Metaheuristic Algorithms Based on Compromise Programming for Multi-Objective Urban Shipment Problem

The Vehicle Routing Problem (VRP) and its variants are found in many fields, especially logistics. In this study, we introduced an adaptive method to a complex VRP. It combines multi-objective optimization and several forms of VRPs with practical requirements for an urban shipment system. The optimizer needs to consider terrain and traffic conditions. The proposed model also considers customers' expectations, shipper considerations as goals, and the common goal like transportation cost. We offered compromise programming to approach the multi-objective problem by decomposing the original multi-objective problem into a minimized distance-based problem. We designed a hybrid version of the Genetic algorithm with the Local Search algorithm to solve the proposed problem. We evaluate the effectiveness of the proposed algorithm with the Tabu Search algorithm, the original Genetic algorithm on the tested dataset. The results show that our method is an effective decision-making tool for the multi-objective VRP and an effective solver for the new variation of VRP.

Distillery decarbonisation and anaerobic digestion: balancing benefits and drawbacks using a compromise programming approach

The anaerobic digestion (AD) of distillery by-products presents benefits such as greenhouse gas (GHG) emission savings and electricity savings, as well as drawbacks such as reduced animal feed and protein production and the potential import of animal feeds. This work balances these benefits and drawbacks using compromise programming (CP). The best combination of byproducts (from 9,261 scenarios) to use in AD was selected based on criteria chosen by management of a large distillery. The use of all by-products maximises benefits and drawbacks; the contrary also applies. When benefits and drawbacks are equally important, CP recommends using 50% of available draff, 50% of available thick stillage, and 55% of available thin stillage. The best combination when accounting for criteria weights chosen by distillery management is the use of 100% of available draff and 100% of available thick stillage. This could replace 48% of natural gas consumption at the distillery, reduce Scope 1 emissions by 45%, achieve a Scope 3 emissions savings of 22% of current Scope 1 emissions, and reduce electricity consumption in the feeds recovery plant of the distillery by 63%. Protein loss of 9,618 t could require the import of 19.59 kilo-tonne wet weight of material (ktwwt) of distillers grains and 9.15 ktwwt of soybean meal. If different criteria or criteria weights were used, a different result would be recommended. The methodology developed herein can aid in decarbonising the food and beverage industry by allowing decision-makers to balance the benefits and drawbacks of AD while accounting for subjective preferences.

Topology Optimization Based Parametric Design of Balloon Borne Telescope’s Primary Mirror

For balloon-borne telescopes, the primary mirror is the most important optical element, but designing a primary mirror with an excellent overall performance is a challenge. To comprehensively consider the contradictory objectives of the root mean square (RMS) surface error under gravity in the X and Z directions, the mass and fundamental frequency of the primary mirror, a parametric primary mirror design using the compromise programming method based on topology optimization is proposed. The parametric design of the compromise programming method based on topology optimization is used to find the optimal solution for X-direction RMS (RMSx), Z-direction RMS (RMSz), mass, and fundamental frequency. Compared with the initial primary mirror structure designed according to traditional experience, the overall performance is improved. Results show that the respective mass of the primary mirror, the RMSx and the RMSz decreased by 8.5%, 14.3% and 10.5% compared to those before optimization. Comprehensive consideration can prove the effectiveness of parametric design based on the topology optimization of the primary mirror. This method provides a reference for the design of other primary mirrors for balloon-borne telescope and space cameras.

Integrated Herfindahl–Hirschman Index, Compromise Programming, and ε-Constraint Method For Multicriteria Performance-Based Transportation Budget Allocation

This paper introduces a new method for multicriteria performance-based transportation budget allocation. First, the Herfindahl–Hirschman Index (HHI) that has long been used in economics for measuring the level of monopolization in a marketplace is employed to derive the relative weights of multiple non-commensurable transportation performance criteria. Next, a compromise programming (CP) model is formulated to help transform the multicriteria optimization formulation for transportation budget allocation to a single-objective optimization model solvable by minimizing the Chebyshev distance to the ideal levels of performance targets associated with individual performance criteria. Finally, the ε-constraint trade-off analysis method is incorporated into the combined use of HHI and CP framework to iteratively derive the optimal decision outcome. Six-year data on candidate investment projects proposed for a U.S. state-maintained rural Interstate highway system along with data details of the available budget is used in a computational study for method application. Comparative analysis of decision outcomes is conducted with the STEP method for cross validation. It has revealed that the proposed HHI-CP ε-constraint method outperforms the existing method and can be adopted by state and local transportation agencies to carry out effective budget allocation.