities dynamic cellular manufacturing systems mixed-integer non-linear programming

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Constructing A Shortest Path Overhearing Tree With Maximum Lifetime In WSNs

Constructing A Shortest Path Overhearing Tree With Maximum L...

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Hawaii International Conference on System Sciences

作者： Wael Y. Alghamdi Hui Wu Wenguang Zheng Salil S. Kanhere Sch. of Comput. Sci. & Eng. Univ. of New South Wales Sydney NSW Australia

ISBN: (纸本)9781509019816

Secure data collection is an important problem in wireless sensor networks. Different approaches have been proposed. One of them is overhearing. We investigate the problem of constructing a shortest path overhearing tree with the maximum lifetime. We propose three approaches. The first one is a polynomial-time heuristic. The second one uses ILP (integer linear programming) to iteratively find a monitoring node and a parent for each sensor node. The last one optimally solves the problem by using MINLP (mixed-integer non-linear programming). We have implemented the three approaches using MIDACO solver and MATLAB Intlinprog, and performed extensive simulations using NS2.35. The simulation results show that the average lifetime of all the network instances achieved by the heuristic approach is 85.69% of that achieved by the ILP-based approach and 81.05% of that obtained by the MINLP-based approach, and the performance of the ILP-based approach is almost equivalent to that of the MINLP-based approach.

关键词： Overhearing integer linear programming mixed-integer non-linear programming network lifetime routing tree secure data collection

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A novel hybrid approach to allocate renewable energy sources in distribution system

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SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS 2015年 10卷 1-11页

作者： Singh, A. K. Parida, S. K. IITRAM Dept Elect Engn Ahmadabad Gujarat India Indian Inst Technol Dept Elect Engn Patna Bihar India

The integration of renewable energy sources (RESs) based DGs into grid has a great importance in improving system reliability. Many methods were proposed in the literature for finding best locations for DG placement considering various criteria. Sometime, it becomes difficult for combined placement of different kinds of renewable based DGs, such as solar, wind and fuel cell. The criterion of minimizing total system cost was used previously by many researchers for locating the optimal sites for DGs using OPF formulations. In this case, three different cost functions are formulated for different kinds of renewable energy sources (RESs). By taking combined cost function of all the RESs in the OPF to identify location for each different kind of sources becomes very cumbersome task. It would be difficult to find the exact locations for various kinds of RESs that is where to place which type of RESs. In order to solve this difficulty, three different objectives have been considered separately for determining the optimal locations for each kind of RESs using mixed integer nonlinear programming (MINLP) method considering loadability, losses and cost. Having many alternatives with these three objectives, analytic hierarchy process (AHP) has been used to make a decision over getting the optimal locations for these different kinds of RESs. The proposed methodology has been demonstrated on 15- node radial distribution system and 69-node mesh distribution system. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Analytical hierarchical process Distributed generation mixed-integer non-linear programming Optimal power flow Renewable energy sources

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Complexity of transmission network expansion planning NP-hardness of connected networks and MINLP evaluation

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2014年第1期5卷 179-207页

作者： Oertel, David Ravi, R. Karlsruhe Inst Technol Karlsruhe Germany Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

Transmission network expansion planning in its original formulation is NP-hard due to the subproblem Steiner trees, the minimum cost connection of an initially unconnected network with mandatory and optional nodes. By using electrical network theory we show why NP-hardness still holds when this subproblem of network design from scratch is omitted by considering already (highly) connected networks only. This refers to the case of extending a long working transmission grid for increased future demand. It will be achieved by showing that this case is computationally equivalent to 3-SAT. Additionally, the original mathematical formulation is evaluated by using an appropriate state-of-the-art mixed integer non-linear programming solver in order to see how much effort in computation and implementation is really necessary to solve this problem in practice.

关键词： Transmission network expansion planning NP-hard mixed-integer non-linear programming Electrical network

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Designing fair 8-and 16-team knockout tournaments

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2013年第3期24卷 321-336页

作者： Prince, Mike Smith, J. Cole Geunes, Joseph Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

In an eight-team single-elimination tournament without reseeding, teams are seeded from best (1) to worst (8). Teams 1/8, 4/5, 2/7 and 3/6 are paired in the first round, with the 1/8 winner facing the 4/5 winner in the second round and so on. However, such tournaments are potentially unfair in the sense that inferior teams can be more likely to advance to certain stages of the tournament than better teams. For instance, if the top five teams are comparable in strength and are markedly better than the bottom three teams, then seeds 2 and 3 may be more likely to advance to the finals than team 1. We assign each team a unique power value and assume that the victory probability in a match-up is proportional to the teams' powers. We investigate properties of fair tournaments and formulate a non-linear optimization model that prescribes a fair tournament given the relative strengths of the teams involved. Although the problem is highly non-convex, we demonstrate how to consistently obtain all fair tournaments for 8- and 16-team problems.

关键词： OR in sports mixed-integer non-linear programming implicit enumeration single-elimination tournament

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Optimal design of single-story steel building structures based on parametric MINLP optimization

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JOURNAL OF CONSTRUCTIONAL STEEL RESEARCH 2013年 81卷 86-103页

作者： Kravanja, Stojan Turkalj, Goran Silih, Simon Zula, Tomaz Univ Maribor Fac Civil Engn SI-2000 Maribor Slovenia Univ Rijeka Fac Engn Rijeka 51000 Croatia

The paper presents an optimal design of single-story industrial steel building structures based on the parametric mixed-integer non-linear programming (MINLP) optimization approach and Eurocode specifications. The optimal design of the structures was investigated for factors which have significant influence on the structure mass: vertical variable load on the structure, horizontal variable load, structure span, structure height, type of standard cross-sections and strength of structural steel. For this purpose, parametric MINLP optimization was performed for a number of combinations between different parameters, i.e. different values of the mentioned influence factors. The single-story steel building superstructure was generated and the MINLP optimization model developed. The objective function of the structure's mass was defined. The modified outer-approximation/equality-relaxation (OA/ER) algorithm and the three-phase MINLP strategy were used to perform the optimization. The minimal possible structure mass, the optimal topology and the optimal standard cross-sections were obtained through each individual MINLP optimization. Based on the obtained optimal results, the recommended optimal design for single-story/single-bay structures and the comparative mass diagrams were developed. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Optimization Topology optimization Discrete sizing optimization mixed-integer non-linear programming MINLP Single-story industrial steel building

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Stochastic binary problems with simple penalties for capacity constraints violations

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MATHEMATICAL programming 2013年第1-2期138卷 199-221页

作者： Fortz, B. Labbe, M. Louveaux, F. Poss, M. Univ Libre Brussels Fac Sci Dept Comp Sci Brussels Belgium Univ Namur FUNDP Dept Business Adm Namur Belgium Univ Coimbra Dept Math CMUC P-3001454 Coimbra Portugal

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly -hard in general. We provide pseudo-polynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and strictly positively distributed random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branch-and-cut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem.

关键词： Stochastic programming Knapsack problem Pseudo-polynomial algorithm mixed-integer non-linear programming Branch-and-cut algorithm

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