An efficient algorithm for bi-objective combined heat and power production planning under the emission trading scheme

The growing environmental awareness and the apparent conflicts between economic and environmental objectives turn energy planning problems naturally into multi-objective optimization problems. In the current study, mixed fuel combustion is considered as an option to achieve tradeoff between economic objective (associated with fuel cost) and emission objective (measured in CO2 emission cost according to fuels and emission allowance price) because a fuel with higher emissions is usually cheaper than one with lower emissions. Combined heat and power (CHP) production is an important high-efficiency technology to promote under the emission trading scheme. In CHP production, the production planning of both commodities must be done in coordination. A long-term planning problem decomposes into thousands of hourly subproblems. In this paper, a bi-objective multi-period linear programming CHP planning model is presented first. Then, an efficient specialized merging algorithm for constructing the exact Pareto frontier (PF) of the problem is presented. The algorithm is theoretically and empirically compared against a modified dichotomic search algorithm. The efficiency and effectiveness of the algorithm is justified.Peer reviewe

Exact And Representative Algorithms For Multi Objective Optimization

In most real-life problems, the decision alternatives are evaluated with multiple conflicting criteria. The entire set of non-dominated solutions for practical problems is impossible to obtain with reasonable computational effort. Decision maker generally needs only a representative set of solutions from the actual Pareto front. First algorithm we present is for efficiently generating a well dispersed non-dominated solution set representative of the Pareto front which can be used for general multi objective optimization problem. The algorithm first partitions the criteria space into grids to generate reference points and then searches for non-dominated solutions in each grid. This grid-based search utilizes achievement scalarization function and guarantees Pareto optimality. The results of our experimental results demonstrate that the proposed method is very competitive with other algorithms in literature when representativeness quality is considered; and advantageous from the computational efficiency point of view. Although generating the whole Pareto front does not seem very practical for many real life cases, sometimes it is required for verification purposes or where DM wants to run his decision making structures on the full set of Pareto solutions. For this purpose we present another novel algorithm. This algorithm attempts to adapt the standard branch and bound approach to the multi objective context by proposing to branch on solution points on objective space. This algorithm is proposed for multi objective integer optimization type of problems. Various properties of branch and bound concept has been investigated and explained within the multi objective optimization context such as fathoming, node selection, heuristics, as well as some multi objective optimization specific concepts like filtering, non-domination probability, running in parallel. Potential of this approach for being used both as a full Pareto generation or an approximation approach has been shown with experimental studies

Characterizing coherence, correcting incoherence

Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible

Multiple Objective Programming Support

This paper gives a brief introduction into multiple objective programming support. We will overview basic concepts, formulations, and principles of solving multiple programming problems.To solve those problems requires the the intervention of a decision-maker. That's why behavioral assumptions play an important role in multiple objective programming. Which assumptions are made affects which kindof support is given to adecision maker. We will demonstrate how a free search type approach can be used to solve multiple objective programming problems

An efficient algorithm for bi-objective combined heat and power production planning under the emission trading scheme

Abstract The growing environmental awareness and the apparent conflicts between economic and environmental objectives turn naturally energy planning problems into multi-objective optimization problems. Combined heat and power (CHP) production is an important highefficiency technology to promote under emission trading scheme. In CHP production, joint characteristics of heat and power mean that the production planning must be done in coordination. A long-term planning problem decomposes into thousands of single period sub-problems. In this paper, a bi-objective multi-period linear programming CHP planning model is presented first. Then, an efficient specialized merging algorithm for constructing the exact Pareto frontier (PF) of the problem is presented. The algorithm is (theoretically and empirically) compared against a modified dichotomic search algorithm. The efficiency and effectiveness of the algorithm is justified

On the simplex, interior-point and objective space approaches to multiobjective linear programming

Most Multiple Objective Linear Programming (MOLP) algorithms working in the decision variable space, are based on the simplex algorithm or interior-point method of Linear Programming. However, objective space based methods are becoming more and more prominent. This paper investigates three algorithms namely the Extended Multiobjective Simplex Algorithm (EMSA), Arbel’s Affine Scaling Interior-point (ASIMOLP) algorithm and Benson’s objective space Outer Approximation (BOA) algorithm. An extensive review of these algorithms is also included. Numerical results on non-trivial MOLP problems show that EMSA and BOA are at par and superior in terms of the quality of a most preferred nondominated point to ASIMOLP. However, ASIMOLP more than holds its own in terms of computing efficiency

Biobjective Optimization over the Efficient Set Methodology for Pareto Set Reduction in Multiobjective Decision Making: Theory and Application

A large number of available solutions to choose from poses a significant challenge for multiple criteria decision making. This research develops a methodology that reduces the set of efficient solutions under consideration. This dissertation is composed of three major parts: (i) the formalization of a theoretical framework; (ii) the development of a solution approach; and (iii) a case study application of the methodology. In the first part, the problem is posed as a multiobjective optimization over the efficient set and considers secondary robustness criteria when the exact values of decision variables are subjected to uncertainties during implementation. The contributions are centered at the modeling of uncertainty directly affecting decision variables, the use of robustness to provide additional trade-off analysis, the study of theoretical bounds on the measures of robustness, and properties to ensure that fewer solutions are identified. In the second part, the problem is reformulated as a biobjective mixed binary program and the secondary criteria are generalized to any convenient linear functions. A solution approach is devised in which an auxiliary mixed binary program searches for unsupported Pareto outcomes and a novel linear programming filtering excludes any dominated solutions in the space of the secondary criteria. Experiments show that the algorithm tends to run faster than existing approaches for mixed binary programs. The algorithm enables dealing with continuous Pareto sets, avoiding discretization procedures common to the related literature. In the last part, the methodology is applied in a case study regarding the electricity generation capacity expansion problem in Texas. While water and energy are interconnected issues, to the best of our knowledge, this is the first study to consider both water and cost objectives. Experiments illustrate how the methodology can facilitate decision making and be used to answer strategic questions pertaining to the trade-off among different generation technologies, power plant locations, and the effect of uncertainty. A simulation shows that robust solutions tend to maintain feasibility and stability of objective values when power plant design capacity values are perturbed

Integrating multiple criteria decision analysis and production theory for performance evaluation: framework and review

Accounting, life cycle assessment (LCA) and data envelopment analysis (DEA) are examples of various research areas that independently develop and apply diverse methodologies to evaluate performance. Though, many methods have in common that the results to be assessed are mainly determined by the inputs and outputs of the activities which are to be evaluated. Based on both production and decision theory, our comprehensive framework integrates and systematically distinguishes specific types of production-based performance assessment. It allows to examine and categorise the existing literature on such approaches. Our review focuses on sources which explicitly apply concepts or methods of multiple criteria decision analysis (MCDA). We did not find any elaborated methodology that fully integrates MCDA with production theory. At least, a basic approach to multicriteria performance analysis, which generalises the methodology of data envelopment analysis, appears to be well-grounded on production theory. It was already presented in this journal in 2001 and has rarely been noticed in the literature until now. A short overview outlines its recent insights and main findings. A key finding is that a category mistake prevails among well-known methodologies of efficiency measurement like DEA. It may imply invalid empirical results because the inputs and outputs of production processes are confused with resulting impacts destroying or creating values (to be minimised or maximised, respectively). We conclude by defining open problems and by indicating prospective research directions