Combining Fix and Relax Heuristic and LP-Metric Method to Solve the Multi-Objective Integrated Production-Routing Problem

Production routing problem is one of the problems of the integrated planning that interests in optimizing simultaneously production, inventory, and distribution planning. This chapter has the purpose of developing two mono-objective models for the production-routing problem: one of them minimizes the total costs which is the classical objective while the other one minimizes the energy consumed by the production system. A bi-objective model is then proposed to combine the two objectives mentioned previously using LP-metric method. To solve big instances of the problem in reasonable time, an approximate approach is proposed using the rolling horizon-based fix and relax heuristic. Finally, computational results are presented to compare the solutions obtained by both approaches.

Optimal Economic–Environmental Operation of BESS in AC Distribution Systems: A Convex Multi-Objective Formulation

This paper deals with the multi-objective operation of battery energy storage systems (BESS) in AC distribution systems using a convex reformulation. The objective functions are CO2 emissions, and the costs of the daily energy losses are considered. The conventional non-linear nonconvex branch multi-period optimal power flow model is reformulated with a second-order cone programming (SOCP) model, which ensures finding the global optimum for each point present in the Pareto front. The weighting factors methodology is used to convert the multi-objective model into a convex single-objective model, which allows for finding the optimal Pareto front using an iterative search. Two operational scenarios regarding BESS are considered: (i) a unity power factor operation and (ii) a variable power factor operation. The numerical results demonstrate that including the reactive power capabilities in BESS reduces 200kg of CO2 emissions and USD 80 per day of operation. All of the numerical validations were developed in MATLAB 2020b with the CVX tool and the SEDUMI and SDPT3 solvers.

A multi-objective selective maintenance optimization method for series-parallel systems using NSGA-III and NSGA-II evolutionary algorithms

Aiming at the problem that the downtime is simply assumed to be constant and the limited resources are not considered in the current selective maintenance of the series-parallel system, a three-objective selective maintenance model for the series-parallel system is established to minimize the maintenance cost, maximize the probability of completing the next task and minimize the downtime. The maintenance decision-making model and personnel allocation model are combined to make decisions on the optimal length of each equipment’s rest period, the equipment to be maintained during the rest period and the maintenance level. For the multi-objective model established, the NSGA-III algorithm is designed to solve the model. Comparing with the NSGA-II algorithm that only considers the first two objectives, it is verified that the designed multi-objective model can effectively reduce the downtime of the system.

A Two-sided Matching Decision-making Approach based on PROMETHEE Under the Probabilistic Linguistic Environment

Matching problems in daily life can be effectively solved by two-sided matching decision-making (TSMDM) approaches. The involved matching intermediary is to match two sides of subjects. This paper proposes a TSMDM approach based on preference ranking organization method (PROMETHEE) under the probabilistic linguistic environment. The probabilistic linguistic evaluations are firstly normalized and transformed to the benefit types. Then, the preference degrees of a subject over other subjects from the same side are obtained by using six types of preference function. Afterwards, groups of preference degrees of a subject are aggregated to the preference indexes by considering the weights of criteria. Hereafter, the preference degrees of a subject over other subjects from the same side are aggregated to the outgoing flow, while the preference degrees of other subjects from the same side over this subject are aggregated to the incoming flow. Furthermore, the net-flows, which is recognized as the satisfaction degrees are calculated by using outgoing flows to minus incoming flows. On the basis of this, the multi-objectives TSMDM model is built by considering the matching aspirations. A model with respect to the matching aspirations is built and solved by using the Lagrange function. The multi-objectives TSMDM model is further transformed to the single-objective model, the solution of which is the matching scheme. A matching problem related to the intelligent technology intermediary is solved to verify the effectiveness and the feasibility of the proposed approach.