Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.Comment: 11 pages, 2 tables; v3: minor revisions, to appear in Journal of Global Optimizatio

Multi-objective integer programming: An improved recursive algorithm

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.Comment: 11 pages, 6 tables; v2: added more details and a computational stud

Multi-objective decision-making for dietary assessment and advice

Unhealthy diets contribute substantially to the worldwide burden of non-communicable diseases, such as cardiovascular diseases, cancers, and diabetes. Globally, non-communicable diseases are the leading cause of death, and numbers are still rising, which makes healthy diets a global priority. In Nutrition Research, two fields are particularly relevant for formulating healthier diets: dietary assessment, which assesses food and nutrient intake in order to investigate the relation between diet and disease, and dietary advice, which translates food and nutrient recommendations into realistic food choices. Both fields face complex decision problems: which foods to include in dietary assessment or advice in order to pursue the multiple objectives of the researcher or fulfil the requirements of the consumer. This thesis connects the disciplines of Nutrition Research and Operations Research in order to contribute to formulating healthier diets. In the context of dietary assessment, the thesis proposes a MILP model for the selection of food items for food frequency questionnaires (a crucial tool in dietary assessment) that speeds up the selection process and increases standardisation, transparency, and reproducibility. An extension of this model gives rise to a 0-1 fractional programming problem with more than 200 fractional terms, of which in every feasible solution only a subset is actually defined. The thesis shows how this problem can be reformulated in order to eliminate the undefined fractional terms. The resulting MILP model can solved with standard software. In the context of dietary advice, the thesis proposes a diet model in which food and nutrient requirements are formulated via fuzzy sets. With this model, the impact of various achievement functions is demonstrated. The preference structures modelled via these achievement functions represent various ways in which multiple nutritional characteristics of a diet can be aggregated into an overall indicator for diet quality. Furthermore, for Operations Research the thesis provides new insights into a novel preference structure from literature, that combines equity and utilitarianism in a single model. Finally, the thesis presents conclusions of the research and a general discussion, which discusses, amongst others, the main modelling choices encountered when using MODM methods for optimising diet quality. Summarising, this thesis explores the use of MODM approaches to improve decision-making for dietary assessment and advice. It provides opportunities for better decision-making in research on dietary assessment and advice, and it contributes to model building and solving in Operations Research. Considering the added value for Nutrition Research and the new models and solutions generated, we conclude that the combination of both fields has resulted in synergy between Nutrition Research and Operations Research.</p

Energy Management of Grid-Connected Microgrids, Incorporating Battery Energy Storage and CHP Systems Using Mixed Integer Linear Programming

In this thesis, an energy management system (EMS) is proposed for use with battery energy storage systems (BESS) in solar photovoltaic-based (PV-BESS) grid-connected microgrids and combined heat and power (CHP) applications. As a result, the battery's charge/discharge power is optimised so that the overall cost of energy consumed is minimised, considering the variation in grid tariff, renewable power generation and load demand. The system is modelled as an economic load dispatch optimisation problem over a 24-hour time horizon and solved using mixed integer linear programming (MILP) for the grid-connected Microgrid and the CHP application. However, this formulation requires information about the predicted renewable energy power generation and load demand over the next 24 hours. Therefore, a long short-term memory (LSTM) neural network is proposed to achieve this. The receding horizon (RH) strategy is suggested to reduce the impact of prediction error and enable real-time implementation of the energy management system (EMS) that benefits from using actual generation and demand data in real-time. At each time-step, the LSTM predicts the generation and load data for the next 24 h. The dispatch problem is then solved, and the real-time battery charging or discharging command for only the first hour is applied. Real data are then used to update the LSTM input, and the process is repeated. Simulation results using the Ushant Island as a case study show that the proposed online optimisation strategy outperforms the offline optimisation strategy (with no RH), reducing the operating cost by 6.12%. The analyses of the impact of different times of use (TOU) and standard tariff in the energy management of grid-connected microgrids as it relates to the charge/discharge cycle of the BESS and the optimal operating cost of the Microgrid using the LSTM-MILP-RH approach is evaluated. Four tariffs UK tariff schemes are considered: (1) Residential TOU tariff (RTOU), (2) Economy seven tariff (E7T), (3) Economy ten tariff (E10T), and (4) Standard tariff (STD). It was found that the RTOU tariff scheme gives the lowest operating cost, followed by the E10T tariff scheme with savings of 63.5% and 55.5%, respectively, compared to the grid-only operation. However, the RTOU and E10 tariff scheme is mainly used for residential applications with the duck curve load demand structure. For community grid-connected microgrid applications except for residential-only communities, the E7T and STD, with 54.2% and 39.9%, respectively, are the most likely options offered by energy suppliers. The use of combined heat and power (CHP) systems has recently increased due to their high combined efficiency and low emissions. Using CHP systems in behind-the-meter applications, however, can introduce some challenges. Firstly, the CHP system must operate in load-following mode to prevent power export to the grid. Secondly, if the load drops below a predefined threshold, the engine will operate at a lower temperature and hence lower efficiency, as the fuel is only half-burnt, creating significant emissions. The aforementioned issues may be solved by combining CHP with a battery energy storage system. However, the dispatch of CHP and BESS must be optimised. Offline optimisation methods based on load prediction will not prevent power export to the grid due to prediction errors. Therefore, a real-time EMS using a combination of LSTM neural networks, MILP, and RH control strategy is proposed. Simulation results show that the proposed method can prevent power export to the grid and reduce the operational cost by 8.75% compared to the offline method. The finding shows that the BESS is a valuable asset for sustainable energy transition. However, they must be operated safely to guarantee operational cost reduction and longer life for the BESS

Maximum precision-lifetime curve for joint sensor selection and data routing in sensor networks

In many classes of monitoring applications employing battery-limited sensor networks, periodic sampling of an area with a given precision level is required. For such applications, we provide mathematical programming formulations for deriving the optimal trade-off curve between network lifetime and data precision, and design a practical heuristic for near-optimal operation. The properties of our models and the effectiveness of our heuristic are demonstrated by computational experiments

Suppliers Selection In Manufacturing Industries And Associated Multi-Objective Desicion Making Methods: Past, Present And The Future

Nowadays, many manufacturing companies have decided to use other companies’ competencies and outsource part of their manufacturing processes and business to suppliers globally in order to reduce costs, improve quality of products, explore or expand new markets, and offer better services to customers, etc. The decisions have rendered manufacturing organizations with new challenges. Organizations need to evaluate their suppliers' performance, and take account of their weakness and strength in order to win and survive in highly competitive global marketplaces. Hence, suppliers evaluation and selection are taken as an important strategy for manufactring enterprises. This paper aims to provide a comprehensive and critical review on suppliers selection and the formulation of different criteria for suppliers selection, the associated multi-objctive decision makings, selecion algorithms, and their implementation and application perspectives. Furthermore, individual and integrated suppliers selection approaches are presented, including Analytic hierarchy process (AHP), Analytic network process (ANP), and Mathematical programming (MP). Linear programming (LP), Integer programming (IP), Data envelopment analysis (DEA) and Goal programming (GP) are discussed with in-depth. The paper concludes with further discussion on the potential and application of suppliers selection approach for the broad manufacturing industry

Heat integration of multipurpose batch plants through multiple heat storage vessels

Master of Science in Engineering by research: “A dissertation submitted to the Faculty of Engineering and Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering.” Johannesburg, 05 February 2018In most industrial processes, energy is an integral part of the production process; therefore, energy consumption has become an intensified area in chemical engineering research. Extensive work has been done on energy optimisation in continuous operations; unlike in batch operations because it was believed that due to the small scale nature of batch plants, small amounts of energy is consumed. Certain industries such as the brewing and dairy industries have shown to be as energy intensive as continuous processes. It is, therefore, necessary for energy minimisation techniques to be developed specifically for batch processes in which the inherent features of batch operations such as time and scheduling are taken into account accordingly. This can be achieved through process integration techniques where energy consumption can be reduced while economic feasibility is still maintained. Most of the work done on energy minimisation either focuses on direct heat integration, where cold and hot units operating simultaneously are integrated, or indirect heat integration, where units are integrated with heat storage. The schedules used in these models are, in most cases, predetermined which leads to suboptimal results. This work is aimed at minimising energy consumption in multipurpose batch plants by using direct heat integration together with multiple heat storage vessels through mathematical programming. The proposed approach does not use a predetermined scheduling framework. The focus lies on the heat storage vessels and the optimal number of heat storage vessels together with their design parameters, namely size and the temperature at which the vessels are initially maintained, are determined. The formulation developed is in the form of a mixed integer non-linear program (MINLP) due to the presence of both continuous and integer variables, as well as non-linear constraints governing the problem. Two illustrative examples are applied to the formulation in which the optimal number of multiple heat storage vessels is not known beforehand. The results rendered from the model show a decrease in the external utilities, in the form of cooling water and steam, compared to the base case where no integration is considered and the case where only one heat storage vessel is used.MT 201

Bartering integer commodities with exogenous prices

The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and computational details associated to the mathematical programming based approaches proposed by Nasini et al. (accepted 2014) to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analyzed processes in the context of computational economics is provided, along with a Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table

Modelling and solution methods for portfolio optimisation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 16/01/2004.In this thesis modelling and solution methods for portfolio optimisation are presented. The investigations reported in this thesis extend the Markowitz mean-variance model to the domain of quadratic mixed integer programming (QMIP) models which are 'NP-hard' discrete optimisation problems. In addition to the modelling extensions a number of challenging aspects of solution algorithms are considered. The relative performances of sparse simplex (SSX) as well as the interior point method (IPM) are studied in detail. In particular, the roles of 'warmstart' and dual simplex are highlighted as applied to the construction of the efficient frontier which requires processing a family of problems; that is, the portfolio planning model stated in a parametric form. The method of solving QMIP models using the branch and bound algorithm is first developed; this is followed up by heuristics which improve the performance of the (discrete) solution algorithm. Some properties of the efficient frontier with discrete constraints are considered and a method of computing the discrete efficient frontier (DEF) efficiently is proposed. The computational investigation considers the efficiency and effectiveness in respect of the scale up properties of the proposed algorithm. The extensions of the real world models and the proposed solution algorithms make contribution as new knowledge