Stochastic optimization methods are used for optimal design and operation of surface water reservoir systems under uncertainty. Chance-constrained (CC) optimization with linear decision rules (LDRs) is an old approach...
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Stochastic optimization methods are used for optimal design and operation of surface water reservoir systems under uncertainty. Chance-constrained (CC) optimization with linear decision rules (LDRs) is an old approach for determining the minimum reservoir capacity required to meet a specific yield at a target level of reliability. However, this approach has been found to overestimate the reservoir capacity. In this paper, we propose the reason for this overestimation to be the fact that the reliability constraints considered in standard CC LDR models do not have the same meaning as in other models such as reservoir operation simulation models. The simulation models have fulfilled a target reliability level in an average sense (i.e., annually), whereas the standard CC LDR models have met the target reliability level every season of the year. mixedinteger nonlinear programs are presented to clarify the distinction between the two types of reliability constraints and demonstrate that the use of seasonal reliability constraints, rather than an average reliability constraint, leads to 80-150 % and 0-32 % excess capacity for SQ-type and S-type CC LDR models, respectively. Additionally, a modified CC LDR model with an average reliability constraint is proposed to overcome the reservoir capacity overestimation problem. In the second stage, we evaluate different operating policies and show that for the seasonal (average) reliability constraints, open-loop, S-type, standard operating policy, SQ-type, and general SQ-type policies compared to a model not using any operation rule lead to 190-460 % (200-550 %), 100-200 % (80-300 %), 0-90 % (0-60 %), 30-90 % (0-20 %), and 10-90 % (0-10 %) excess capacity, respectively.
This is the second part of a series papers on modeling and path planning of the City-Climber robot. This paper presents a path planning method for the City-Climber robot using mixed integer linear programming (MILP) i...
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ISBN:
(纸本)9781424447749
This is the second part of a series papers on modeling and path planning of the City-Climber robot. This paper presents a path planning method for the City-Climber robot using mixed integer linear programming (MILP) in 3D building environments that consist of objects with primitive geometrical shapes. In order to use MILP to solve obstacle avoidance problems, we first simplify and decouple the robot dynamic model by introducing a restricting admissible control. The decoupled model and obstacle can be rewritten as a linear program with mixedintegerlinear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the AMPL and CPLEX optimization software with a Matlab interface. Simulation results show that the framework of MILP is well suited for path planning and obstacle avoidance problems for the wall-climbing robot in 3D environments.
A common problem encountered in steel companies is that of allocating the surplus slabs to customer orders so as to minimize the total cost of production and inventory. Due to many unpredictable events arising in prac...
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A common problem encountered in steel companies is that of allocating the surplus slabs to customer orders so as to minimize the total cost of production and inventory. Due to many unpredictable events arising in practical manufacture environment, slab yields and customer demands are full of uncertainties. This paper focuses on such uncertainties and studies the stochastic version of the slab allocation problem that has received little attention in the literature. Using a scenario-based approach, we formulate the problem as a mixed integer linear programming (MILP) model. To make the MILP model more concision, we reformulate it with less variables and constraints by using a scenarios aggregation approach. The commercial optimization software such as IBM ILOG CPLEX can solve the model to optimality for small and medium scale instances, but fail to solve large scale instances to optimality. Thus, a scatter search algorithm with directed local search based on follow-up technique is proposed to solve the problem approximately. Moreover, we introduce a random perturbation strategy to avoid search process being tapped in local optimum. Computational results on randomly generated instances show that the proposed algorithm is effective.
In this paper, a methodology for multi-objective optimization of trigeneration plants is presented. It is primarily applicable to the systems for buildings' energy supply characterized by high load variations on d...
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In this paper, a methodology for multi-objective optimization of trigeneration plants is presented. It is primarily applicable to the systems for buildings' energy supply characterized by high load variations on daily, weekly and annual bases, as well as the components applicable for flexible operation. The idea is that this approach should enable high accuracy and flexibility in mathematical modeling, while remaining efficient enough. The optimization problem is structurally decomposed into two new problems. The main problem of synthesis and design optimization is combinatorial and solved with different metaheuristic methods. For each examined combination of the synthesis and design variables, when calculating the values of the objective functions, the inner, mixed integer linear programming operation optimization problem is solved with the branch-and-cut method. The applicability of the exploited metaheuristic methods is demonstrated. This approach is compared with the alternative, superstructure-based approach. The potential for combining them is also examined. The methodology is applied for multi-objective optimization of a trigeneration plant that could be used for the energy supply of a real residential settlement in Nis, Serbia. Here, two objectives are considered: annual total costs and primary energy consumption. Results are obtained in the form of a Pareto chart using the epsilon-constraint method.
We address the portfolio selection of social projects in public organizations considering interdependencies (synergies) affecting project funds requirements and tasks. A mixed integer linear programming model is propo...
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We address the portfolio selection of social projects in public organizations considering interdependencies (synergies) affecting project funds requirements and tasks. A mixed integer linear programming model is proposed incorporating the most relevant aspects of the problem found in the literature. The model supports both complete (all or nothing) and partial (a certain amount from a given interval of funding) resource allocation policies. Numerical results for large-scale problem instances are presented.
The purpose of this study is to develop a decision support system (DSS) for design and management of anaerobic digestion based biomass to energy supply chains in a cost effective and environment friendly manner by tac...
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The purpose of this study is to develop a decision support system (DSS) for design and management of anaerobic digestion based biomass to energy supply chains in a cost effective and environment friendly manner by tackling inherent uncertainties. To this aim, a fuzzy multiobjective mixed integer linear programming (MILP) model is constructed. To explore the viability of the proposed model, computational experiments are performed on a real world problem. The results reveal that the proposed model can effectively be used in practice. (C) 2014 Elsevier Ltd. All rights reserved.
In this work we present efficient solution strategies for the task of designing supply chains with the explicit consideration of the detailed plant performance of the embedded facilities. Taking as a basis a mixed-int...
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In this work we present efficient solution strategies for the task of designing supply chains with the explicit consideration of the detailed plant performance of the embedded facilities. Taking as a basis a mixed-integerlinearprogramming (MILP) model introduced in a previous work, we propose three solution strategies that exploit the underlying mathematical structure: A bi-level algorithm, a Lagrangean decomposition method, and a hybrid approach that combines features from both of these two methods. Numerical results show that the bi-level method outperforms the others, leading to significant CPU savings when compared to the full space MILP. (C) 2013 Elsevier Ltd. All rights reserved.
This paper presents a road-network search route planning algorithm by which multiple autonomous vehicles are able to efficiently visit every road identified in the map in the context of the Chinese postman problem. Si...
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This paper presents a road-network search route planning algorithm by which multiple autonomous vehicles are able to efficiently visit every road identified in the map in the context of the Chinese postman problem. Since the typical Chinese postman algorithm can be applied solely to a connected road-network in which ground vehicles are involved, it is modified to be used for a general type of road map including unconnected roads as well as the operational and physical constraints of unmanned aerial vehicles (UAVs). For this, a multi-choice multi-dimensional knapsack problem is formulated to find an optimal solution minimising flight time and then solved via mixed integer linear programming. To deal with the dynamic constraints of the UAVs, the Dubins theory is used for path generation. In particular, a circular-circular-circular type of the Dubins path is exploited based on a differential geometry to guarantee that the vehicles follow the road precisely in a densely distributed road environment. Moreover, to overcome the computational burden of the multi-choice multi-dimensional knapsack algorithm, a nearest insertion and auction-based approximation algorithm is newly introduced. The properties and performance of the proposed algorithm are evaluated via numerical simulations operating on a real village map and randomly generated maps with different parameters.
The multiobjective optimization (MOO) of industrial water networks through goal programming is studied using a mixed-integerlinearprogramming (MILP) formulation. First, the efficiency of goal programming for solving...
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The multiobjective optimization (MOO) of industrial water networks through goal programming is studied using a mixed-integerlinearprogramming (MILP) formulation. First, the efficiency of goal programming for solving MOO problems is demonstrated with an introductive mathematical example and then with industrial water and energy networks design problems, formerly tackled in literature with other MOO methods. The first industrial water network case study is composed of 10 processes, 1 contaminant, and 1 water regeneration unit. The second, a more complex real industrial case study, is made of 12 processes, 1 contaminant, 4 water regeneration units, and the addition of temperature requirements for each process, which implies the introduction of energy networks alongside water networks. For MOO purposes, several antagonist objective functions are considered according to the case, such as total freshwater flow rate, number of connections, and total energy consumption. The MOO methodology proposed is demonstrated to be very reliable as an a priori method, by providing Pareto-optimal compromise solutions in significant less time compared to other traditional methods for MOO.
This paper presents the solution algorithm and test results of the market-splitting approach, proposed in the first part of this two-paper series, for the clearing of the forthcoming Internal Electricity Market. The m...
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This paper presents the solution algorithm and test results of the market-splitting approach, proposed in the first part of this two-paper series, for the clearing of the forthcoming Internal Electricity Market. The market-splitting approach is implemented in a Europe-wide level, indicatively defining three power pools and 22 power exchanges, comprising 42 bidding areas in total, with each local/national market respecting the standard market regulatory framework of power pools and power exchanges (PXs). The performance and computational requirements of this implementation is presented;the model is tested in terms of problem solvability to its limits, considering a day-ahead market clearing time threshold equal to one hour. The results demonstrate that a viable solution to the clearing of the Internal Electricity Market can be attained with the current state-of-the-art of computers' processing power. Further discussion is made concerning the viability of the proposed approach and other harmonization issues that should be considered for successful market integration.
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